by Judith Curry
There has been much discussion of this topic on open thread, which is getting unwieldily. Here is a new thread to continue this discussion.
by Judith Curry
There has been much discussion of this topic on open thread, which is getting unwieldily. Here is a new thread to continue this discussion.
Thank you, Wagathon!
And that information is getting to the masses – despite the best efforts of the gatekeepers of public knowledge listed on CJ Orach’s site:
http://orach24463.wordpress.com/2014/11/30/musings-from-the-leaders-of-the-climate-change-movement-seeking-to-save-the-earth-from-humanity/comment-page-1/
See Steven Goddard’s report on “Spectacular Malfeasance from the World’s Greatest Climate Scientist”
http://stevengoddard.wordpress.com/2014/12/06/spectacular-malfeasance-from-the-worlds-greatest-climate-scientist/
The sun supplies the energy, but it has no thermostat and feedback.
Ice and Water on Earth has a set point and does provide the thermostat.
When Earth gets warm, polar sea ice thaws and clouds and snowfall are increased until the warming is reversed. When Earth gets cold, polar oceans freeze and clouds and snowfall are decreased until the cooling is reversed. Look at the data for the past ten thousand years. Earth temperature is regulated right here on earth. The sun cannot know if we need warming or cooling. Polar Oceans and Polar Sea Ice do know.
Waggy, making fun of old Tim Ball isn’t nice. Doesn’t he have enough problems? Show some sympathy.
Here are some essential references for this topic. If someone wishes to read only one, read the first. And for toying with a molecular dynamics simulator, follow the last two links.
Coombes and Laue, ‘A Paradox Concerning the Temperature Distribution of a Gas in a Gravitational Field,’ Am. J. of Physics, 1985.
http://tallbloke.files.wordpress.com/2012/01/coombes-laue.pdf
Pekka Pirilä, ‘Kinetic gas theory for gas in gravitational field’
http://pirila.fi/energy/kuvat/barometric_derivation.pdf
Berberan-Santos, Bodunov, Pogliani, ‘On the Barometric Formula’, Am. J. of Physics, 1997.
http://web.ist.utl.pt/ist12219/data/43.pdf
http://scienceofdoom.com/2010/08/16/convection-venus-thought-experiments-and-tall-rooms-full-of-gas/#comment-81966
http://physics.weber.edu/schroeder/md/InteractiveMD.html
That really is a generalized discussion considering most of the CO2 in the Earth’s atmosphere is around our ankles.
Wagathon wrote:
“That really is a generalized discussion considering most of the CO2 in the Earth’s atmosphere is around our ankles.”
Only to the extent all air is. CO2’s concentration is pretty much constant with tropospheric height:
http://is.gd/CAxdWo
There is a change of about 3-5 ppm in the stratosphere:
“Concentration of CO2 in the Upper Troposphere and Lower Stratosphere,” H. W. GEORGII & D. JOST, Nature 221, 1040 (15 March 1969); doi:10.1038/2211040a0
http://www.nature.com/nature/journal/v221/n5185/abs/2211040a0.html
Also see Figure 4a here, which goes from 10-25 km:
“Carbon dioxide atmospheric vertical profiles retrieved from space
observation using ACE-FTS solar occultation instrument,” P. Y. Foucher1Atmos. Chem. Phys., 11, 2455–2470, 2011
http://www.atmos-chem-phys.net/11/2455/2011/acp-11-2455-2011.pdf
Pierre-Normand, I read the Coombes and Laue paper you linked to. I didn’t think it presented a very strong argument, mainly for two reasons:
1. It claims to “restrict analysis to a one-dimensional model in which molecules can only move in the vertical direction”. This scenario would constrain all molecules to move along the same path, a path defined by a vertically oriented line. The molecules would not be able to pass by one another. At any given height there could only be at most one molecule. The molecules would exchange kinetic energy, and momentum, up and down the path and both would decrease as a function of height due to gravity. This result would be contrary to the paper’s conclusion.
2. The analysis seems to ignore collisions (eg in the appendix), which would also affect the paper’s conclusion.
As another point, I am not a big fan of the proof because it assumes a fixed M-B distribution over a finite vertical distance. I consider that starting with a premise such as this is begging the question somewhat. The M-B distribution is a theoretically derived distribution, derived from assuming an isothermal condition. It therefore becomes uncertain to me whether the proof is possibly starting with the assumption of a constant temperature over a narrow vertical band (dz) and then extrapolating it across the full height being considered.
Hi Willb,
I had postponed discussion of this topic until there would have been an open thread mainly because of you. And then Judith created this special thread when it became unwieldy in the previous one. I’m glad you showed up!
I think you are overstating the scope and significance of the simplifying assumptions in Coombe and Laue. The aren’t considering a 1 dimensional gas, but rather a three dimensional ideal gas (in a 3D box) while simply abstracting from the two horizontal components of the speeds (or momenta). They are demonstrating the vertical speed distributions corresponding to the isothermal case to be stationary, contrary to naive expectation. This result also is achieved much more directly (but less illuminatingly) from applying the Bolzmann distribution law to the full 3-dimensional case (as shown in section D of the “On the Barometric Formula” paper, and a couple other references that I provided earlier.
Now let me make two more specific points in response to your objections. For an ideal gas in thermodynamic equilibrium, the rate of collisions isn’t relevant. The random collisions simply enable the gas to achieve equilibrium in the first place. After this has been achieved, the collisions can be ‘turned off’, as it were, and all the relevant statistical configurations (speed and density distributions at various locations) will be maintained. See further some of the comments at the end of Pekka’s note, regarding molecular collisions.
Secondly, you are right that the vertical component of kinetic energy isn’t conserved in individual 3D collisions. However the three components of the momenta *are* conserved separately. The Coombes and Laue treatment is based on a consideration about two volumes in phase space that are shown to be equal. (This is an interesting special case of Liouville’s theorem). This result is true, independently, for any of the three 2D planar projections of the whole box (as does the Liouville theorem, more generally) because phase space is a space of positions and momenta, and both positions and momenta do factorize along the three spatial dimensions. Of course, after it has been shown that the momenta distributions are equal for all heights, and also for the two horizontal dimensions, then it follows trivially that kinetic energy distributions are equal too.
Rather more accurately, I should say that the Coombes and Laue 1D model readily generalizes to 3 dimensions because it is equivalent to a full 3D model where the two horizontal dimensions simply are abstracted (or summed over).
Willb wrote:
“As another point, I am not a big fan of the proof because it assumes a fixed M-B distribution over a finite vertical distance. I consider that starting with a premise such as this is begging the question somewhat.”
It is not question begging against their intended target, and this target is the claim that speed distributions *must* vary vertically because molecules collectively lose speed while rising against the gravitational field.
“The M-B distribution is a theoretically derived distribution, derived from assuming an isothermal condition.”
I think it rather derives from the assumption that entropy is maximized at equilibrium. It applies to the canonical ensemble of microstates of a mechanical system that is free to thermally exchange energy with an external thermal bath, and it is true that if the external thermal bath itself isn’t isothermal (with multiple points of contact at different temperatures) then it becomes unclear how the formalism applies to the system.
However, proponents of a gravito-thermal effect take it to be realized in a fully isolated system and the finding by Velasco et al. — that the result for the microcanonical case is equivalent (at the thermodynamic limit) to the result for the canonical case (within a thermal bath) — is instructive. It would be queer that a temperature gradient spontaneously develops in an open system (with some mechanism that ensures no heat flows at the boundary though continuously adjusting the external gradient in the bath to match the gradient that develops in the system) and then slowly vanish again after the system is isolated.
“…that ensures no heat flows at the boundary [through] continuously adjusting…”
Sorry.
I wrote: “Secondly, you are right that the vertical component of kinetic energy isn’t conserved in individual 3D collisions.”
I am referring to a fact that you had highlighted in our earlier discussion and that I had overlooked at first.
Pierre-Normand, from reviewing the last few posts at CE I see you have attracted quite a large fan base :)
With respect to the Coombes and Laue analysis, if their paper is not actually based on a one-dimensional scenario then I think they should state their specific assumptions explicitly. The claim that the paper is going to “restrict analysis to a one-dimensional model in which molecules can only move in the vertical direction” is otherwise somewhat misleading.
I don’t see a problem with their abstracting the vertical dimension from the two horizontal dimensions to conduct an analysis. However, their analysis result is radically different from that obtained in analyzing a one-dimensional model. I think they need to explain why their abstraction is valid in the face of this difference.
Concerning the M-B distribution, you say “I think it rather derives from the assumption that entropy is maximized at equilibrium.” You say potato and I say Solanum tuberosum. I still think assuming a fixed M-B distribution over a non-zero, finite vertical width is begging the question somewhat if your subsequent analysis results in an isothermal condition across the entire height.
Concerning your point about “turning off the collisions”, I expect you could get away with this only if you “froze time” while deriving statistics. Moving molecules across a distance ‘dz’ to derive statistics, as Coombes and Laue do, would not be allowed.
Willb,
For some reason I have a really hard time locating our previous short discussion on this topic. I’d like to review your original argument again before commenting further.
OK, at long last I found your earlier argument. I guess I was looking too far back:
http://judithcurry.com/2014/10/25/week-in-review-30/#comment-641674
Willb,
Let me run through some steps of your earlier argument.
“3. In the horizontal direction, the mean atom velocity is zero ==> therefore all kinetic energy is thermal energy.”
If the initial state at t_0 is isothermal, and the molecules have the same Maxwell speed distribution everywhere, then this is true also in the vertical dimension at t_0.
“4. In the vertical direction, the mean atom velocity is shifted by gravity in the downward direction (i.e away from zero) ==> therefore some portion of the vertical KE is no longer thermal energy.”
Coombes and Laue demonstrate that this can’t possibly result from the effects of gravity alone. Notice that if it were true for the entire molecular population at some higher level, at any time t > t_0, then the speed distribution would not be isotropic anymore and there would be a net downward motion of the gas at that level. (Since, by the same argument, molecules that fall to this level from higher up all have a *larger* average KE than they had at t_0, and hence also a preferentially downward motion). The density profile would not possibly be stationary.
“5. At height H + Δh, some of the non-thermal vertical KE is ‘lost’ to PE. To re-balance horizontal and vertical KE and maintain equilibrium under equipartition, a portion of horizontal KE must be converted to vertical KE.”
So, now, this doesn’t follow anymore since it depends on (4). Though particles that are able to rise from the lower level to some z level higher up lose some kinetic energy, the average kinetic energy of all the molecules that will have been able to end up at this level z at some time t+dt will have the very same isotropic speed distribution that they had earlier at any level (as demonstrated by Coombes and Laue).
Pierre-Normand,
Just to remind us both, my previous argument was based on a simulation in which balls were bouncing in 2D space. Now, as to your comments on my argument:
Regarding my step 3, I agree with your comment. I also think that the molecules, at any given height, will have the same M-B speed distribution in all directions.
Regarding my steps 4 and 5, I disagree with your comments. Even though gravity shifts the mean vertical velocity in the downward direction, there is no overall, average downward motion of the molecules at any level. This is because, under equilibrium and at each height level, horizontal KE is instantaneously transferred to vertical KE through collision. The speed distribution remains isotropic through collision. However as height increases, the continual removal of horizontal KE to maintain this balance results in a non-zero lapse rate.
IMHO the Coombes and Laue analysis has a hole in it because it ignores collisions.
Willb,
Did you read Pekka’s note (which I listed in my reference list near the top of this thread? He deals with collisions. See also his recent comment in this thread:
http://judithcurry.com/2014/12/01/gravito-thermal-discussion-thread/#comment-653204
Consider the case of a diffuse gas where the mean free path is very much larger than the size of the box. The molecules would still collide once in a while. The spatial density and speed density functions of an ideal gas will be the same at equilibrium regardless of the collision rates (or mean free path). That’s because the partition functions of the phase space are unchanged by those assumption. It’s just the size of a volume in phase space, and the number of cells (defined by the relevant partition function) that it covers, that determines the probability for the system to realize a state that is located within that volume. It would just take a longer time for a gas to equilibrate in such conditions (provided only the initial condition with lower entropy nevertheless yields an ergodic trajectory).
If you feel Pekka’s rather simpler explanations don’t fully address your issue about collisions, then feel free to tell me why.
Pierre-Normand,
It will take me some time to fully absorb Pekka’s note. In the meantime I’d like to comment on the comment you linked to. First I will paraphrase the experiment description so you can see if I understand it correctly:
1) There are three main components to his experiment: a horizontal planar surface, a gas above the surface and a gravity field pulling the gas towards the surface.
2) The gas molecules are in a state of thermal equilibrium with an M-B speed distribution.
3) The gas is extremely rarefied such that collisions can now be ignored when analyzing the motion of the molecules in the gas.
4) Pekka claims that, even though collisions can be ignored, it can be shown that the gas molecules have the same speed distribution at all heights and in all directions, including along the axis normal to the surface.
Is this a correct interpretation of the experiment? I have a feeling I’ve missed something because I don’t understand how Pekka arrives at his claim. For example, I get this paradox:
Consider the subset of molecules at the surface, i.e. at height h = 0, at time t = 0.
a) The equilibrium density profile establishes that there are more molecules at h = 0 than at any other height h.
b) The equilibrium vertical speed distribution of the molecules is identical for all values of h, with a velocity for the mode (the maximum value of the distribution) of |V|_mv.
c) From a) and b), there are more molecules at h = 0 with |V|_mv than at any other height h.
d) At time t = T, the molecules that were at h = 0 travelling at vertical speed |V|_mv are now at h = H1 = ½gT² with vertical speed |V|_mv-gT.
e) There are now more molecules at H1 with vertical speed |V|_mv-gT than with vertical speed |V|_mv. This contradicts b) above and the claim that the speed distribution is the same for all heights and for all directions.
… h = H1 = |V|_mvT-½gT² …
–Pierre-Normand, I read the Coombes and Laue paper you linked to. I didn’t think it presented a very strong argument, mainly for two reasons:
1. It claims to “restrict analysis to a one-dimensional model in which molecules can only move in the vertical direction”. This scenario would constrain all molecules to move along the same path, a path defined by a vertically oriented line. The molecules would not be able to pass by one another. At any given height there could only be at most one molecule. The molecules would exchange kinetic energy, and momentum, up and down the path and both would decrease as a function of height due to gravity. This result would be contrary to the paper’s conclusion.–
I would say in troposphere, that faster or slower molecules are not going up or down [or sideways or whatever direction]. And that faster or slower molecule is only “one” of the faster or slower for fraction of nanosecond. A molecule of air can travel through out that atmosphere- but faster one or slower one can not.
Air packets are not the same molecules moving up [or whatever direction] a air packet are more like a memory of energy being transferred. It’s kinetic energy momentum which goes up [or whatever direction] not a molecules or pack of molecules moving, but the result of the past movement which moving.
Once get into more rarefied air, then a faster molecules might be able to travel some distance for more than a fraction of nanosecond.
My problem with article is:idea that kinetic energy of molecules decease
with elevation. It’s only that density is reduced with elevation- or million molecules at 500 meters don’t have less kinetic energy as a million molecules at 5000 meter- assuming dry air/ideal gases are only involved. So 5000 meter air per number rather than volume have same kinetic energy- plus they have PE which is not expressed as temperature. It is only expressed if air falls- atmosphere as whole contracts. the 5000 meter air colder because there are less of them per a volume..
Gbaikie wrote: “My problem with article is:idea that kinetic energy of molecules decease with elevation. It’s only that density is reduced with elevation […]”
That’s indeed what Coombes and Laue conclude. The isothermal profile (same kinetic energy distribution at all elevations) together with the barometric vertical density gradient constitutes a stable configuration.
Absolutely amazing that Coombs and Laue only got two citations since 1985mover 30 years for a paper that “proves” a controversy about gravity acting at the quantum scale that’s never been proven since proposed since 19th century golden age of physics. We still don’ t to THIS day have a theory of quantum gravity. Amazing that such definitive abstract “proof” can be asserted about an imaginary physical system that doesn’t actually occur in nature.
David Springer wrote: “What you are overlooking is that the Boltzmann energy distribution will ensure that as molecules bump together at the same level there will be a continuous supply (but diminishing in frequency) supply of them with the energy required.”
The Boltzmann energy distribution law as applied to an ideal monatomic gas column under gravity also yields an isothermal profile (with the Maxwell speed distribution for T at all heights) while the vertical density distribution conforms to the barometric formula. This is demonstrated at p.210 of Reif, Fundamentals of Statistical and Thermal Physics.
http://judithcurry.com/2014/10/21/ethics-of-communicating-scientific-uncertainty/#comment-643688
It is also demonstrated in section D of this paper:
Berberan-Santos, Bodunov, Pogliani, ‘On the Barometric Formula’, Am. J. of Physics, 1997.
http://web.ist.utl.pt/ist12219/data/43.pdf
Willb,
I think you are overlooking that fact that the molecules that have the most likely speed |V|_mv at height H0 (h = 0) are going to sweep a layer of thickness dz at height H1 at a different speed than those from the same layer (which departed from H0 at another time) that are sweeping the same layer with the terminal speed |V|_mv. Hence they will not contribute equally to the speed distribution at H1 (since they don’t spend the same amount of time at this level of thickness dz) and this consideration ought to resolves your paradox.
Consider also the case where the level H1 is such that m*g*H1 > (1/2)*m*(|V|_mv)^2. That is, molecules that start up with speed |V|_mv at H0 don’t even have enough (vertical) kinetic energy to reach the level H1 before falling back down. Then, a fortiori, *those* molecules aren’t going to be more numerous than those that have speed |V|_mv at H1. There will be zero of them.
Pierre-Normand,
Your first comment doesn’t make sense and your second comment is irrelevant to my argument that a paradox exists. I suspect you are probably too pre-occupied at the moment with JimD and perhaps we should continue this discussion at another time.
Willb,
You are saying that constancy of speed distribution at all height together with a density gradient yields a paradox. That’s because, if I understand you correctly, you are saying that molecules at the peak of the speed distribution (where the probability density is largest) that reach a higher level H1 (where they will be slower) will be more numerous than those that have this very same initial speed at that level, and this contradicts the assumption that the speed distribution is the same. But you didn’t correctly account for the ratio of the number of molecules with those two speeds at the two levels (that is, the molecules that have speeds [v1, v1+dv], and [v2, v2+dv]) at levels H0 and H1. Here, I am using v1 for your maximum value ‘|V|_mv’ at H0, the level at the bottom of the box, and v2 is v1 – gt.
My point is that if you want to compare the number of molecules that have speed v1 and v2 at height H1, in order to see if the ratio is the same as the ratio between molecules that have those two speeds (within the same dv intervals) at height H0 at any given time, then you must check how many of them there are at that level at some given time. However, in order to backtrack molecular populations in time, or track them forward in the future, you must define your populations precisely in phase space. You must not just delimit the initial or final speed ranges (e.g. [v1, v1+dv]) but also the initial and final volumes where they are located at some definite time (e.g. [H0, H0+dz] and [H1, H1+dz]). That’s because, molecules that start up with an initial velocity range in some small volume can end up (as it is the case here) in a larger volume at a later time, and if this change in volume isn’t identical for two different initial speed ranges, then this will incorrectly skew the ratio between them. Coombes and Laue do this correctly because they define volumes in phase space that jointly define velocity and ranges and location ranges, and map them exactly with the equations of motion.
The explanation from shifting of exponential functions is simplest. When the Maxwell distributions of speeds (Gaussian) are the same, then so are the kinetic energy distributions. The latter are (negative) exponential functions of EK (Boltzmann energy distributions). The effect of gravity on rising molecules merely shifts the exponential function (probability distribution) along the KE axis. This causes a drop off of the molecules that don’t have enough KE to reach the new level, and accounts for the barometric density formula, but the new shifted exponential function that represents the new (normalized) distribution is invariant under this transformation.
Pierre-Normand,
“You are saying that constancy of speed distribution at all height together with a density gradient yields a paradox.”
Ans) Yes, that is correct.
“That’s because, if I understand you correctly, you are saying that molecules at the peak of the speed distribution (where the probability density is largest) that reach a higher level H1 (where they will be slower) will be more numerous than those that have this very same initial speed at that level, and this contradicts the assumption that the speed distribution is the same.”
Ans) Yes, that is correct. All of the molecules that leave H0 with a vertical speed component v1 will arrive at H1 at precisely the same time with a vertical speed component v2. The only thing I might change in your wording is to remove the word “initial” to clarify my meaning, since the distribution is constant over time.
“But you didn’t correctly account for the ratio of the number of molecules with those two speeds at the two levels (that is, the molecules that have speeds [v1, v1+dv], and [v2, v2+dv]) at levels H0 and H1. Here, I am using v1 for your maximum value ‘|V|_mv’ at H0, the level at the bottom of the box, and v2 is v1 – gt.”
Ans) I didn’t calculate the ratio explicitly. I showed that, at height H1 and at time T, the number of molecules with vertical speed component v2 is greater than the number of molecules with vertical speed component v1. This follows from my statement a) and violates my statement b). This is the paradox.
Willb,
The mode of the vertical velocity is zero at every altitude. Thus molecules at the mode are at just at the point, where they switch from rising to falling.
…Coming to think of it, indeed, in three dimensions the Maxwell speed distribution peaks at some finite speed, but in one dimension, the distribution is Gaussian around zero. So, the mode is zero. This rather short circuits the formulation of your paradox. I should have thought of that first.
http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/maxdev.html#c5
The velocity mode is 0, not the mode of the speed, which is the magnitude of the velocity.
“The velocity mode is 0, not the mode of the speed, which is the magnitude of the velocity.”
There is a rather unfortunate tendency in kinetic theory to speak of “speed” to designate velocity (vector) rather than speed (magnitude). This use, however, matches the common usage in French (vitesse; vecteur, et vélocité; module). But here, it’s inconsequential, I think. When the distribution of the one-dimensional velocity (vector) along z is Gaussian, then the mode of speed (magnitude of velocity) also will be zero!
If the speed mode were 0 then no molecules would be moving at all.
“This use, however, matches the common usage in French (vitesse; vecteur, et vélocité; module).”
I just checked, and it seems that I am wrong about the French usage!
“If the speed mode were 0 then no molecules would be moving at all.”
Why? It’s just the peak of the probability distribution. For the molecules to be moving at v, where dv > v > 0 is more probable than them moving at any other speed +- dv/2.
I am assuming the speed follows a Maxwell-Boltzmann distribution.
Also, the reason why the Maxwell speed distribution has a mode larger than 0 for particles that are free to move in three dimensions in spite of the fact that the mode of each one-dimensional component of the velocity distribution being 0 is because of the properties of the volume integral, as explained in the hyperphysics item referenced earlier. Though it is most likely for the speed projection along any one direction to be around zero, it’s much less likely for it to be around zero along three orthogonal directions all at once.
Yes, that’s correct. The two expression are used interchangeably. “In physics, particularly statistical mechanics, the Maxwell–Boltzmann distribution or Maxwell speed distribution describes particle speeds in idealized gases where the particles move freely inside a stationary container” — Wikipedia
Still, in one single dimension, the projection of the isotropic velocity vector distribution that satisfies this scalar speed distribution is a Gaussian distribution rather confusingly called the one dimensional Maxwell ‘speed’ distribution.
Pierre-Normand, thank you. I see now where I was going wrong.
Willb, you are welcome. And thanks to you for the probing questions.
P-N, “…Coming to think of it, indeed, in three dimensions the Maxwell speed distribution peaks at some finite speed, but in one dimension, the distribution is Gaussian around zero. So, the mode is zero. This rather short circuits the formulation of your paradox. I should have thought of that first.”
I believe that is why a spherical shape has greater entropy since it more closely matches the shape of the speed distribution. So if you keep adding pressure to your box it would tend to want to become a sphere or a cylinder rounded at the ends.
Captdallas wrote: “No, thermodynamic temperature isn’t entropy it includes entropy, 1/T=dS/dE. Ideal models eliminate entropy so processes are 100% reversible.”
The models don’t eliminate entropy. They maximize it. All defenders of the gravito-thermal effect have taken it to apply to an ideal gas in thermodynamic equilibrium. It’s not my assumptions that the system is under equilibrium or that the effect applies to an ideal gas. It’s their’s. They don’t argue that it’s a real effect that stems from deviations from ideality. There is one person in the world (that I am aware of) who claims that the gravito-thermal effect only is exhibited in a real atmosphere that doesn’t satisfy those assumptions, and that’s you. But your theory isn’t well worked out yet. Indeed, everyone of your posts so far seems to have express a completely different ad hoc ‘non-ideal’ theory.
Pierre-Normand,
What’s, in your opinion, the correct explanation for the vortex tube effect?
http://en.wikipedia.org/wiki/Vortex_tube#Method_of_operation
Edim,
I don’t know what the correct explanation is, but since the device requires the continuous injection of compressed air this seems to be a process that is far from equilibrium and hence has little bearing on the alleged gravito-thermal effect.
P-N, “But your theory isn’t well worked out yet. Indeed, everyone of your posts so far seems to have express a completely different ad hoc ‘non-ideal’ theory.”
Indeed they do. As I mentioned before this thought experiment is a bit of a waste of time since the parameters can be changed. Call it “Thought-Ball” The real atmosphere is an open system the thought experiment is a closed system that can include any number of assumptions.
My “theory” is and always has been that it is an un-physical problem, a waste of time. There is no such critter as an atmosphere in any kind of equilibrium. Energy is always flowing through an atmosphere making it a “conditional” steady state. You can use “local” thermodynamic equilibrium or hydrostatic equilibrium with proper respect, but they are both steady states with no definite source or sink when you just pick a parcel. You can’t just tap into an energy flow and declare you have usable source of energy because there is a temperature differential.
Now when you say your model is maximizing entropy don’t you mean it is maximizing conductive heat transfer within a volume? Since there is no source or sink, just a volume, you are assuming conduction/convection always wins no matter how tall the z dimension is or how strong the force of gravity is. So there is never a chance of there being a temperature difference between the top and bottom because all of the Ideal relationships derived are truly “ideal”. I believe you have used the term “exactly” a number of times. To me that is just the opposite extreme of “declaring” you have found 2lot violation. In all likelihood there can be a small, completely unusable temperature differential due to gravity in a tall enough box under just the right cherry picked conditions.
CD: “Now when you say your model is maximizing entropy don’t you mean it is maximizing conductive heat transfer within a volume?”
No. A system in thermodynamic equilibrium is, a fortiori, in thermal equilibrium. There is no heat flow anywhere in the system.
Yup. It’s a classic of example of arguing about how many angels can dance on the head of a pin.
P-N, “No. A system in thermodynamic equilibrium is, a fortiori, in thermal equilibrium. There is no heat flow anywhere in the system.”
Again that is solving the problem by decree. The problem started with a thought experiment challenging Boltzmann’s H-theorem.
http://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf
That is a paper by E. T. Jaynes comparing Gibbs and Boltzmann entropies. Once you add gravity there will be some kintetic energy converted to potential energy which would create a density and entropy gradient. that should lead to a very small “theoretical” temperature difference. I have no idea if it would be measurable and I am pretty confident it would never be usable, but if the molecules are above 0K they will be transferring energy between themselves and a gravity field, Each one of those microscopic transfers would need to be 100% reversible for there to be no fluctuations of temperature within the volume.
That lead I believe to the Fluctuation theorem and is a part of the Arrow of Time problem. Pretty obviously, the effect is very small so defining an “equilibrium” using the Boltzmann distribution and H-theorem would eliminate the effect since that is why the effect was proposed to begin with. So far in this conversation we have circular reasoning and angels dancing on pin heads.
CD wrote: “Again that is solving the problem by decree. The problem started with a thought experiment challenging Boltzmann’s H-theorem.”
No, it doesn’t prejudge the relevant issue. Proponents of a gravito-thermal effect characterize this effect as a temperature gradient that *subsists* in a gas column under gravity at equilibrium. There is no vertical heat flow in that case either. If there would remain a net vertical heat flow then the vertical temperature profile would evolve and the system would not be in equilibrium yet.
The ideal gas model explains the temperature profile of the troposphere, if you can specify a temperature/altitude point on the lapse rate curve. To do that, you have to consider the radiation balance for each layer of the atmosphere. This gives you an altitude where the Stefan–Boltzmann equation is satisfied (the equivalent emissions height). Now, you can plot the equilibrium temperature profile of the troposphere and begin to argue about the multitude of other things that affect it (the actual non-ideal, non-equilibrium state).
The problem is that it is not an either/or proposition. Both sets of equations need to be considered, the layer-by-layer lapse rate, and the layer-by-layer, line-by-line radiation balance. Not an easy problem.
The question of what’s the thermodynamic equilibrium temperature profile has perhaps been discussed sufficiently. What’s more important for the real Earth system, are the mechanisms that determine and maintain the circulation and the actual environmental lapse rate.
Circulation can be driven only by an atmospheric heat engine that requires the hot end of low latitude surface and the cold end in the upper off-tropical troposphere. Solar radiation and GHE are essential ingredients of this layout.
Isaac Held wrote two weeks ago a related post, where he lists some constraining factors:
1) Rising air that has reached saturation follows the moist adiabat, i.e. cools at low altitudes less rapidly than the typical environmental lapse rate of 6.5 C/km.
2) Total precipitation is constrained by the rate of heating of the oceans by solar SW.
3) Subsiding air has an absolute moisture controlled by the minimum temperature that the parcel of air has met (the rest has condensed and been removed as precipitation).
Rising and subsiding air get mixed. How that takes place must be an essential factor in explaining, why lapse rates seem to be more uniform at different latitudes (excepting polar winter) than one might expect from simplistic arguments that propose a significantly lower lapse rate in tropics and a higher one at mid latitudes, where subsiding air is common. These questions are related to the case of the “tropical hot spot” as well.
Pekka wrote: “The question of what’s the thermodynamic equilibrium temperature profile has perhaps been discussed sufficiently. What’s more important for the real Earth system, are the mechanisms that determine and maintain the circulation and the actual environmental lapse rate.”
But that’s completely off topic! Nevertheless, I agree.
Thanks for the pointer to Held’s post. Let me also refer again to this recent discussion thread on Nick Stokes’s blog:
http://moyhu.blogspot.ca/2014/10/calculating-environmental-lapse-rate.html
Pekka’s insightful posts within it are worth a read.
CD wrote: “You battle that with statements like, (P-N)’The following paper does exactly that and finds out that the two effects indeed cancel out exactly when the vertical profile initially is isothermal and the density profile is barometric (as a consequence of the ‘drop off’ effect). Hence, this is a stationary state.’
CD: “Amazing, the two effect “exactly” cancel out if there is a lapse rate.”
You misunderstand. Isothermal means *no* lapse rate — i.e. the temperature is uniform. There is a *density* gradient. That’s not a lapse rate.
You really ought to read at least the first few paragraphs of the paper if you want to talk about the topic knowledgeably. It’s a very simple paper aimed at college students and that targets heads on you own “basic premise of the gravito-thermal effect as [you] understand it”.
http://tallbloke.files.wordpress.com/2012/01/coombes-laue.pdf
P-N, Apologies, that should have been no lapse rate. The main point was the “exactly” cancels. Since the average velocity in the +z only direction decreases with altitude. For a layer near the top, the average velocity would still be determined by the Kinetic temperature and as long as there is elastic collision, the M-B distribution would not change since it is not dependent on the direction of the velocities. The average -z velocity of the layer would be slightly higher than average. Given enough time and pressure the system will try to reach an isothermal equilibrium, but the velocity distribution in z is skewed toward -z. The density is skewed toward -z. So the heat capacity is skewed toward -z. To say it “exactly” cancels is a stretch in my opinion.
CD, read the paper. It’s a rigorous mathematical proof, and so it isn’t a “stretch” that the two effect that I have mentioned regarding speed distributions cancel exactly. Also, in all your replies to this argument, you only consider *one* of the two effects discussed in the paper (the asymmetrical variation in speed of individual molecules — both moving up and down) and display no awareness of the second one (the changes in the molecular populations due to some molecules not having enough energy to rise from a lower level to some higher level). How can you doubt that the two effects cancel out when you haven’t so much as acknowledged the second effect?
P-N, I have said a number of times that if the system reaches equilibrium, which can take a long time depending on how an experiment is set up, there is no usable work to be found inside but there could be a small measurable difference in temperature because energy is always flowing in the volume. There is no form of energy transfer that is 100% efficient so “exactly” cancelling would imply that there is no such thing as entropy. You can build as ideal of a container as possible to reduce entropy, but it can never be eliminated. so the problem will eventually boil down to does 1/ KEave=dS/dE. Because of that I would say “for all practical purposes, the system will be isothermal”, but I would not say it exactly will or exactly how long it will take to reach a “true” equilibrium.
When I mention a number of things that could impact results, you respond by saying “my theory” isn’t well derived, when all I am doing is pointing out that “your model” requires perfection. Since I am pretty confident that perfection doesn’t exist I am equally confident entropy does exist meaning with enough perseverance some dolt can discover some higher order “effect” that might actually be “real” and large enough to measure in an un-physically large, “assumed” to be in perfect equilibrium, volume.
I believe when the problem was originally posed, Boltzmann had derived,
http://upload.wikimedia.org/math/e/c/d/ecda8bab6b774183107eb6e69fd31e2c.png
and that, ” In 1876, Loschmidt pointed out that if there is a motion of a system from time t0 to time t1 to time t2 that leads to a steady decrease of H (increase of entropy) with time, then there is another allowed state of motion of the system at t1, found by reversing all the velocities, in which H must increase. ”
A jumbo sized paradox. So I would never use the term “exactly”.
Although I have found Pierre-Normand’s comments to be the most focused, he and Capt. Dallas may have failed to identify the distinction between the kinetic and thermodynamic definitions of temperature.
As I believe Pierre-Normand recognized, gravity does indeed impose a non-zero (but immeasurably small) kinetic-energy gradient in a thermally isolated gas column at equilibrium. So there’s a non-zero kinetic-theory temperature gradient. But, by definition of equilibrium, no net heat flow occurs, so under the thermodynamic definition of temperature there’s no temperature difference: the temperature gradient is zero.
As this layman sees it, much of the confusion in these discussions arises from scientists’ failure to recognize that the several definitions of temperature, although experimentally indistinguishable, have slight differences theoretically: you can have a kinetic-theory lapse rate that differs from the thermodynamic one.
Joe Born,
The alleged gravito-thermal effect that has been discussed on this site, but for a short intermission, isn’t the tiny effect on speed distributions discussed by Velasco et al. (in connection with the microcanonical ensemble). It’s rather the alleged effect that corresponds to the second alternative of the apparent paradox discussed by Coombes and Laue. This alleged effect is dozens of orders of magnitude larger in macroscopic systems than is the effect discussed by Velasco et al. The controversy over *this* effect (C&L) doesn’t have anything to do with any controversy over the definition of temperature. I just wanted to keep those two issues separate.
To the extent that “the alleged effect that corresponds to the second alternative of the apparent paradox discussed by Coombes and Laue” implies a measurable lapse rate, it is indeed different from the effect that Velasco et al. discuss. I haven’t yet been able to explain to myself, though, why the effect that Velasco et al. describe does not ultimately result from molecules’ losing kinetic energy between collisions as they rise.
Joe Born,
The effect that Velasco et al. describe certainly does result from the slowdown of molecules as they rise. I didn’t see anyone deny this on the SoD thread. It was denied that there is a sensible definition of temperature such that we can claim a temperature gradient. I largely agree with that. But your own position isn’t completely indefensible either. If the perfectly isolated column for which the microcanonical ensemble formalism applies were suddenly put into thermal contact with a small thermal bath that has a well defined temperature T, either at the top or bottom of the column, there would be a higher probability that the bath placed at the bottom would be warmed up a little after just a few molecular collisions.
This is most obvious in the degenerate single molecule case. The single molecule that was bouncing up and down in the isolated column would hit the bottom bath with a higher speed than it would have hit the higher bath (if it would reach it at all!). So, the resulting collision would *likely* result in giving up more energy to it (since that depends also on the speed of the molecule from the bath that it will hit).
This probabilistic effect from one single molecule is just about the largest effect that would be exhibited in such a scenario, whatever the number of molecules in the fully isolated system was. This is why the gradient in average kinetic energy of the molecules is so tiny.
Pierre-Normand: “. . . . This is why the gradient in average kinetic energy of the molecules is so tiny.”
I overlooked that comment previously. Excellent explanation.
Not inconsistent with that, and possibly untrue because I haven’t thought it through completely, is my guess that the ensemble of microstates of the system consisting only of the single erstwhile-isolated particle is the same when the (finite) heat bath is coupled to it at a high altitude as when the heat bath is coupled a low altitude.
Neither here nor there, I suppose, but thinking about it gave me a nice respite from dealing with estate issues in which I’m currently embroiled.
While it is rare to be able to prove anything in science, I believe I’ve proven that not only gravity, but no other such process can warm the surface of a planet with a non-radiative atmosphere (i.e. no greenhouse gases) to a temperature warmer than the theoretical Stefan-Boltzmann blackbody temperature. The proof is here</u).
Don't like my proof? There is also a lovely proof by Dr. Robert Brown of Duke University here.
Here’s the short version of my proof. Imagine a rocky planet with no atmosphere in outer space with no nearby stars. It is in radiative equilibrium with the ~ 3 W/m2 of the cosmic background radiation. This means that the surface of the planet is radiating 3 W/m2, and receiving 3 W/m2 of radiation from the cosmos. As a result, its temperature is unchanging.
Now, add a non-radiative atmosphere to the rocky planet, one with no greenhouse gases. IF the crackpot gravity theories were correct, the surface of the planet would warm, and stay warmer than it was with no atmosphere.
But at that point, the surface of the planet would constantly be radiating more energy than it is receiving … which is an obvious physical impossibility.
Short answer? Gravity alone cannot warm the surface of a rocky planet.
Best regards,
w.
This is a perfectly valid argument Willis. But it will appear as a no-brainer to any atmospheric physicist or climate scientist.
Wow, is your transparent atmosphere made of atoms and molecules and held by gravity? If so I argue that this atmosphere will have its own lapse rate even if there were no suns and no cosmic background radiation. The energy that creates this lapse rate is completely unrelated to SB and radiation. There is no violation of conservation.
gymnosperm, IF your situation warms the surface, then the surface will be radiating more energy than it is receiving. This is a violation of conservation of energy.
To argue otherwise, you’d have to identify where the energy to warm the surface is coming from. Surely you don’t think that a lapse rate creates energy from nothingness?
w.
I don’t know if it warms the surface. Doesn’t really happen on earth as the surface is almost always warmer.
Think about your rocky planet alone. It has its own “lapse rate” in the rock as pressure increases towards its core. If some of this mass converted to thermal energy happened to be conducted to the surface and radiated away would you argue it was a violation of conservation? Mass and energy transmography. Energy = Mass x that weird square light thing.
Gymnosperm,
It doesn’t matter if there is or isn’t a lapse rate. After a steady state is achieved, there will not be any conductive flow from the surface to the atmosphere since the atmosphere is unable to cool to space and doesn’t gain any energy from the Sun. So, the only energy flows will be from the Sun to the surface and from the surface to space. The latter only is a function of surface temperature. So the atmosphere is irrelevant to the steady state surface temperature when the atmosphere is not radiatively active .
Pierre, we took the suns and all external energy sources away. I argue that there will be a purely adiabatic lapse rate due to the mass of this transparent atmosphere just as there is non diabolical lapse rate in the rock of the planet itself.
Let’s be trite and say the lapse rate in this atmosphere is from 1K at the surface to 0K at the top. You get radiation from this 1K that may warm the rock depending on the rock’s temperature or just zoom off to space because this is not a resonating atmosphere.
I do not believe any of this violates conservation.
The atmosphere – not active in the IR bands by assumption – would be warmed by conduction and convection. The energy would accumulate until emissions again balanced incoming energy. You would need to know the makeup of the ‘atmosphere’ to have any idea of the atmospheric physics which is where it all becomes inuterably ridiculous.
What you need to do is divest yourself of the notion that strange little thought experiments explain anything interesting at all.
Willis, a sideways digression, If the planet is big enough , Say 6 times the size of the sun what would happen??
Basically it would become a sun right, as it collapses under the effect of the enormous gravity. This would then lead to heating up of the compressed atoms and a sun would be born. All powered by the effect of gravity causing heat.
This overcomes your objections about the planet being a source of energy when as you say, small enough like the earth or a meteor There is not enough gravitational force to stoke up the engines.
Tell me where I am going wrong.
“Basically it would become a sun right, as it collapses under the effect of the enormous gravity.” “All powered by the effect of gravity causing heat.” The height from which it collapses is potential energy. If a surface packet of the your planet were to fall to the center of mass which was small, when it hit it, its speed would be cashed in, probably as heat. The heat potential was already there. We just realized it. If there is water behind hydro power generating dam, gravity allows potential storage. A timing difference again. Where does the energy reside? Perhaps in the distance between the center of gravity and the water. Maybe it’s an acceleration potential? The potential comes from separating two things that attract each other. When they move closer together it’s a transfer, the creation of this potential came when they got further apart in the first place. Something banked the energy.
Willis,
In your thought experiment, what sort of density curve of the non-radiative gases would you expect from the top of the atmosphere to the bottom? How are you measuring the “temperature”. Are you assuming an even density of the gas across the entire height of this atmosphere? This assumption would seem to indicate a certain conclusion as to the temperature at the surface of this planet versus the top of the atmosphere.
R. Gates,
The temperature and density profiles of a non-radiating atmosphere would not have any incidence on the surface temperature. Since such an atmosphere would not radiate heat to space, then the conductive flux at the surface would tend to average to zero over diurnal/seasonal/etc. cycles at (average) steady state. Hence the surface would only warm enough to radiate to space with the same power received from the Sun. Whatever the atmospheric temperature profile would be (as measured by thermometers!) the temperature of the lowest layer would closely match the surface temperature.
Thanks Willis,
Interesting and clear. Good enough for me.
And like nearly all the down-in-the-weeds climate science is irrelevant for input to policy analysis.
Willis, is there any matter that does not absorb, at all, in the Far-IR and microwave region?
Hey, Doc, good question. Yes, any mono-atomic gas doesn’t either absorb or emit thermal IR. The usual example is argon. Gases can only absorb and emit IR by flexing, stretching, twisting, or otherwise disturbing the bonds between the molecules that make up the gas … but being mono-atomic, argon has no such bonds.
Argon can absorb and radiate at other frequencies, absorbing radiation by kicking an electron up to a higher orbit and radiating it when the electron drops down again. But thermal radiation at the temperatures found on earth doesn’t have enough energy to kick an electron out of orbit.
w.
“Gases can only absorb and emit IR by flexing, stretching, twisting, or otherwise disturbing the bonds between the molecules that make up the gas …”
…and rotating! (for molecules that have permanent electric dipoles, such as CO2 and H2O)
and collisional perturbations. Noble gases are not ideal.
Willis, where does the energy come from to “float” your non-radiative atmosphere?!?!
kuhnkat | December 1, 2014 at 9:24 pm
Thanks, kuhnkat, but I fear I have no Idea what you mean. What does “float” signify regarding atmospheres?
w.
Kuhnkat, it is in thermal contact with the surface.
I agree with P-N it’s obvious that gravity doesn’t add energy to the atmosphere. Basic knowledge of star formation provides that understanding, Willis. An isolated cloud of gas in interstellar space collapse in on itself under the force of gravity eventually bringing pressure and temperature to fusion ignition point. Gravity concentrates mass- energy that’s already there. In an isolated cloud it would be violation of conservation for total energy to increase.
Willis, please be careful about talking in absolutes (“No other such process”). Imagine a source of a neutron flux (the Sun qualifies) which causes a certain (probably small, granted) amount of activation / isotopic shift resulting in radioactive heating or even fission. And therefore … heating.
“add a non-radiative atmosphere to the rocky planet”
Be a bit difficult adding an atmosphere to a rocky planet at such a low temperature…
Bingo. The proposed PM2K by Eschenbach-Brown stop running when the height of the columns is reduced below the contact points for the hot and cold sides of the heat engine or thermopile.
Dear Mr. Eschenbach,
Thank you for the clear example. I would go even further.
In this specific case, radiative equilibrium with the cosmic background being equal in all directions, there would never be a temperature gradient anywhere in or on this planet, between any part of the atmosphere, or on the surface, right down to the core, no matter what the composition of the rocks or atmosphere.
A temperature gradient never comes into existence spontaneously. Period.
Brownian motion and Boltzman distribution means any atmosphere will have an abudance of molecules both above and below the average temperature. Just for sake of argument say helium remains a gas at 3K. There will be many atoms both above and below that temperature. Gravity simply sorts them into non-Boltzmann distribution. However there is not an energy gradient established as the average mechanical energy is the same at all layers in the atmosphere with potential energy substituting for kinetic in one-to-one correspondence with altitude.
I cannot stress strongly enough that this configuration, mechanical energy the same at all levels in the atmosphere, is the highest entropy state of the atmosphere and hence the *only* state which doesn’t violate 2LoT.
DS, Individual atoms don’t have a temperature.
DS, Also, gravity doesn’t sort gas molecules (of identical masses) into different layers with different speed distributions depending on height. This naive expectation is disproved by the Coombes and Laue paper cited earlier. You never acknowledged their argument.
Secondly, the Boltzmann distribution law for energy isn’t countered by the effect of gravity. This law takes the gravitational potential energy of the molecules into account and merely results in a vertical density gradient together with uniform Maxwell speed distributions (for an ideal gas) at all height. See section D in the paper “On the Barometric Formula” referenced earlier.
Gravity does tend to sort molecules into independent barometric density distributions in accordance with their masses, but this effect doesn’t change the isothermal profile either.
Hi,
Now that I’ve poked my nose into this ants nest, I’ll take my statement a bit further.
I agree that Willis Eschenbach gives a good example of a rocky planet alone in outer space.
However, Willis qualifies his argument with the conditions that the planet is dry rock, that the atmosphere was non-radiative (no greenhouse gases) and that there was only cosmic background radiation of 3 W/m2.
Here I disagree As long as the incident radiation over the entire sky is homogeneous, these qualifiers are quite unnecessary.
Imagine our Earth, as is, in utter loneliness in some space, with a homogeneous sky radiating eternally at 22C. Sound comfortable?
Given enough time, the planet would come to equilibrium. What would this be like?
There would eventually be no temperature differential, anywhere
Not between surface and atmosphere
Not between light and shade
Not between the core of the planet and the top of the atmosphere
There would be
No convection
No wind
No clouds
No lapse rate
Homogeneous humidity everywhere
Oceans smooth as glass
No non-random mechanical processes whatsoever
You could not burn your finger with a magnifying glass
Solar power would not work because it could never drive anything
(it would be like trying to drive a turbine in a circular pipe full of water)
No plants, since they couldn’t transpire
No wild animal
All that would remain would be brownian motion, which is the only thing that would prevent the atmosphere from stratifying according to molecular weight
You could live there, but only as long as you have some sort of energy stored somewhere. (chemical, nuclear) You could then be your own personal temperature anomaly, until your stockpile ran out. I suppose that you could use gravitation to transport rocks from the tops of mountains to the bottom of the sea until everything was flat.
Anything that happens on our Earth is only because the sun shines on one spot at a time, and the spot keeps moving. A temperature differential is a very fine thing indeed!
Ken W,
I agree with almost everything you wrote. It’s a nice twist on Willis’s thought experiment thought it makes a rather different point since in this case the reason why there is no surface warming from a greenhouse effect, or any other cause, is because there is no Sun — no source of low entropy (shortwave) radiation; and everything has achieved thermal equilibrium with the background radiation of space.
“All that would remain would be brownian motion, which is the only thing that would prevent the atmosphere from stratifying according to molecular weight”
There would still be some stratification since Brownian particles and molecules alike have vertical density distributions according to mass at thermodynamic equilibrium.
See figure 4 (and associated discussion) as well as section C in the following paper:
Berberan-Santos, Bodunov, Pogliani, ‘On the Barometric Formula’, Am. J. of Physics, 1997.
http://web.ist.utl.pt/ist12219/data/43.pdf
…In our out of equilibrium troposphere it isn’t molecular diffusion but rather convective mixing that prevents the aforementioned partial stratification of molecules according to molecular mass.
The stratification can also be seen with this online 2D simulator (not the same one that I linked to earlier). For best visualization, reduce the number of balls to 50, increase both gravity and temperature to the max, and chose three different masses, with uniform sizes in order not to introduce a confounding factor. (Blue balls are lightest, and red ones are heaviest.)
Pierre-Normand,
thank you for the link, also interesting history,
and you are correct, I hadn’t considered quite to infinity.
That’s even worse than I thought!
KenW, “Now that I’ve poked my nose into this ants nest, I’ll take my statement a bit further.” Then “I hadn’t considered it quite to infinity.”
The ant’s nest is the nature of the problem. If you assume that a certain state is “equilibrium” then it turns out that isn’t really equilibrium, it appears that work was done in the process of moving toward a “real” equilibrium. Since equilibrium is a concept, not a reality, how you frame the experiment determines the results.
If you assume that all gases will be equally well mixed in the volume and the temperature is perfectly isothermal, gravity would tend to separate molecules by weight so that the bottom is more well mixed than the top. Your experiment failed. Now you have to change your concept of equilibrium.
The problem was originally posed over the definition of entropy. Boltzmann’s H-theorem defined a maximum entropy using ideal perfectly hard round balls without real consideration of gravity, so his entropy and therefore equilibrium are only accurate for near ideal cases. The less “ideal” an experiment you design the greater the violation of the 2 law can appear. So if you use the kinetic definition of temperature, you can find a temperature gradient. There is no “real” difference in energy between altitudes other that gravity which is external to the system. when you use an ideal column of air to perform your calculations on.
If you pose a spherical planet, now the “most” of force of gravity is internal to the system. So if you pose a rock core instead of an all gas planet you will find a different equilibrium IF you use Boltzmann’s H-theorem, which does not consider the interaction of the individual molecules.
That was all the problem was intended to do, make ya think. So no matter what “proof” someone comes up with, you can continue to pick nits until some “real” truth appears to fit every conceivable case.
Right now Gibbs Entropy appears to be a better “truth”. There would be some density gradient depending on the mixture in the volume and the total force of gravity “felt” at each point in the volume. Because of the 2nd law, no experiment would have runaway heating or cooling if the system is in a real equilibrium state which should take an infinite amount of time to be realized. In the real world there is always some dissipation until you reach some point where gravity ultimately wins and starts sucking everything back together. At that point physics will have a brand new set of observations to describe.
So you can continue to defend your concepts of entropy and equilibrium or bite the bullet and consider non-equilibrium thermodynamics which allows various concepts of entropy. On the whole, physics is close enough for government work if you aren’t into tiny nits.
Captian Sir,
my point was that Willis went out of his way to provide his model planet with a non-radiative atmosphere and his sky with a very low temperature, I felt this wasn’t necessary because his sky is uniform. If his planet exists long enough, even the rocks will stratify.
Good evening to you, Ken
There won’t be an atmosphere on your rocky planet, Willis. Even helium is a liquid at 3K.
Yeah, you’re right, David … so make it a rocky planet with a natural nuclear reaction at the core that keeps the surface at 15°C. Then add an atmosphere without any GHGs. The principle is identical, as is the result—gravity cannot heat the surface with a non-GHG atmosphere, because then the surface would be radiating more heat than it gets from the core. This, of course, violates conservation of energy.
w.
Conduction would heat the atmosphere with energy unable to be dissipated to space radiatively. Is that 2 silly little thought experiments in a row from Willis?
Along with agreeing with FOMBS about not getting stellar temperatures in centrifuges. Yeah – you don’t.
Thanks. The surface gas would be 15C but does not follow there isn’t a lapse rate so upper atmosphere is less.
Willis you seem to be under the mistaken impression that gravito-thermal effect makes the surface warmer than it would be without gravity. That is not true. The mechanical energy is 100% kinetic at the surface and the temperature the same as if there were no gravitation confinement.
Understand the question before answering please.
Would the theoretical planet with an atmosphere now have an ERL which would be seen to be radiating 3 watts out. This would be at some height above the surface which would have a higher temperature than the ERL unless the theoretical planet has no lapse rate.
That Mr. Eschenbach’s and Dr. Brown’s proofs are invalid is explained here: http://wattsupwiththat.com/2014/08/18/monday-mirthiness-spot-the-troll/#comment-1711550.
Joe, I’ve just given a very simple proof above. Perhaps you can explain where it is wrong.
Thanks,
w.
Mea culpa. In light of the Coombes-Laue discussions and Dr. Brown’s post which was directed to the zero-lapse-rate proof, I didn’t read further. It is the proof of a zero equilibrium lapse rate that I object to.
No, I see nothing wrong with the proof that a transparent gas blanket won’t warm the planet.
Yes, Willis’s reference to Brown’s proof was misleading. I hadn’t paid attention to that link. (Unless Brown also has a proof similar to this one?)
I can and did explain a few comments above this one.
Joe Born, that’s not the same proof. What Willis talks about here isn’t the lapse rate, but rather the surface temperature, whatever the lapse rate may be.
I have argued with Joe Born on his claim at SoD. That’s a point about the properties of perfectly isolated systems of finite number of molecules. The effect disappears, when the system is allowed to interact with the rest of the world. Any measurement performed on the system introduces so much interaction that nothing can be observed even in principle. It’s also impossible to create such an isolation, because that requires exactly zero energy transfer with the walls that enclose the system. We are discussing here effects that are changed by a single molecular collision with external world.
“The effect disappears, when the system is allowed to interact with the rest of the world. Any measurement performed on the system introduces so much interaction that nothing can be observed even in principle.”
I’ve never contended that the effect would be great enough to measure. But it will take more than Dr, Pirilä’s mere assertion for me to accept that the (admittedly immeasurable) effect that according to Velasco et al. does prevail will disappear suddenly when some interaction, however slight, is permitted. While it is true that the absolute isolation on which the microcanonical ensemble is based is not encountered in real life, neither is it true that the infinite-heat-capacity heat bath on which the canonical ensemble is based encountered in real life. Therefore, the exactly zero kinetic-energy gradient isn’t either. In any event we’re talking about ideal cases, not what we see in the world around us.
Consider two identical initially isolating containers of the same-molecular-weight ideal monatomic gas. The containers extend infinitely high in a uniform gravitational field. One of them has twice as much gas as the other. Velasco et al. says that the first should have a lower, but non-zero, kinetic-energy gradient than the second.
Now couple the two containers thermally, say at two different altitudes, without allowing the amounts of gas in either container to change. Will the interaction–which, notice, now permits a variation in each gas column’s total energy and therefore makes its possible microstates no longer constitute a microcanonical ensemble–cause either gas column’s kinetic-energy gradient suddenly to drop to zero?
Dr, Pirilä never seems to give me a straight answer to this. I say the answer is no, and I say that Roman, White, and Velasco demonstrate that it’s no. I don’t see how Dr, Pirilä’s quote above is correct if Roman et al. are right.
Joe Born wrote: “Now couple the two containers thermally, say at two different altitudes, without allowing the amounts of gas in either container to change. Will the interaction–which, notice, now permits a variation in each gas column’s total energy and therefore makes its possible microstates no longer constitute a microcanonical ensemble–cause either gas column’s kinetic-energy gradient suddenly to drop to zero?”
The (grand) canonical, or microcanonical ensembles represent the sets of microstates that are accessible to the non-isolated (in equilibrium with a thermal bath), or fully isolated systems, respectively. The statistical properties of those sets are relevant to the probabilities of finding the system, at any given time, to occupy some subset of those accessible microstates. Temperature not only is a macrostate, is also is an ensemble property rather than a microstate represented by a small cell in phase-space. So, yes, when the two columns are put in thermal contact and aren’t isolated anymore, then whatever ensemble property you may wish to call ‘temperature’ immediately changes since the set of accessible microstates to both systems immediately changes.
Pierre-Normand: “So, yes, when the two columns are put in thermal contact and aren’t isolated anymore, then whatever ensemble property you may wish to call ‘temperature’ immediately changes since the set of accessible microstates to both systems immediately changes.”
While I’m not sure, I think I agree with this, but it depends on which definition of temperature you use. Perhaps muddied the water by gratuitously using “suddenly.” But the point I was intending to make was instead that the mean-molecular-kinetic-energy gradient–whether or not it would change “suddenly”–would not fall all the way to zero.
Of course, even in the context of ideal monatomic gases there are definitions of temperature that differ from mean molecular kinetic energy. But in Dr. Brown’s proof, in which he assumes a non-zero equilibrium lapse rate–and therefore different temperatures at different altitudes–that’s the only definition that is consistent with his initial assumption. Under the thermodynamic definition, equilibrium by definition means no lapse rate, and, as you say, the statistical-mechanics definition makes temperature an ensemble property that it is conceptually difficult to assign to different values for different altitudes of the single molecule set that the macrostate characterizes.
“the surface of the planet would warm, and stay warmer than it was with no atmosphere.”
It clearly does.
“But at that point, the surface of the planet would constantly be radiating more energy than it is receiving … which is an obvious physical impossibility.”
At that point the surface radiates 255K to space but the other 33K is locked into convective adiabatic overturning whereby conductive ascent takes heat from the surface exactly as fast as convective descent returns it to the surface so that the surface cannot radiate to space at more than 255K
Stephen Wilde,
The emission power from a surface only is a function of its temperature and emissivity. You can’t reduce it through allowing the surface to conduct heat away (or though latent heat release). If it’s allowed to conduct heat away, then it will just lose heat at an even higher rate. If this weren’t the case, one would think it would have been observed in the laboratory already.
The emission power at the surface remains at 288K (for Earth). It is just that it can only radiate to space at 255K because the surface is exchanging energy with the atmosphere at the same time.
During the very first convective cycle the surface does indeed lose energy at a faster rate than 255K because as well as trying to radiate to space at 255K it loses energy into the developing convective cycle.
Thus, during that first convective cycle surface temperature temporarily dipped below 255K
When the first convective cycle completed then radiation to space recovered back to 255K but the other 33K remained locked into the continuing convective overturning.
And there it will remain as long as mass, gravity and insolation remain constant.
Pierre-Normand, December 1, 2014 at 12:23 pm:
“The emission power from a surface only is a function of its temperature and emissivity. You can’t reduce it through allowing the surface to conduct heat away (or though latent heat release). If it’s allowed to conduct heat away, then it will just lose heat at an even higher rate. If this weren’t the case, one would think it would have been observed in the laboratory already.”
It should be a pretty obvious fact, almost to the point of being intuitive, that a body of water struck with the first round of a solar SW flux and thus heated to depth by it, will not be able to also shed this particular amount of energy within a similar period of time by radiating (LWIR) back out from its surface. Why? Because the energy coming in as SW is absorbed across the three dimensions of the volume of water, but the energy going back out as LW is only emitted from the two-dimensional surface.
The SW flux is after all not instantly able to warm the body of water up to the point where its surface temperature correlates to a LW emission flux equal to the originally absorbed SW one.
In a hypothetical, purely radiative setting, this would pose no problem. The system would simply move towards a steady state (dynamic equilibrium), by incoming (SW) energy gradually accumulating inside the volume, until the point where the surface temperature did finally reach exactly that level. At this point, the incoming and outgoing radiative fluxes would match and there would be no more warming.
(This is how normal, real-world objects warm, after all, by energy gradually accumulating inside them (internal energy, U, growing), fast at first, then progressively slower up to the point of balance between heat (Q) IN and heat OUT. Then the increase in U, and in T, stops.)
On our planet, however, there’s an atmosphere on top of the solar-heated body of water, and the ocean releases most of its absorbed energy back out into this atmosphere by way of evaporation to stay in balance with its incoming from the Sun.
This means that on real Earth, the water surface will reach its steady state temperature long before radiative balance has been accomplished, i.e. as much energy is released from the surface as taken up by the volume of water per unit of time even at much lower temperatures than the ideal Stefan-Boltzmann blackbody situation would seem to demand. Courtesy of the release of latent heat through evaporation.
So yes, it would seem that putting an atmosphere on top of a water surface would enable it to reach its heat IN/OUT balance point at a lower steady state temperature than without such an atmosphere. This, however, is not because the evaporative loss comes IN ADDITION TO the radiative loss. It is because it comes INSTEAD OF a large part of the previous radiative loss.
You see, emissive power from a surface is only a function of its temperature and emissivity alone if that surface happens to be a pure/ideal emitter, that is, its entire heat loss comes via radiation, meaning it’s isolated in a vacuum at 0 K or simply very much hotter than its surroundings. There is nothing in the Stefan-Boltzmann equation suggesting otherwise. The S-B law applies only to purely radiative situations. Just like Planck’s and Kirchhoff’s laws do. The idea that it applies no matter what has no empirical basis and it ignores simple energy budgetting principles.
“putting an atmosphere on top of a water surface would enable it to reach its heat IN/OUT balance point at a lower steady state temperature than without such an atmosphere.”
The heavier an atmosphere the warmer the water has to become to supply the necessary latent heat of vaporisation to fuel evaporation.
The amount of energy required to effect the phase change is pressure related. If there were zero atmospheric pressure the oceans would evaporate instantly, freeze and fall to the ground as a solid.
Stephen,
Indeed. But first we have to get Pierre-Normand and his kind to understand that radiation is not some divine entity that operates completely independent from all other physical processes in this universe, like for instance other heat loss mechanisms for a warm object (radiation is, after all, simply one of several heat loss mechanisms).
“Indeed. But first we have to get Pierre-Normand and his kind to understand that radiation is not some divine entity that operates completely independent from all other physical processes in this universe […]”
This claim is to vague for me to either endorse or disown. My claim simply is that a solid surface emits the same gross radiant power, as a function of its temperature only (and emissivity), and this power is unaffected by the rate of conduction with a gas it is in thermal contact with. Why would the mere existence of the nearby gas molecules changes the rate of emission of the surface?
The rate of conduction just relates to the probabilities that some molecules at the surface will exchange various amounts of energy in random collisions with gas molecules. If the gas is warmer than the surface, then individual collisions are more likely to transfer energy from the gas to the surface, and conversely. In between the collisions, the molecules of the surface emit photons with some probabilities dictated by temperature only. Before some molecules at the surface will emit a photon, they don’t care at all how likely they are to either lose or gain some energy in the future from incoming gas molecules. This is basically why the rates of the two processes, conduction and radiation, are independent. (Though the interactions of the gas with the surface may have a small effect of the surface emissivity, but that’s something else.)
“may have a small effect [on]… “
Pierre-Normand,
So you of course chose to not read my main comment, just two stops up from the one you replied to.
I’ll quote from it:
“You see, emissive power from a surface is only a function of its temperature and emissivity alone if that surface happens to be a pure/ideal emitter, that is, its entire heat loss comes via radiation, meaning it’s isolated in a vacuum at 0 K or simply very much hotter than its surroundings. There is nothing in the Stefan-Boltzmann equation suggesting otherwise. The S-B law applies only to purely radiative situations. Just like Planck’s and Kirchhoff’s laws do. The idea that it applies no matter what has no empirical basis and it ignores simple energy budgetting principles.”
You repeat:
“My claim simply is that a solid surface emits the same gross radiant power, as a function of its temperature only (and emissivity), and this power is unaffected by the rate of conduction with a gas it is in thermal contact with.”
No, Pierre-Normand. This is just the flawed idea that has been allowed for too long to disseminate among the rGHE believers of this world. It only constitutes a fact in a purely radiative setting. All these laws are originally and fundamentally made for (and thus apply to) a radiation only scenario.
Beyond that world, you need to start accounting for you energy gains and losses. You can’t just add whatever suits you. You need to have the energy available. This is the domain of THERMODYNAMICS.
Niels Bohr once said, and pay close attention to this, Pierre-Normand, all the old guys knew this (Planck too), they had no illusions about being able to actually observe directly what they described:
“There is no quantum world. There is only an abstract quantum physical description. It is wrong to think that the task of physics is to find out how nature is. Physics concerns what we can say about nature …”
We only ever detect the HEAT moving between two objects in heat transfer (that is, at different temperatures), that’s the actual TRANSFER of energy across the radiation field between them. The whole principle of a two-stream photon exchange between the two objects is just that … a principle, a model, a theoretically based assumption of how things might work. Such a two-stream photon exchange in a heat transfer has NEVER experimentally been observed. It CANNOT physically be observed, you cannot detect two separate fluxes moving in opposite directions inside one continuous, integrated radiation field. All that nature reveals to us is the heat, the actual transfer of energy through that field. Which CAN be detected. Because it is actually able to affect the two bodies directly, something we can measure, a physical change, in their internal energy (U) and thus their temperature (T).
“Why would the mere existence of the nearby gas molecules changes the rate of emission of the surface?”
Enter thermodynamics. You need to account for your energy gains and losses, Pierre-Normand. Not just assume that your radiative law remains untouched and independent no matter what happens. When the surrounding conditions change, physical relationships change too. Other laws and processes come into play.
An object just seeks (dynamic) equilibrium with its surroundings. Radiation is no more than a method of attaining such balance. It is a heat loss mechanism. Pure and simple. It is there to balance the heat gain. This is thermodynamics at its most fundamental level.
If a no-atmo BB planet in space after equilibration with its heat source gets 2 parts IN and emits 2 parts OUT, all as radiative heat, then if we surround it with an atmosphere and keep the heat input from the source constant, then after new equilibration, the heat IN to the surface will still be 2 parts and the heat OUT from the surface will still be 2 parts, only now there is 1 part escaping through conduction > convection and 1 part escaping through radiation. The surface at any one time only absorbs 2 parts of heat from the heat source, meaning that it always has 2 parts only of heat to shed. If 1 of these parts go out through conduction > convection, there is only 1 part left to radiate. And this is regardless of the new steady state surface temperature.
The mean global surface of the Earth gains 165 W/m^2 worth of radiative HEAT from the Sun, its only source of energy (except geothermal). This flux is balanced by the total heat OUT, which is made up of 53 W/m^2 of radiative heat and 112 W/m^2 of conductive/evaporative heat. 165 W/m^2 IN, 165 W/m^2 OUT. Still, the surface temperature is 289K.
The postulated 398 W/m^2 radiative flux postulated to leave the surface is a mere mathematically derived temperature POTENTIAL. Based directly on the surface temperature (289K). It has never been separately detected. It cannot physically be separately detected. Only the HEAT flux can ever be detected. The 398 W/m^2 would be the radiative HEAT flux from a BB surface radiating into a vacuum at 0 K. It is NOT a real flux. It is a temperature potential, a temperature potential facing some air temperature potential, generating in between them a spontaneous radiative HEAT flux from warmer to cooler, up from sfc, towards atm. If the air warms without the surface doing the same, the difference in temperature potentials is reduced and the heat flux from the surface up is consequently reduced as well.
P/A = es(T_sfc^4 – T_atm^4)
P/A is the only actual radiative flux involved here, the heat transfer. The righthand side of the equation simply shows the temperature POTENTIALS facing each other. These potentials would constitute real radiative heat fluxes only if the two bodies were isolated from each other and surrounded by perfect vacuums at 0 K.
Too many people look at this formula thinking that they see two physically opposing thermodynamic fluxes (transfers) of energy. That concept is only mathematically derived. In reality, in the real physical world, there is but one flux, one transfer of energy, and in a spontaneous heat transfer situation, it always and only moves from hot to cold.
This is what Bohr was pointing to. The only thing we KNOW is the heat and the temperatures. The quantum explanation behind is pure speculation, simplistic models of reality in an attempt to make some sense of it.
“So you of course chose to not read my main comment, just two stops up from the one you replied to.”
I can’t always reply to all the posts that are addressed to me.
Sure. No one can force you not to cherry-pick your responses. It just speaks volumes when you do …
Gentleman here is Kristian at his best.
” I took for granted that it was empirically shown (out there in the real earth system) how more CO2 in the atmosphere will and does in fact help to warm the surface, and that the reason we are able to even live on this planet at all is because of an ‘Atmospheric Radiative GreenHouse Effect’ (rGHE) where so-called ‘GreenHouse Gases (GHGs)’ – like CO2 – make it so that some of the energy that leaves the surface of the earth never manages to escape the system as a whole to space, but is rather ‘recycled’ internally between atmosphere and surface, creating ‘extra’ atmospherically induced warming of the surface on top of the original solar warming.”
When he starts from a mistaken view of the greenhouse effect, as Kristian does, there is no point talking to him.
The same parcel of kinetic energy at the surface cannot both radiate to space and hold the atmosphere up against gravity simultaneously.
If it radiates to space it cannot replenish the PE reservoir in the atmosphere and if it is replenishing that reservoir it cannot be radiating to space.
Stephen Wilde,
Sure. Your first sentence is true. Which is why a surface that is allowed both to conduct heat away and radiate to space will cool faster than a surface that only is allowed to cool radiatively. Still, the radiating power only is a function of temperature. It not an either/or proposition. When it does both, then it cools faster.
“When it does both, then it cools faster”
Not once the first convective cycle has completed it doesn’t because the energy going into conduction on the ascent is from then on being returned on the descent for a net zero thermal effect.
In that scenario you get back to the original rate of surface cooling to space (255K) but in addidtion you have that separate net zero energy exchange in the adiabatic convective loop which holds up the atmosphere against gravity for as long as the sun keeps shining.
A non-radiating atmosphere would not be able to lose heat to space, which means it would eventually come into thermal equilibrium with the surface – at which point the surface would no longer lose net heat to it by conduction.
phatboy,
The atmosphere can never come into equilibrium even without GHGs.
In the vertical plane an atmosphere is always in thermodynamic DISequilibrium (with or without GHGs) due to work done against gravity in holding the mass of the atmosphere off the surface converting KE to PE to produce an inevitable lapse rate even in a GHG free atmosphere.
For a GHG free atmosphere all radiation to space would indeed have to be from the surface but the surface for Earth would still need to be at 288K to get 255K out to space due to conduction and convection enabling the mass of the atmosphere to obstruct the free flow of radiation to space.
The ERL would still be at the height where the temperature is 255K i.e. some distance off the surface and not at the surface.
You can only have 255K at the surface if there is no atmosphere at all.
Mass not radiative capability creates the greenhouse effect.
There is also a lot of confusion about the connection between the greenhouse effect and the lapse rate. You cannot have one without the other.
Gravity merely sets the scale of the adiabatic lapse rate in a planetary atmosphere. It does not ‘generate’ a lapse rate through barometric pressure or some other magic. Heat needs to flow through the atmosphere to maintain convection. That is the role of greenhouse gases. Radiative transfer from the surface causes a temperature gradient steepening towards radiative equilibrium. Convection (and evaporation) are then ‘powered’ to limit the temperature gradient to the Dry/Moist adiabatic lapse rate.
Now imagine that you could somehow switch off gravity while keeping an atmosphere of pure CO2 held to the surface by some membrane or other. There would be no greenhouse effect at all! The temperature of the CO2 atmosphere would thermalize to Tsurf and an equal flux of radiation would be emitted to space from the top of the atmosphere as was absorbed at the bottom.
http://clivebest.com/blog/?p=6305
Clivebest, Fully agreed.
clivebest | December 1, 2014 at 12:24 pm | Reply
Actually, they have nothing to do with each other. You don’t even need an atmosphere at all to have a greenhouse effect. See my posts The Steel Greenhouse and People Living In Glass Planets for an explanation.
Regards to all,
w.
Willis,
In a sense your examples have something equivalent to lapse rate in form of a radiating layer at a lower temperature than the surface.
That’s part of the point of radiative GHE: A layer of lower temperature absorbs IR coming from below and emits less upwards, because it has the lower temperature.
The second part of the argument explains, why the temperature of the outer layer is lower than that of the surface.
My above sentences can be applied both to your examples and to the atmosphere.
Willis,
Both your examples generate a ‘lapse rate’ although with just 2 data points.
The fully transparent IR shell corresponds to the case of an atmosphere without greenhouse gases – say 100% N2 or argon.
Clivebest,
“Now imagine that you could somehow switch off gravity while keeping an atmosphere of pure CO2 held to the surface by some membrane or other. There would be no greenhouse effect at all!”
There is a heat flux from the surface passing through the atmosphere until full dissipation. Heat flux mean gradient. And thus a higher surface temperatrue than at your upper atmosphere. Gravity is not necessary to have a greenhouse effect.
Phi,
There is an equal and opposite radiative flux throughout a 100% CO2 atmosphere without any gravity. There can be no temperature gradient because there can be no lapse rate. Convection is meaningless. Exactly the same number of 15 micron photons are absorbed at the bottom of the atmosphere as will be emitted from the top of the atmosphere to space.
I think this fact should be more widely known.
CO2, per se, cannot warm anything at all. Lab experiments purporting to explain global warming by placing some beaker of CO2 in front of a furnace have absolutely nothing to do with the greenhouse effect on earth and are mostly junk.
Clivebest,
“There is an equal and opposite radiative flux throughout a 100% CO2 atmosphere without any gravity.”
Why is that? There is only one IR flux, it goes from the warm source (the surface) to the cold source (space).
“There can be no temperature gradient because there can be no lapse rate”
The temperature gradient is related to heat flux, not to gravity.
“Convection is meaningless.”
There is no convection and thus the heating effect of CO2 is even more important.
“Exactly the same number of 15 micron photons are absorbed at the bottom of the atmosphere as will be emitted from the top of the atmosphere to space.”
1. You must not limit to the center frequency.
2. The photon model is not suitable for thermodynamic reasoning.
3. The 15 micron frequency is practically saturated in your example, there is virtually no thermal effect on that wavelength throughout the thickness of the atmosphere. By cons, 15 microns emits very efficiently into space at the top.
In the hypothetical case of CO2 held to a surface without and gravity, I see the atmosphere as being an integral part of the surface. There is no pressure gradient and acts like a perfect gas. It has to be isothermal in the same way as sand on a beach is isothermal.
Clivebest,
The sand will be isothermal only if there is no heat flow therethrough. Your atmosphere without gravity is cooled at the top by IR emission and heated from below by conduction and radiation. Thus, there is a thermal flow from bottom to top and thus a temperature gradient.
It is also heated from below by radiation (absorbed 15 micron photons). There can be no lapse rate because the CO2 gas must reach thermal equilibrium in all 3 spatial directions.
Clive,
Without gravity the atmosphere would act essentially as a layer of solid insulator on top of a heated surface and cooled from the upper surface. There’s no reason to assume that it would be isothermal. The density differences between the warmer parts and the cooler parts would not induce convection in absence of gravity.
Pekka,
yes but it’s not a solid. The molecules are moving at an average speed of over 500 m/s and will rapidly thermalize to a constant temperature throughout the bulk of the atmosphere. Radiation will escape to space from a skin layer at the top exactly balancing the absorbed skin radiation at the bottom while 90% of surface radiation passes straight through the atmosphere to space.
I admit that the top skin layer will not be in perfect thermal equilibrium so there could be a very small greenhouse effect.
Clive,
Both solid insulators and gas conduct heat, but heat conduction is a not an efficient way of heat transfer in gas. We know that it can be ignored relative to both convection and radiative heat transfer in most applications. In your example no convection is present, because nothing will initiate convection in absence of gravity, but the relationship between radiative heat transfer and conduction remains unchanged, i.e. conduction can be ignored, when gases like CO2 are present.
“The molecules are moving at an average speed of over 500 m/s and will rapidly thermalize to a constant temperature throughout the bulk of the atmosphere.”
The relation between heat transfer in a gas (or liquid) and molecular speed distribution is quite indirect. If there is no convection, and no radiative heat transfer, then there remains only conduction. And the heat conductivity of air is extremely low, as you must know, contrary to naive expectation from high average molecular speed.
…[thermal] conductivity…
Build a sphere of 9 billion miles in diameter with its temperature set at 4K, incorporating a gravity neutralizer, that gets rid of all the gravity within the sphere. Add 2×10^30 Kg of 4He, at 4K, and allow the gas to come to thermal equilibrium within the large flask. When at equilibrium and when the gas is equally dense throughout the flask switch the gravity neutralizer off.
The gas will become attracted to the center of the container and form a very hot body. The body will radiate the same amount of energy as the inward radiation from the vessels walls, however, the vessel has a much greater surface area than the solid/liquid/gas spherical body in the center.
DocMartyn,
But the internal surface of the isolating vessel ought to have the same temperature as the spherical body, at equilibrium, and so, if both are black-bodies, we have a paradox, right?
I think the solution of the paradox (if I understood your puzzle correctly) simply is that, though the internal surface of the vessel emits with the same power (per unit surface), most of the radiation that it emits misses the core and falls back unto other internal areas of the vessel. If it emits as a Lambertian radiator, as a black-body should, then everything will appear at the same brightness at any point withing the vessel, either from some vantage point on the internal surface of the vessel, or from the surface of the spherical body.
No Paradox.
The matter inside the sphere is in equilibrium when gravity is switched on and when switched off.
In one case we have a dispersed gas and in the other we have a hot, dense mass.
In one case there is a thermal gradient and in the other there isn’t.
You can do P=TV when gravity is switched off and get the same numbers, but not when switched on.
DocMartyn, then I don’t understand the point of the thought experiment. After gravity is switched on, there is a collapse and gravitational potential energy is converted to internal energy during the collapse. Things heat up withing the collapsing body. The initial equilibrium is lost for a while until the inside surface of the container will warm up to the same temperature. (I had imagined it as a black-body with an external adiabatic coating.)
P-N. After a few million yours you will have a hot body in the center in dynamic equilibrium with the flask.
The system will have extreme temperature and pressure gradients, when gravity is switched on.
And then there is also Miskolczy’s theory which states that the effect of increasing co2 on the radiative imbalance is counteracted by a decrease in water vapour so that there is no net radiative warming effect.
Hans
I thought Miskolczy had made a substantial mathematical error in his complex calculations which some say has invalidated his theory? Also that it has been pointed out to him but he has not responded?
tonyb
off topic
Steven Mosher: off topic
Golly! I’ll bet that smarts.
This topic is so endlessly silly – even Miskolczy is a welcome distraction.
A radiatively inert atmosphere must still have a reducing temperature with height even without GHGs simply because the work done against gravity during convective uplift converts KE to PE and PE is not heat and cannot radiate.
Then all one needs to initiate convective overturning is uneven surface heating which places parcels of air of different densities next to one another in the horizontal plane. Uneven surface heating is inevitable for a rotating sphere.
So there is never going to be an isothermal atmosphere even without GHGs.
The examples that purport to show that an isothermal atmosphere will develop all rely on a thermal equilibrium being attainable. In reality it can never be attained because of that conversion of KE to PE with height.
In the vertical plane the atmosphere around a planet will never be in equilibrium so all those examples are invalid.
There will always be convective overturning and a lapse rate.
There will always need to be an additional kinetic energy store at the surface to sustain the ongoing convective overturning and that requires a surface temperature enhancement above S-B.
“A radiatively inert atmosphere must still have a reducing temperature with height even without GHGs simply because the work done against gravity during convective uplift converts KE to PE and PE is not heat and cannot radiate.”
___
Yep.
Quite relevant to this discussion, the formation of early atmosphered around planets, where the gravity of the planet determines the ultimate size of the atmosphere. Interesting charts on this site related to atmospheric pressure/temperature curves that many should find quite enlightening:
http://astro.berkeley.edu/~ormel/science.html
Temperature gradients due to Gravity
For the impact of gravity on conduction (WITHOUT convection OR Solar radiation etc.) see the experiments and theory developed by Roderich W. Graeff.
Viewing The Controversy Loschmidt –Boltzmann/ Maxwell Through Macroscopic Measurements Of The Temperature Gradients In Vertical Columns Of Water Roderich W. Graeff
Version: Descript 372_dec6 December 9, 2007
At FirstGravityMachine
The Production of Electricity out of a Heat Bath
RODERICH W. GRAEFF , AIP Conf. Proc. 1411, 193 (2011); http://dx.doi.org/10.1063/1.3665239
Graeff is a rare case as he thinks that his experiment proves that a perpetum mobile of second kind can be used to produce work. That’s contrary to most of those, who argue for a heat gradient in equilibrium, and think that such a situation is consistent with the Second Law and that it doesn’t make perpetum mobiles of the second kind possible.
Both Graeff and those others are wrong. Graeff’s experiments are far too crude to tell anything about the real phenomena. His results are surely only empirical errors.
Pekka
Graeff’s “engine” is insignificant power wise. However I encourage you to review Graeff’s experimental data and show where they are off. I see how they could be improved 10x or more, but the base case with no circulation looks interesting.
The most important reason that makes the experiment extremely difficult is that the mechanism that brings the system to the isothermal state according to standard physics is conduction. Conduction in gas is a really weak process, but the experiment tells nothing unless all other heat fluxes combined are guaranteed to be weaker than internal conduction in the gas volume. Very weak heating or cooling of the walls of the enclosure are likely to lead to larger heat fluxes and to convective flows that produce the lapse rate inside the volume.
For an experiment to have any value it must be shown by reliable measurements and calculations that no external influence affects the outcome. I have looked at the papers of Graeff and found that he does not present such analysis. I have also observed that he has not done the experiment with such care that there were a change that he ends up with valid measurements.
This is a deceptive experiment. Most errors in the execution of the experiment lead towards the same wrong result. Only extremely careful work has any change of avoiding on error of that type. He is looking at an issue, where the standard physical understanding predicts that he finds a “confirmation” of his “theory” even when he is wrong, because he is unlikely able to avoid conductive fluxes inside his apparatus.
FOMD’s Self-Evaluation Test of
Thermodynamic and Heat-Transport Intuition
Your spouse gives you a vacuum-flask thermos in which boiling-hot tea loses temperature at an initial rate of 20 C per hour.
http://upload.wikimedia.org/wikipedia/commons/c/c4/Vacuum_flask_diagram.png
As an experiment, you dismantle the thermos, and pack the vacuum-space with thin aluminized mylar, then reassemble the thermos (finishing by pumping a fresh vacuum).
Question The modified thermos will show:
(1) much faster heat-loss
(2) about the same heat-loss
(3) much slower heat loss
Answer the question with both a closed-form mathematical analysis and references to the engineering literature; include a quantitive description of the effects of aluminizing the mylar, and of the significance (or not) of the thickness of the mylar. How good does the vacuum need to be, in order to reach the point of diminishing returns?
http://upload.wikimedia.org/wikipedia/commons/thumb/0/08/Huygens_thermal_multilayer_insulation.jpg/800px-Huygens_thermal_multilayer_insulation.jpg
Self-assessment People who firmly believe that they understand the basic principles of thermodynamics and energy transport, and yet can’t answer the test question (or answer it incorrectly), and/or are entirely ignorant of the engineering literature, are displaying Dunning-Kruger cognition!
Follow-on “thermos” self-evaluation questions
(2)Blackened mylar: does it insulate better than aluminized mylar? Does it insulate better than no mylar all?
(3)Infrared-absorbing, optically transparent plastic film: does it insulate at all?
Note By design, option (3) has similar radiation and heat-transport properties to a non-advective CO2/H20/CH4-laden atmosphere!
Conclusion Yes Virginia, there is a CO2-driven greenhouse effect!
WAG, just for fun, from a not-so-confident idiot: if “packing” implies thermal contact then it will lose heat faster due to conduction.
Why use a vacuum?
Why not use CO2 to reflect the IR back into the thermos?
FOMBS was armwaving about the symplectic manifold of the Hamiltonian – somehow in connection to a Wikipedia cartoon of a box of ideal gas molecules. A fantastic and improbable juxtaposition with the symplectic manifold seeming to have only a symbolic significance. A talisman of cargo cult science.
For my sins – I introduced the Fronsdal paper as an example of a Hamiltonian of the atmosphere – that – intriguingly – suggested a gravito-thermal effect.
Rob, “For my sins – I introduced the Fronsdal paper as an example of a Hamiltonian of the atmosphere – that – intriguingly – suggested a gravito-thermal effect.”
Yep, it is all your fault.
Confident ignorance by Rob Ellison, well-regarded dynamics textbook by the celebrated mathematician Vladimir Arnold!
http://scientificrussia.ru/data/auto/material/big-preview-on_vladimir_arnold.jpg
JC SNIP
FOMBS use of the symplectic manifold is symbolic. As is the vague arm waving toward arbitrary bits of science and maths that he has little understanding of. A symplectic manifold simply says that the Hamiltonian is differentiable. But there is no sense in which FOMBS uses it in for any concrete purpose – merely arm waving about a ‘well-regarded dynamics textbook by the celebrated mathematician Vladimir Arnold!’ whose only purpose is a symbolic one of demonstrating a ‘confident ignorance’ of deniers. FOMBS cargo cult science – in which the symbol supplants the reality.
It’s not my fault – btw – and my banter – which a guy would understand was banter and not take it seriously – got snipped. It is getting way too politically correct around here.
Banter is fine, hitting them with the facts repetitively is better.
JC SNIP suggests the banter was disappearing and beyond a guy’s simple understanding.
Personally I think use of the symplectic manifold is better in a car magazine blog, because I don’t understand it while the two of you do.
Is there a simpler expression?
The banter was aimed at Capt. Dallas – and wouldn’t have been a problem.
The Hamiltonian is an extension of Newtonian dynamics using energy instead of force. The symplectic manifold is of interest as the solution space of the Hamiltonian.
http://arxiv.org/pdf/physics/0004029v1.pdf
FOMBS use of the jargon is a talisman intended to show how clever he is and how dumb deniers are. Does he even understand the words let alone the math? Over the time he has been here making this same symbolic use of scientific and mathematical talisman – there is little to show that he does. It seems all sham and bluster – and it seems far from an isolated case.
A rational person would wonder why.
Thanks Rob
A more productive lesson, Rob Ellison, is that climate-change skeptics who seek to remake the foundations of thermodynamics are well-advised to heed the sage advice of Landau and Lifshitz:
Conclusion Young researchers (especially) are well-advised to study thermodynamics the modern way … via the language of geometric dynamics … with particular care that every macroscopic thermodynamical assertion is solidly and explicitly grounded in statistical mechanics and (microscopic) Hamiltonian flows.
The scientific rewards of this program are *AWESOME* !!!
https://www.youtube.com/watch?v=RIW65QLWsjE
Best wishes are extended to you Rob Ellison, and to all Climate Etc readers, for continued enjoyment and success in appreciating thermodynamics and statistical mechanics and geometric dynamics the modern way: as one unified subject!
Is it true that this is like talking about balance sheets and income statements? Starting with Eschenbach’s example a 3 watts incoming planet. Adding any kind of gas at most delays radiation back to space. Any GHG effect is simply borrowing. It’s having a policy of holding all bills for two weeks before paying them so that we have short term cash or heat. Assume the gas has some vertical gas circulation. That’s not income. It is a transfer like from a money market to a checking account. In the end I think the books must balance. Beginning stuff plus changes equals ending stuff.
Yes, if you add GHGs they allow radiation to space from within the atmosphere which is earlier expenditure than if it were returned to the surface in convective descent before being radiated out to space.
Then the energy having been lost to space (spent) the convective descent returns less to the surface than was taken up in the ascent so there is net deficit (cooling).
But the convective overturning having been weakened the atmosphere contracts a little which increases density at the surface and that increased density picks up more energy from the surface (earned) and that balances the expenditure from GHGs.
But since it is all about mass in the first place you would never notice the variation caused by GHGs. It would disappear in the rounding.
‘It is important to ask to what extent the observed polytropic relations are to be attributed to the intrinsic properties of the gas or to radiation. Although the question is somewhat academic, since it does not directly affect the main applications, it is natural to ask: what are the natural configurations of an isolated atmosphere, one that is not exposed to radiation? Our understanding of atmospheres will not be complete without an answer to this question.
The statement that any two thermodynamic systems, each in a state of equilibrium with a well defined temperature, and in thermal equilibrium with each other, must have the same temperature is a central tenet of thermodynamics. A natural generalization is that the temperature, in an extended, but closed system in a state of equilibrium, that must be uniform, and there is a wide spread opinion that this remains true in the presence of gravitational fields. This is important for the understanding of terrestrial and stellar atmospheres, where the gravitational forces create a non-uniform density distribution.’
http://www.mdpi.com/1099-4300/16/3/1515
So this is the question being investigated by Christian Frønsdal with his ‘action principle’. It is a very old question with very little in the way of convincing exposition either way. In a sense – it is merely academic. It may or not underlie radiation and convection processes in the real atmosphere – which are likely far more significant. Indeed as the original protagonists – Loschmidt and Boltzmann – concluded long ago.
I propose two corollaries:
1. That silly little thought experiments resolve nothing of any significance.
2. That it is hugely unnecessary to take a position on each and every point of contention. Science advances by observation and experiment – see proposition 1.
As we discussed with P-N in the previous thread his approach lacks exactly those mechanisms that lead to the correct isothermal solution. I cannot be absolutely certain that we found the correct reason for his strange results, but the explanation seems to be as follows.
His hydrodynamical equations (Euler’s equations) do not include viscosity. He doesn’t even mention the word in his paper. He does discuss thermal conduction at one point in the introductory discussion, but he does not include that in his theory, as far as I can see. Thus his theory lacks both dissipative mechanisms that are always present in real gases. Without dissipation he can maintain convection indefinitely long without any input of energy. His equations allow the non-equilibrium states persist for ever, and he cannot describe the approach to equilibrium. Therefore he gets wrong results.
Furthermore he proposes the centrifuge experiment using erroneous arguments that he just assumes without presenting any support for them beyond a few words that just state the wrong argument.
It’s a very long time since I used the Action Principle for anything. Thus I had to refresh my knowledge on that. A suitable source seems to be here
http://www.scholarpedia.org/article/Principle_of_least_action
One thing that we can learn from this presentation is that the Action Principle cannot be used for dissipative processes (with some exceptions). For that reason the principle is not at all suitable for the study of the thermodynamic equilibrium. It can describe only isentropic processes, but the approach to equilibrium is fundamentally not isentropic, but dependent on the rise of entropy towards its maximal value.
The alternatives suffer from a circularity of argument that is unconvincing at best. There is very little in the way of mathematical exposition or physical theory. There is little to distinguish it from symbolic logic.
There is certainly no notions of viscosity, convection or conduction in the alternatives – merely handwaving at fundamental principles. I rather fear that Pekka’s quibbles fall into the same trap. We have some maths that suggests that a gravito-thermal gradient exists in an isolated system under gravity – and Pekka arm waves about conduction and convection countering the effect to get the ‘true’ result of a uniform temperature. It is so far from proven as to be laughably unconvincing.
Here’s the experimental apparatus as visualised by Clive Best I presume.
http://clivebest.com/blog/wp-content/uploads/2012/09/loschmidt1.png
It relies only on the centrifuge simulating a large enough gravity to enable easy measurement of a temperature gradient. Seems simple enough.
http://ak0.picdn.net/shutterstock/videos/625078/preview/stock-footage-a-centrifuge-spins-vials-of-liquid-in-a-laboratory-test.jpg
These babies pull 70,000 “g’s” (and more!).
http://blog.lakos.com/Portals/56238/images/laboratory_centifuge.jpg
After a run, when you take out the fluid-filled tubes, their tops aren’t frozen and theirs bottoms aren’t hot … the tubes are the same temperature from top-to-bottom … precisely as orthodox thermodynamics predicts.
It’s a pleasure to increase your knowledge, Rob Ellison!
I would assume the bottom of the test tubes doesn’t heat up because the centrifuge spins them around like an air-cooled WW-I rotary engine on steroids. They will remain exactly at the ambient air temperature.
‘This experiment would be of moderate cost and well within the means of a university physics department. My personal opinion is that initially adiabatic compression will create a temperature gradient which then rapidly conducts through collisions to a single uniform temperature. Despite this, such an experiment is still worthwhile because it would resolve this dispute once and for all. Perhaps it has even already been done !’ http://clivebest.com/blog/?p=4101
The effect – if it exists – is consistent with conduction. For me this is just more arm waving around fundamental principles. Again – hardly conclusive but it is just framed as an opinion.
The predictions – consistent with Lochsmidt’s original calcualtions – assuming a gravito-thermal effect with a quite ill defined physical mechanism – is here. Although the right hand axis seems a bit odd.
http://clivebest.com/blog/wp-content/uploads/2012/09/Centrifuge.png
I presume that once the device is switched off
the gas quickly returns to it’s original state – hence the need for thermocouples to measure temp under the simulated gravity.
It is a pleasure to demonstrate what an utterly superficial bore FOMBS is.
fan of *MORE* discourse | December 1, 2014 at 6:07 pm |
Rob Ellison wonders about a “centrifuge simulating a large enough gravity to enable easy measurement of a temperature gradient.”
After a run, when you take out the fluid-filled tubes, their tops aren’t frozen and theirs bottoms aren’t hot.
Really??
Perhaps it is because they cool the whole darn system?
“The continuous cooling starts with each rotor standstill of the Centrifuge 5418 R in order to maintain the preselected nominal temperature of the rotor chamber not only during centrifugation”.
Details on frictional forces and heating in centrifuge tubes are very hard to find with a google search. Perhaps someone or Fan himself could quote the relevant science and articles.
Rob,
I have explained in two comments reasons that make all experiments of this nature extremely difficult
http://judithcurry.com/2014/12/01/gravito-thermal-discussion-thread/#comment-651710
http://judithcurry.com/2014/11/27/open-thread-thanksgiving-edition/#comment-651583
In the first I discuss Graeff’s experiment, in the second the proposal of Frønsdal, which is essentially the same as that discussed by Clive Best.
Finding a temperature difference in those experiments proves nothing without a lot of additional evidence to verify that the result is not due to an imperfection in the experimental setup, because most errors in the setup would lead to a spurious positive answer by maintaining circulation. A very weak circulation is enough to dominate over conduction, and to make the experiment faulty.
A related effect applies to atmospheres. An extremely weak GHE is enough to maintain some circulation and a lapse rate that might actually be closer to the adiabatic lapse rate than the present one. Under such conditions the Earth surface would be as cold as without atmosphere, and the whole troposphere much colder than the present one. Thus the strength of the GHE and the difference between the surface temperature and the tropopause temperature are not strongly linked (although there’s limited causal dependence). This observation is background to my first comment in this thread
http://judithcurry.com/2014/12/01/gravito-thermal-discussion-thread/#comment-651632
If this centrifuge experiment give positive results (that aren’t errors) then it will provide the basis for building a perpertual motion machine of the second kind. Indeed, if the positive result comes from measurements with a thermocouple, then it will already be such a perpetual motion machine.
It is a pleasure to assist Climate Etc knowledge seekers!
The relevant science Under the Gravito-Thermal hypothesis, a fluid body (whether gas or liquid) of particles of mass
, in an acceleration field 
, of height 
, will come to an equilibrium having a top-to-bottom temperature difference 
given by the simple expression
where
is the Boltzmann constant.
Checkpoint No other expression for
, depending upon the variables 
, is dimensionally consistent.
Now load three test tubes, each of height two centimeters, respectively with benzene, xenon gas, and mercury, into a high-end Beckman-Coulter Optima™ MAX-XP desktop ultracentrifuge, with the all-titanium MLA-130 Rotor. This bad boy pulls one million “g’s” at a rotational speed of 130,000 rpm.
http://www.laborgeraete-beranek.de/bilder/gebraucht/id2338_2.jpg
Is this spinning rotor comparably dangerous to a stick of dynamite?
http://www.chem.purdue.edu/chemsafety/newsandstories/centrifuge1.gif
You bet these rotors are dangerous!
Predictions of gravito-thermal theory
These temperature differences are large enough to carbonize the benzene, heat the xenon vapor to incandescence, vaporize the mercury, and melt-through the titanium.
Observation In ordinary laboratory usage, none of these disasters happens.
Experimental conclusion Ordinary laboratory experience with desktop ultracentrifuges falsifies the Gravito-Thermal hypothesis.
Thank you for your well-considered question, angech!
Thanks Fan.
But.
They do have cooling mechanisms to prevent it heating up, yes?
And they do have equations for this heat which you supplied. Can you explain why the equations do not match your version of reality.
Can you state categorically that there is no extra heat in the distal test tube.
And, seeing the whole tube is spinning at these high rates and hence under the same G, would one really expect gigantic amounts of heat in such a small separation distance. We are talking 30 mm, not 30 Kilometers.
We have arm waving at perpetual motion, experimental error without an experimental design and a litany of mad FOMBS assertions that are typically not worth reading.
There would be horrendously more energy being put in than could be extracted, there is a time to critique experimental design and that would seem to be after the design is complete and really we are not discussing the creation of energy by the mere fact of rotation. One can’t create horrendous temperatures in a centrifuge out of nothing. On a scale of silliness – the last ‘bad boy’ is a million.
FOMD wrote: “Checkpoint No other expression for \delta T, depending upon the variables {m, g, h}, is dimensionally consistent.”
This consideration yields proportionality at best, not equality. Also, the dry adiabatic lapse rate depends on c_p rather than molecular mass, so there are other possibilities that are dimensionally consistent.
No. Unltracentrifuge rotors spin hour after hour with no rotor-cooling whatsoever.
Were it not for friction in the bearings, the rotor would spin forever with no heating.
No rotor-cooling is needed for this simple reason: there is no Gravito-Thermal effect.
It is a pleasure to assist your understanding, angech!
The alone have Iranians have 20,000 centrifuges running ! The Lochsmidt experiment test that I originally proposed has therefore been performed many times, and no-one reports any temperature gradients. I am convinced it does not work!
The Ranque-Hilsch vortex tube separates a pressurized gas into hot and cold components. However the explanation is likely mechanical and energy is being consumed in the process!
A fan of *MORE* discourse | December 2, 2014 at 5:59 am |
” angech wonders “Thanks Fan. But. They do have cooling mechanisms to prevent it heating up, yes?”
No. Unltracentrifuge rotors spin hour after hour with no rotor-cooling whatsoever.”
This is absolutely untrue as any simple Google search would show. Why do you post untrue statements?
One of many quotes,
“Refrigerated centrifuges offer the added benefit of cooling to protect from sample degradation caused by heat generated by the action of spinning.”
You also said
“Were it not for friction in the bearings, the rotor would spin forever with no heating.”
But there is friction in the bearings which the rotors spin on.
No rotor-cooling is needed for this simple reason: there is no Gravito-Thermal effect.
The rotors are cooled. but not because of the the GT effect which is a separate question.
It is a pleasure to assist your understanding, angech!
Rob is right, you really get a kick out of deliberate misrepresentation. But unlike him I do encourage you to keep going as efforts with this sort of input only fool people a little while until they check, then you lose all support. Hm, are you really a skeptic using negative psychology?
No.
Summary Gravito-thermal theory straightforwardly predicts temperature differentials of several thousand degrees in ultracentrifuge tubes.
Question Why don’t the ultra-high temperatures predicted by gravito-thermal theory utterly destroy any and all ultracentrifuge samples, and/or the titanium rotors that hold the sample-tubes?
The world wonders!
Oh wait, the world doesn’t wonder … because there is no gravito-thermal effect!
FOMD: “Question Why don’t the ultra-high temperatures predicted by gravito-thermal theory utterly destroy any and all ultracentrifuge samples, and/or the titanium rotors that hold the sample-tubes?”
(Note: I don’t believe the effect exists, myself)
That could be because the hypothesized gradient is an equilibrium state. As it tends to be established in the gas sample, though internal diffusion, any external conduction with the solid parts of the device tends to destroy it at the very same time. One would need to put the sample in a good insulator, and, as already noted, inhibit any convection that would have the same effect as the hypothesized gravito-thermal effect. However, I now grant you that the effect is larger than I thought. (1,000,000 g, holy c**p !!)
Concentric rotating cylinders have been considered in the following papers.
Howard Brenner, Steady-state heat conduction in a gas undergoing rigid-body rotation. Comparison of Navier–Stokes–Fourier and bivelocity paradigms, International Journal of Engineering Science, 70 (2013) 29–45.
a b s t r a c t
This paper proposes a seemingly unequivocal experimental and/or molecular dynamics simulation test of the viability of the compressible Navier–Stokes–Fourier (NSF) equations for gases in the continuum region, namely for near-zero Knudsen (Kn) numbers. While experimental gas kineticists have long known of the inadequacy of the NSF equations for rarefied gases (i.e., noncontinua), for which Kn is no longer small, it is nevertheless believed by fluid mechanicians that the NSF equations remain valid for gaseous continua. The author is, however, unaware of the existence of any unequivocal experimental (or simulation) data to support this view. Indeed, based upon recent work by the author and others on the subject of bivelocity hydrodynamics [Brenner, H. (2013). Proposal of a critical test of the Navier–Stokes–Fourier paradigm for compressible fluid continua. Physical Review E 87, 013014]; [Brenner, H., Dongari, N., & Reese, J. M. (2013). A molecular dynamics test of the Navier–Stokes–Fourier paradigm for compressible gaseous continua. arXiv:1301.1716 [physics.flu-dyn]], ample reasons exist for believing that the NSF equations may not, in fact, be valid for compressible continua. Given the fundamental role played by the NSF equations in both theoretical and applied physics, it would obviously be well if the assumption of the viability of the compressible NSF equations was put to a variety of experimental tests, particularly if the interpretations of those tests were seemingly unequivocal as a consequence of the simplicity of their interpretation and ease of execution. This paper adds one such test to that cited above. It involves contemplating a gaseous continuum confined in the annular space between two co-axial circular cylinders rotating steadily at the same angular velocity while, at the same time, both cylinder walls are maintained at a common temperature, say Tc. In such circumstances the NSF equations, assumed to govern the resulting rigid-body rotation of the fluid, trivially predict the gas’s temperature to be uniform at the value Tc throughout the entire annular body of gas between the cylinders. The proposed test consists of measuring the temperature distribution so as to establish if, in fact, this predicted temperature uniformity is actually observed in practice — and, if not, of establishing whether the observed temperature distribution varies with such experimentally- controllable parameters as the cylinders’ angular velocity or the gas’s mean pressure. Was the temperature distribution found to be nonuniform the compressible NSF equations for continua would have to be abandoned as physically unsound. Anticipating that outcome we have, for the prescribed experimental arrangement and protocol, solved the corresponding bivelocity equations in order to establish if this model accords better with the test data. For, in contrast with NSF behavior, the bivelocity temperature distribution is predicted to be nonuniform.
Howard Brenner, Nishanth Dongari, Jason M. Reese A molecular dynamics test of the Navier-Stokes-Fourier paradigm for compressible gaseous continua
Knudsen’s pioneering experimental and theoretical work performed more than a century ago pointed to the fact that the Navier-Stokes-Fourier (NSF) paradigm is inapplicable to compressible gases at Knudsen numbers (Kn) beyond the continuum range, namely to noncontinua. However, in the case of continua, wherein Kn approaches zero asymptotically, it is nevertheless (implicitly) assumed in the literature that the compressible NSF equations remain applicable. Surprisingly, this belief appears never to have been critically tested; rather, most tests of the viability of the NSF equations for continuum flows have, to date, effectively been limited to incompressible fluids, namely liquids. Given that bivelocity hydrodynamic theory has recently raised fundamental questions about the validity of the NSF equations for compressible continuum gas flows, we deemed it worthwhile to test the validity of the NSF paradigm for the case of continua. Although our proposed NSF test does not, itself, depend upon the correctness of the bivelocity model that spawned the test, the latter provided motivation. This Letter furnishes molecular dynamics (MD) simulation evidence showing, contrary to current opinion, that the NSF equations are not, in fact, applicable to compressible gaseous continua, nor, presumably, either to compressible liquids. Importantly, this conclusion regarding NSF’s inapplicability to continua, is shown to hold independently of the viability of the no-slip boundary condition applied to fluid continua, thus separating the issue of the correctness of the NSF differential equations from that of the tangential velocity boundary condition to be imposed upon these equations when seeking their solution. Finally, the MD data are shown to be functionally consistent with the bivelocity model that spawned the present study.
+1
Just out of interest I used equation 107 from page 70 of G&Ts paper
http://arxiv.org/pdf/0707.1161v4.pdf
This was to contrast the radiative loss from a bottom face of a cubic metre of dry air with the radiative loss from the top face of a cubic metre of water.
This is the most common interface on our planet covering almost 70% of the surface area.
For both the calculated temperature drop is a modest one unit from 300K to 299K
The loss of internal energy would be typical for night time conditions
For air answer is 2 milliseconds
For water it is 2.54 hours
We don’t even need to invoke the second law to note that radiative warming of the surface by the atmosphere is pretty far fetched.
Yep. Yet when I mention that there is really two greenhouses to consider, the oceans and the atmosphere all you hear is crickets.
Two greenhouses to consider… agreed. Greenhouse gases are fluids with the defining properties of being transparent to shortwave and opaque to longwave. Water is a fluid possessing both definitive properties just as water vapor is a fluid with both properties.
For those that seem to enjoy here the mental gymnastics of the gravito-thermo paradox as laid bare both logically and mathematically by Pierre-Normandes link to Combes-Lau, I highly recommend Thinking Physics is Gedanken Physics. No math (which after all is just a precise way to describe for calculation purposes the Gedanken). Willis’ posted ‘proof’ above of the gravito-thermo paradox is a classic Gedanken. As were Einstein’s elevators and trains for relativity.
Book covers all introductory physics subfields: mechanics, vibrations (mechanics with complications), optics (light), EM, fluids, heat (a fluid problem with complications), and even relativity (mostly special). Really hones critical thinking skills useful for climate science and this blog.
Author is Lewis Epstein. My version is the third edition ISBN 0-935218-08-4.
Dedication paraphrased from the inside cover (subbing math for algebra):
“Mathematics is a wonderful invention. It allows fools to do physics without understanding.”
Another of those ‘sipping’ books (as I hope some will find Blowing Smoke) to be savored one chapter at a time.
And, for those who cannot live without the math, Feynman’s 1962-63 Cal Tech Lectures on Physics provide all the requisite rigorous math for every problem in Thinking Physics (and then some), just in a different order. RF always emphasized the physical intuition first–“if you cannot explain it simply, then you do not really understand it yourself”. His treatment of fluid dynamic boundaries (aka ‘the religious epiphany in Volume 2 chapter 41 verse 6’) is a classic (having to do with with the mysteries hidden inside the Navier-Stokes equations and the use of renormalization groups, just as he also did with his quantum electrodynamics).
Hope some the more technically inclined on this thread find this reference suggestion both useful and enjoyable. And lest you think thinking about physics has lttle to do with climate, see ‘Hot and Sticky’, in my edition the problem beginning page 238.
Regards all.
“And, for those who cannot live without the math, Feynman’s 1962-63 Cal Tech Lectures on Physics provide all the requisite rigorous math for every problem in Thinking Physics (and then some), just in a different order.”
They also include their fair share of enlightening thought experiments. And they now are available online. I had been delighted as an undergraduate student (not in his classroom!) by his discussion of the “ratchet and pawl” perpetual motion machine of the second kind, and how Brownian motion prevents the machine to work as intended, and thereby rescues the second law of thermodynamics.
http://www.feynmanlectures.caltech.edu/I_46.html
Yes, I think we are in an equilibrium state at present, unlike the twentieth century when we had two rises in global average temperature. We are in equilibrium now because the global average temperature has been almost constant since 1997. Why is that? The 1940 singularity provides the answer. Before 1940 the global average temperature had been rising at 0.15C/decade, after 1940 global average temperature actually fell despite extra CO2 concentration, until 1970. That 30 year gap was enough to start overcoming the transport lag in the oceans, so the oceans started to respond to the1910- 1940 ramp in temperature. But why did it stop in 1997? Carbon in CO2 can have up to six neutrons/carbon atom. Neutrons are heavy particles and can readily vibrate, absorbing energy from the earth’s IR at 14.99 microns, when the vibration reaches 100% of its absorption capability, it can absorb no more heat, so heat escapes to space and the earth cools. That is what I believe happened in 1040. But heat was still being absorbed by N2, O2 and H2o and that provides the equilibrium of today.
Darn.
There is friction of the water on the seabed, of the waves crashing against each other and the shore, of raindrops through air and gravity waves upwelling the earth constantly by deforming said earth and sea.
Where there is a rotating planet air and water particles that move away from the mid line gain or lose potential energy due to the Coriolis force. This in turn generates the jet streams and currents and possibly even shapes the land very slowly.
It is enough over time to wear out steel railway wheels in trains traveling North /South. We had a German machine in Darwin to cut the wheels back into shape.
There is heat in the center of the Earth put down to Nuclear heating. Why? Because Gravity ensures enough energy input to force out these reactions.
The Sea is compressed at 5000 meters and way away from any sun but does not freeze. The earth crust heat is very hot at 5000 meters depth but still not enough to warm that top comparative 10 microns of the Earth’s surface and radiate any heat to space Probably 1 meter in temperate zones in Winter, referred to as the Frost line for cement fillings.
The mystery of the way heat, and geothermal heat interacts on this planet and the fact that no one here can convince 97% of people here, some of them very good brains, leaves me baffled.
Rob or Fan or Dallas is there a text cited on this please.
Or so help me I’ll go read Science of Doom.
The problem for “the gravito-thermo paradox as laid bare both logically and mathematically by Pierre-Normandes link to Combes-Lau, ”
is that the question assumes that a thermal equilibrium is attainable.
Since work against gravity changes KE to PE and work with gravity chanmges PE to KE the vertical structure of an atmosphere is in permanent thermal disequilibrium so there can be no paradox and the whole issue is a straw man.
Stephen, the reason why the atmosphere is out of equilibrium is because it is heated by the warm Sun (mainly via the heating of the surface below) and it is radiating back to the cool space. Gravity alone can’t prevent a gas (either a planetary atmosphere or some gas in a box) from attaining thermodynamic equilibrium. Your argument about the effect from gravity on the balance of kinetic and potential energy of individual molecules is refuted in the papers that I have linked to at the beginning of this thread.
http://judithcurry.com/2014/12/01/gravito-thermal-discussion-thread/#comment-651619
I also summarized the flaw in the PE+KE balance argument here:
http://judithcurry.com/2014/11/27/open-thread-thanksgiving-edition/#comment-651519
Combes-Lau uses an assumed statistical relationship to achieve an assumed outcome. This sort of hand waving at so called fundamental principles is convincing only for those already convinced. Little math – little data – and little minds. A dangerous conflation.
As I said – there seems little need or reason to take a position on something so fundamentally peripheral to the real issues – and something with so little real science – as in experimentation – involved. I guess it makes for a perfect playground for pedants.
Rob Ellison: “Combes-Lau uses an assumed statistical relationship to achieve an assumed outcome. ”
What they did was to show why a seemingly valid argument is invalid. This invalid argument has been endorsed quite explicitly by Captdallas (who called it the “basic premise of the gravito-thermal effect”), David Springer, Stephen Wilde, and Doug C. You yourself seem to have been impressed by it in earlier threads.
When the logical flaw in the argument is disclosed, then the standard result from kinetic theory doesn’t seem paradoxical anymore. This standard result, as Coombes and Laue note, can be obtained directly from the Boltzmann energy distribution law, but this isn’t going to impress college students since it is too abstract and it doesn’t highlight in an intuitive way what really is occurring among the different molecular populations at various heights. That’s the pedagogical virtue of their contribution.
They aren’t proving anything controversial. The standard result is also proven in standard statistical mechanics textbooks (I referenced two of them) and a few other physics papers (I referenced three of them, not including Pekka’s useful note). It also is exhibited in the newer 2D molecular dynamics simulator that I linked to. (This also rebuts your earlier claim that molecules bouncing around elastically in a box don’t tend to exhibit a vertical density gradient at equilibrium.)
““The time integral of the kinetic energy of any atom will be equal to the time integral of the kinetic energy of any other atom. This truism is simply and solely all that the Boltzmann–Maxwell doctrine asserts for a vertical column of a homogeneous monatomic gas.” Kelvin – See more at: http://www.mdpi.com/1099-4300/16/3/1515/htm#sthash.hzabWZj7.dpuf
I have been consistent all along – hand waving at so called fundamental principles – as indeed Boltzman and Maxwell did – inspires little confidence. P-N infinitely less so.
I have of course stopped reading P-N – simply endless repetition of the same points. So few of them – so trivial – so little actual distillation and synthesis of science. Much verbiage and some few references waved around as talisman.
But I caught the tail end of the last comment. 2-D bouncing balls with a free surface is not remotely the box of gas at the classical limit. It’s pretty. It ‘rebuts’ nothing at all.
Rob Ellison wrote: “But I caught the tail end of the last comment. 2-D bouncing balls with a free surface is not remotely the box of gas at the classical limit. It’s pretty. It ‘rebuts’ nothing at all.”
In what relevant respect isn’t the 2D simulation relevant to an ideal gas at equilibrium in a box? What might be the cause of the vertical density gradient in the simulation such that it would not occur for an real monatomic gas? What is missing in the simulation?
Pierre-Normand
I think your rebuttal of the gravito thermal effect is flawed because you are seeing kinetic energy simply as forward or sideways motion in a single plane.
Kinetic energy also arises when gas molecules are forced together under pressure so that their vibratory movements are confined within a smaller space and become faster so as to release kinetic energy in the form of heat.
It is that type of kinetic energy that changes back and forth between KE and PE not simple movement up, down or sideways.
What happens is that the sun is constantly pumping the atmosphere up from the surface in regions of ascending air and gravity is constantly compressing the atmosphere in regions of descending air so that the heat of compression is being constantly replenished once the first convective cycle has been completed.
That heat of compression is then locked into the adiabatic process in the form of PE and cannot escape to space as radiation. The process requires a reserve of kinetic energy at the surface to continue holding the atmosphere off the ground. That is our 33K greenhouse effect.
That is a completely different scenario to simple one off gravitational compression which allows the heat to dissipate once the pumping and contraction stops.
“Kinetic energy also arises when gas molecules are forced together under pressure so that their vibratory movements are confined within a smaller space and become faster so as to release kinetic energy in the form of heat.”
You are talking about adiabatic compression of a descending parcel of air, right? The source of the increase in internal energy (including kinetic energy), in that case, is the work from the surrounding on the boundary of the compressed air parcel. It isn’t gravitational potential energy.
I for one am very impressed both by Pierre-Normand’s persistence and his understanding of the issue. This is particularly so since I have observed on the blogosphere that most scientists blow smoke on the issue, making incorrect or irrelevant arguments that force us laymen to figure it out for ourselves.
The only place I think he may have gone wrong is his (http://judithcurry.com/2014/11/27/open-thread-thanksgiving-edition/#comment-651592) of the purported refutation of an equilibrium lapse rate by way of the perpetual-motion argument. Although I can’t say I know exactly what the result of connecting a thermocouple would be, I believe that such an approach suffers from the same logical flaw that Dr. Brown’s purported proof had. As I mentioned above, I had dealt with that flaw here: http://wattsupwiththat.com/2014/08/18/monday-mirthiness-spot-the-troll/#comment-1711550.
But a shorter, different way to look at it is this: it seems unlikely that connecting a thermocouple to an otherwise-isolated ideal-gas column will magically convert its ensemble of possible microstates into a canonical ensemble, i.e. into the ensemble that would result from being bathed in an infinite-heat-capacity heat bath.
Be that as it may, I take my hat off to Pierre-Normand’s stamina–and ability to stick to the issue.
Joe Born,
Thank you for the kind words.
Notice that in the post that you linked to, where I was replying to David Springer, the effect at issue was the ordinarily discussed gravito-thermal effect which is very many orders of magnitudes larger than the effect discussed by Velasco et al. This alleged effect doesn’t rely on the system being fully isolated from its surrounding. In that case, the consequence from using a thermocouple is that energy can be extracted from the column while this energy can be replenished spontaneously from a thermal bath that is is in contact with it (anywhere along the length of the column). This is in violation of the second law and it constitutes a perpetual motion machine of the second kind.
@Joe Born
I refuted Brown’s PM2K years ago on WUWT. In a gravity confined gas column the volume is variable with temperature. As you cool the hot side and warm the cool side the column heights diminish and grow respectively until the difference in lapse rate is nullified. The PM2K grinds to a halt well before you’ve extracted enough useful work to reduce both gas columns to solid ices at the bottom.
David Springer, the second law of thermodynamics doesn’t merely imply that you can’t extract enough energy from a unique thermal bath and thereby perform enough macroscopic work to usefully reduce your energy utility bills. It states that you can’t extract *any* energy in that fashion.
Your understanding of perpetuum mobiles of the second kind is wrong.
Suggest you read up on 2LoT PM’s here:
http://lectureonline.cl.msu.edu/~mmp/kap12/cd333.htm
PM2K’s are not prohibited by thermodynamics. They are prohibited by engineering reality that ideal things like frictionless bearings, perfect vacuums, isolated systems, ideal gases, and so forth are physical impossibilities. No device known can turn heat into work with 100% efficiency thus all PM2Ks stop running at some point.
In the world of engineering we simplify as much as practical but no more than that. For instance if we are timing an air race we don’t make relativistic corrections for differences in local gravity and inertial reference frames at different race courses. However if we are meausuring nanosecond differences in precision clock rates in orbiting satellites vs. the clock in the ground receiver in GPS applications we must correct for relativistic effects or live with errors large enough to spell the difference between hitting a schoolhouse with a GPS guided missile instead of the munitions factory across the street from it. In space exploration we don’t try to compute intractable effects of multi-body orbital mechanics we instead make mid-course corrections based on empirical measurement of location and velocity. For a friction example we don’t worry about the effect of air-drag on some wheeled vehicles like earth movers but we must do it for Formula 1 cars to be competitive. It’s all about context.
David Springer: “PM2K’s are not prohibited by thermodynamics.”
Yes, perpetual motion machines of the *second* kind are prohibited because they violate the *second* law of thermodynamics. (While perpetual motion machines of the *first* kind violate the *first* law: conservation of energy.) That’s because they operate in such a manner that heat extracted from a thermal bath is converted into macroscopic work with no compensating heating of a colder thermal bath (as is the case with ordinary thermal engines) and, as a result, the total entropy of the Universe is reduced.
If work is extracted from a column of gas that exhibits a spontaneous gravito-thermal gradient, then the column can be warmed back through putting it in contact with a large thermal bath. Then the initial temperature profile will be spontaneously restored after a while and some more work can be extracted. Through iterating this process, one is steadily converting heat from the large thermal bath into usable macroscopic work (and hence reducing its entropy) without generating nearly enough waste heat to satisfy the second law.
If a gravito-thermal gradient exists – we may presume that it doesn’t contravene the first or second law.
Rob Ellison: “If a gravito-thermal gradient exists – we may presume that it doesn’t contravene the first or second law.”
But you do agree with me that perpetual motion machines of the second kind contravene the second law. Don’t you? That was my issue with Singer.
Your penchant for personal abuse is appreciated, Rob Ellison!
Especially to assist your understanding, a simplified (yet vivid!) mathematical analysis/laboratory experiment has now been posted on this thread.
It is a continuing pleasure to assist your understanding of basic thermodynamical and statistical mechanical principles, Rob Ellison!
Yes I noted. I just replied.
We have arm waving at perpetual motion, experimental error without an experimental design and a litany of mad FOMBS assertions that are typically not worth reading.
There would be horrendously more energy being put in than could be extracted, there is a time to critique experimental design and that would seem to be after the design is complete and really we are not discussing the creation of energy by the mere fact of rotation. One can’t create horrendous temperatures in a centrifuge out of nothing. On a scale of silliness – the last ‘bad boy’ is a million.
And as I have said before – the whining by such as FOMBS about insults and abuse is simply sanctimonious hypocrisy.
Beside I was being helpful – as I have tried to be many times with P-N. I have stopped reading and this is why. A few few hundred comments saying the same things – and I might pass over fewer.
FOMBS I nearly always pass over – unless he directs his comment at me. Then I want to be as abrasive as possible simply to discourage the behaviour. Negative reinforcement. The level of FOMBS silliness is just too great to want to have much to do with it.
A few hundred less…
Please consider the ultracentrifuge test-case to be cheerfully directed toward gravito-thermal enthusiasts in general!
The rotors spin without creating energy? What a shame – we would otherwise be able to power the world using FOMBS comments.
FOMD wrote: “Were it not for friction in the bearings, the rotor would spin forever with no heating.
No rotor-cooling is needed for this simple reason: THERE IS NO GRAVITO-THERMAL EFFECT.”
I don’t get this argument. There ought to be some friction in the bearings and hence some warming. If no rotor-cooling mechanism is supplied that must be because the warming isn’t large enough to need it. If there were a gravito-thermal effect, and if it would affect the rotor as a whole, then it would carry heat away from the rotor (since the simulated gravitational field would be directed outside, radially). So, the complete absence of any heating near the axis would rather *favor* the existence of a gravito-thermal effect!
I rather think, for reasons Pekka gave, that the alleged effect is too small to be detected with this setup.
Pierre-Normand said:
“You are talking about adiabatic compression of a descending parcel of air, right? The source of the increase in internal energy (including kinetic energy), in that case, is the work from the surrounding on the boundary of the compressed air parcel. It isn’t gravitational potential energy.”
If the process is adiabatic then the work done is against gravity (ascent) or with gravity (descent). By definition.
Any work done on surrounding molecules is diabatic. By definition.
How is the PE derived from or lost to the adiabatic process not gravitational potential energy ?
Does it matter anyway?
Whether the PE locked into the overturning cycle is gravitational or not it still requires a store of KE at the surface to sustain continued convective overturning once the first convective cycle has completed and that KE at the surface cannot be radiated to space or the atmosphere will fall to the ground.
Hence 288K instead of 255K at the surface.
This is not a simple matter of one off gravitational compression. It is a continuing process that needs fuel in the form of KE at the surface to sustain it. That is where the radiative theory is flawed. It makes no provision for such an ongoing mechanical process or the surface energy needed to keep it running.
“If the process is adiabatic then the work done is against gravity (ascent) or with gravity (descent). By definition.
Any work done on surrounding molecules is diabatic. By definition.”
That’s incorrect. A process is adiabatic if it doesn’t involve flows of heat or matter. One typical example is the second stage of the Carnot cycle. The gas in the cylinder expands and thereby performs work on the receding piston. Though the gas loses internal energy (and cools) there is no flow of heat through the piston. Adiabatic compression and decompression of descending and raising air parcels in the atmosphere are likewise adiabatic processes that involve work on (and by) the surrounding. The amount of heat gained or lost in those processes is completely unrelated to the gain or loss of gravitational potential of the air parcels.
See “Stage 2” in the following link:
http://www.massengineers.com/Documents/carnot_cycle.htm
“Stage 2: In the second stage, the heat source is removed; the piston continues to move downward and the gas is still expanding while cooling (lowering in temperature). It is presented by the graphic from point B to point C. This stage is called a adiabatic expansion (Energy stays)”
Energy stays during convective uplift of gases. It is just converted in form from KE to PE
Work done with or against gravity does not involve a flow of heat or matter.
That is why it is adiabatic.
Once a parcel of air detaches from the surface during uplift all further upward movement is adiabatic because all work is done against gravity and not against surrounding molecules.
You think that the word ‘surroundings’ means the adjoining molecules but in fact it means the gravitational field in relation to adiabatic uplift within an atmosphere.
The reason for the lack of interaction with adjoining molecules is that the pressure on the parcel reduces at the same rate as the pressure in the surroundings so the initial temperature differential that caused uplift to begin is maintained throughout the period of adiabatic uplift. If work were being done against adjoining molecules then that would not be the case. Instead the initial temperature differential would quickly decline as heat flowed out of the parcel to the adjoining molecules.
“The amount of heat gained or lost in those processes is completely unrelated to the gain or loss of gravitational potential of the air parcels”
Using work against gravity to drive molecules upward and further apart (thereby cooling) within a gravitational field always results in more gravitational potential energy whether the movement be relative to the surface below or relative to the adjoining molecules.
Wildeco2014 (Stephen Wilde?) wrote:
“Energy stays during convective uplift of gases. It is just converted in form from KE to PE Work done with or against gravity does not involve a flow of heat or matter. That is why it is adiabatic.”
Work done on the surrounding through expansion also is an adiabatic process. You are incorrectly mixing up two different processes.
(1) When an air parcel rises in the atmosphere then it gains potential energy. Work therefore must be performed by the surrounding air in order to lift the parcel against gravity. This work is performed by the buoyant force that results from the vertical barometric pressure gradient around the air parcel. This produces a net force that performs the required work. This works is equal to the gain in potential energy of the rising parcel. But where does the energy come from for performing this lifting work? As the parcel rises, it displaces some air above and other parcels of air replace the evacuated space. The net motion of those other displaced air parcels is downward. Those descending air parcels thus are losing gravitational potential energy at the same rate that the rising parcel gains some. That’s the first process. It conserves gravitational potential energy between *all* the involved air parcels and it has no incidence on molecular kinetic energy. It has no direct effect at all on the internal energy or temperature of the rising and descending air parcels.
(2) The second process, quite independent from the first one just described, is the the adiabatic expansion (or compression) of the rising (or descending) air parcels. This process is governed by variations in ambient pressure around the moving parcels. This is the process that account for the variation in internal energy though work:
dW = P(h)dV, integrated over the vertical displacement of the parcel.
It is quite unrelated to variation in potential gravitational energy of the parcels.
Though mixing up conceptually those two different processes you are not accounting correctly for the energy exchanges. The adiabatically expanding air parcel *must* lose internal energy while it performs work through expanding within its pressurized surrounding. The parcel can’t use up this same energy to lift itself up against the force of gravity. That wouldn’t make sense anyway unless this kinetic energy would result from a net initial upward motion of the bulk of the molecules. But the velocities are random and mostly isotropic. The gain in potential gravitational energy already is accounted for by the external buoyant force.
LoL … in what sense are wrongly-predicted temperature differentials several thousand degrees “too small to be detected”?
Riddle What spins faster than an over-stressed ultracentrifuge rotor?
https://www.youtube.com/watch?v=nDrU22R3gg4
Answer Gravito-thermal enthusiasts confronted by physical evidence!
FOMD: “LoL … in what sense are wrongly-predicted temperature differentials several thousand degrees “too small to be detected”?”
Yes, it’s true 1,000,000 g is quite a large gravitational acceleration. If the gavito-thermal gradient is about as large as the dry adiabatic lapse rate (about 10°K/km), as some proponents allege, then over a radial distance of 1cm, the equilibrium gradient would produce a 100°K differential. That’s indeed larger than I thought. As Pekka notes, though, just a little amount of convection would also produce it, so this would still be a confounding factor that needs to be eliminated.
Yes, and filling the centrifuge-tubes with heavier fluid-molecules like organic solvents (which is routine) or filling the tubes with even-heavier xenon gas or mercury (which is not so common, but is perfectly feasible) increases the gravito-thermal effect in proportion to the increased atomic mass … to several thousand degrees.
Yikes!
Conclusion Naive gravito-thermal theory has perished … at the hands of everyday experiments.
When the centrifuge is turned on, there will be compression at one end and expansion at the other. In addition some work is converted to heat. Thus the effect of heating one end of tubes and cooling of the other end takes place anyway initially. No “gravito-thermal effect” is needed for that.
Whether a “gravito-thermal effect” would enhance the initial heating of the outer end is impossible to tell, because no theory exists that describes the effect, there are only incomplete proposals that cannot answer questions of this type. The existing complete enough theory tells that the temperature difference disappears gradually, if the gas samples are really isolated well enough from external heat sources and sinks.
Compressive/decompressive effects are transient, and moreover are small for nearly-incompressible liquids (such as organic solvents and mercury in the worked example).
Whereas gravito-thermal theory predicts a temperature-differential of several thousand degrees that is sustained throughout centrifuge-runs that routinely last for hours and even days.
And yet even the most delicate ultracentrifuged proteins show no signs of being hard-boiled by gravito-thermal heating.
http://images.fineartamerica.com/images-medium-large/follow-the-dodo-daniel-eskridge.jpg
Conclusion gravito-thermal theory is dead as a dodo!
FOMD: “Conclusion gravito-thermal theory is dead as a dodo!”
Ever since the Dodo went extinct, the Dodos who are dead have been outnumbered by the Dodos who will never be born.
What theory?
I have seen only vague and highly incomplete hypotheses that very likely cannot be expanded to a full theory.
But what could be the source for the energy that results in those high temperatures, if a theory could be formulated. When the transient phase is over, no more energy enters the system.
Dodos have once existed in contrast to theories that include the “Gravito-Thermal effect”.
Pekka said, “What theory?”
Funny how this thought experiment keeps getting promoted. I believe it has led to a few theorems though. The Fluctuation Theorem comes to mind.
It came to my mind that there are centrifuges that operate in the regime, where diffusion is significant relative to convective and turbulent mixing. All gas centrifuges used for isotope separation are such devices. Thus measurements of temperature distributions in such gas centrifuges should provide the evidence.
Pekka, “All gas centrifuges used for isotope separation are such devices. Thus measurements of temperature distributions in such gas centrifuges should provide the evidence.”
I can’t find any. From what I have seen most applications involve heating or cooling to improve separation. What effect there is is so small it would be difficult to measure.
I have a question for Fan & Pierre-Normand.
How do you explain the Atmospheric Temperatures of the Solar Systems Gas Giants?
They are much further from the Sun than Mars and therefore get even less radiation from the Sun and yet their Atmospheric Temperatures are 100s of times higher than Mars and Earth.
It is accepted science that it is due to the Massive Gravity of those worlds.
I’m not sure about that A C Osborn. I’ve heard that a small rate of gravitational collapse accounts for some of the excess energy radiated compared with the solar input but that may not fully answer your question. I don’t know anything about the atmosphere of other planets.
This is interesting:
http://www.teachastronomy.com/astropedia/article/Thermal-Radiation-from-Gas-Giant-Planets
It seems that there are a number of possible reasons why a planet might emit more than it receives from the sun but in the case of Uranus they say:
“Interestingly, Uranus doesn’t appear to have significant excess heat”
but given the very high gas temperatures they must simply mean that it does not emit much excess heat to space i.e. it is in approximate thermal balance with the sun.
Obviously the ‘surface’ (however defined) is hot enough to emit at 83,000 times more than it receives from the sun but the heat is not actually getting out in the form of thermal emissions.
That fits with the proposition that the excess heat within the compressed atmosphere is a result of adiabatic recycling of energy being conducted and convected up and down within the gases in just the same way that I propose the Earth radiates to space at 255K from a surface at 288K but recycles the other 33K adiabatically.
That is different from one off gravitational compression and I think that is where the AGW proponents go wrong.
The adiabatic process involves continuous pumping up by the sun in regions of ascent simultaneously with continuous compression by gravity in regions of descent and so there is constant replenishment of the surface kinetic energy needed to sustain the process and thereby keep the weight of the atmosphere suspended off the surface.
Adiabatic decompression and compression is quite different from simple gravitational compression and given that Uranus has very hot gases but is nonetheless in approximate thermal balance with solar radiation it is a good example to use.
To correct my previous post the temperature of Uranus is not high but the temperature is in excess of that expected from solar input so the basic proposition holds:
“Weather on Uranus functions much as it does on other gas giants. Like Jupiter and Saturn, the planet has bands of zones and belts that orbit parallel to the equator, which is warmer than the poles. The warm temperatures that drive the planet’s weather come from the interior of the planet, rather than from the sun. The significant distance to Uranus from the sun may play a role in why the planet’s interior heat overpowers the faint light from the star.”
from here:
http://www.space.com/18707-uranus-temperature.html
The temperature of Uranus is very high, just not at the outer surface of it’s Atmosphere, as you would expect.
The Wikipedia article about Uranus states that it’s internal heat is unexpectedly low and it isn’t well understood why that is so.
http://en.wikipedia.org/wiki/Uranus#Internal_heat
Yeah, right, “The outermost layer of the Uranian atmosphere is the thermosphere and corona, which has a uniform temperature around 800 to 850 K”
Note that is the outer most layer.
No surprise there. The thermosphere of a planet is heated up by Solar UV. UV radiation is very hot. Further the volumetric heat capacity of the thermosphere is extremely low since it is so sparse. Being largely ionized also gives is a large cross-section to capture UV photons.
You do realise how far away from the Sun the Gas Giants are?
The closest is 5 times as far as the earth.
Sure, A C Osborn. This might explain why the thermosphere of Uranus is so very much colder than the thermosphere of the Earth.
More detail about Uranus:
“The troposphere is the lowest and densest part of the atmosphere and is characterized by a decrease in temperature with altitude. The temperature falls from about 320 K at the base of the nominal troposphere at −300 km to 53 K at 50 km. The temperatures in the coldest upper region of the troposphere (the tropopause) actually vary in the range between 49 and 57 K depending on planetary latitude. The tropopause region is responsible for the vast majority of the planet’s thermal far infrared emissions, thus determining its effective temperature of 59.1 ± 0.3 K.
The troposphere is believed to possess a highly complex cloud structure; water clouds are hypothesised to lie in the pressure range of 50 to 100 bar (5 to 10 MPa), ammonium hydrosulfide clouds in the range of 20 to 40 bar (2 to 4 MPa), ammonia or hydrogen sulfide clouds at between 3 and 10 bar (0.3 to 1 MPa) and finally directly detected thin methane clouds at 1 to 2 bar (0.1 to 0.2 MPa). The troposphere is a very dynamic part of the atmosphere, exhibiting strong winds, bright clouds and seasonal changes”
The troposphere seems to exhibit similar convective phenomena to ours and is as warm as 320K as against Earth’s 288K despite the weakness of insolation so I think that gravito-thermal activity is present in that region just as it in our troposphere.
Lower and denser levels from the base of the troposphere become colder which suggests to me something similar to the structure of our oceans which cool with depth.
Overall it seems a suitable analogue given that the troposphere temperatures cannot be accounted for by insolation or heat coming up from below.
The convective region does seem to require its own store of KE to maintain constant overturning just like on Earth.
From Wiki “The outermost layer of the Uranian atmosphere is the thermosphere and corona, which has a uniform temperature around 800 to 850 K”
You might also enjoy this post over at The Hockey Schtick
http://hockeyschtick.blogspot.co.uk/2014/11/how-can-uranus-have-storms-hot-enough.html
Pierre,
I’ve come across the buoyant force argument before but think it flawed in that buoyancy requires no force against surrounding molecules when the movement is into a region of lower pressure. In that situation the work done is all against gravity and so is purely adiabatic.
The thing is that once a parcel of air heats up and becomes less dense relative to its surroundings then it develops buoyancy within itself and rises spontaneously.
It also applies in reverse. A descending parcel of air does no work against surrounding molecules when descending into a region of greater pressure because the parcel is being compressed at the same rate as its surroundings.
The concept of a buoyancy force external to the parcel has confused a lot of people so you are not alone.
Obviously no process is purely adiabatic so there is some small amount of work done against surrounding molecules but that is then a diabatic process whereby some of the energy in the adiabatic process is able to ‘leak’ out to the surroundings.
I think it is you who is conflating the diabatic and adiabatic processes.
Stephen Wilde,
You must have misread me. I was precisely arguing that the work preformed by the buoyant force is done against gravity and the process involves no change in internal energy. Both the processes that I have described are adiabatic, but only the second one (compression or expansion) yields a change in internal energy of the moving air parcel — and hence a change in average molecular kinetic energy.
An air parcel can’t lift itself up against gravity. That’s nonsense. Likewise, you can’t lift yourself up through pulling on your own bootstraps. Of course, for the buoyant force to begin working against the force of gravity (when the parcel is initially at rest), it must overcome this force. For this to occur, the density of the air parcel must be reduced compared with its surrounding. This can occur through latent heat release (through water vapor precipitation), or radiative heating, etc. In that case, the air parcel begins to rise.
Since the buoyant force is the result of the net external forces from the surrounding air (equal to the pressure of the surrounding air all around the parcel integrated directionally over the whole surface) applied on the parcel, and this force acts over the vertical displacement of the parcel, it performs work. This work is supplied from outside the parcel, and the energy for performing it mainly comes from the lost gravitational potential energy of the air that must descend to fill up the volume evacuated by the rising parcel.
the density of the air parcel must be reduced compared with its surrounding. This can occur through latent heat release (through water vapor precipitation), or radiative heating, etc. In that case, the air parcel begins to rise.”
I don’t see why that cannot be interpreted as the parcel rising spontaneously from its own internal buoyancy with no need for pushing from outside.
“This work is supplied from outside the parcel, and the energy for performing it mainly comes from the lost gravitational potential energy of the air that must descend to fill up the volume evacuated by the rising parcel”
I think that illustrates where the idea of a buoyancy force acting on the parcel from outside goes wrong.
It is a matter of getting cause and effect in the right order.
For you to be right the descending air has to make the first move in order to push the lighter air up by way of exerting an external buoyancy force.
However, in reality the first move is by way of the warmed lighter air starting to move away from the surface due to its own internal buoyancy as imparted to it by surface warmth.
There is a test as to which interpretation must be correct and that is the development of lower pressure beneath ascending warm air as seen in low pressure cells.
Thus the parcel rises first, pressure below it reduces and air is pulled in from the sides which is the opposite of your scenario.
SW wrote: “I don’t see why that cannot be interpreted as the parcel rising spontaneously from its own internal buoyancy with no need for pushing from outside.”
Because that violates Newton’s second law of motion. For the parcel to begin to rise as a whole, you need a net upward force applied on it from outside. Gravity is one component of that force, while buoyancy is another. The internal forces are irrelevant to the acceleration of the parcel as a whole.
SW: “For you to be right the descending air has to make the first move in order to push the lighter air up by way of exerting an external buoyancy force.”
That’s not true. Suppose two identical buckets of water are suspended from two ends of a string that goes over a pulley. If you remove some water from the first bucket, then it will start to rise while the heavier bucket starts to descend. The descending bucked didn’t need to “make the first move”. This first bucket made the first most just through becoming less heavy.
Gases are different to liquids and solids because of their low density and internal mobility.
The more kinetic energy they carry the higher they will drift against gravity without any additional external force being applied.
That is why we need the Gas Laws.
You are focusing on the behaviour of liquids and solids which do operate under Newtonian physics because they are so much heavier and denser with more powerful inter molecular bonds than gases so that they do need an external push.
As for your bucket analogy you are removing mass which is an entirely different situation to reducing the density of the same mass. If you kept the same mass in the bucket but reduced its density it would still have the same weight and neither would move. The difference is that the water in the buckets is not subject to the Gas Laws but to Newtonian physics as you point out.
Stephen, the gas laws apply to gases in addition to the laws of mechanics. They aren’t replacement for them. A system can’t violate Newton’s second law of motion just because is has gaseous or liquid parts.
GW: “If you kept the same mass in the bucket but reduced its density it would still have the same weight and neither would move. The difference is that the water in the buckets is not subject to the Gas Laws but to Newtonian physics as you point out.”
My argument simply refutes your “has-to-make-the-first-move” causal argument. In the bucket case, the net forces on the buckets are the sum total of the force of gravity and the (opposite) tension in the supporting string. In the air parcel case, its the sum total of the weight of the air and the (external) buoyant force on the parcel. The only difference is that the change in net force results from the buoyant force being modified by an initial change in volume (rather than a change in weight). This difference is not relevant to the flaw in your argument from causality. The expanding parcel of air is free to “make the first move” (e.g. though initiation of a condensation process). It will still be caused to rise within the denser fluid as a result of its spontaneous expansion.
SW: “There is a test as to which interpretation must be correct and that is the development of lower pressure beneath ascending warm air as seen in low pressure cells.
Thus the parcel rises first, pressure below it reduces and air is pulled in from the sides which is the opposite of your scenario.”
The pressure below the rising parcel may become lower at this location than it was before the parcel began to rise (just from Bernouilli’s principle). This doesn’t show that the pressure is lower below the parcel than it is *above* the parcel. If this were the case, and the less dense rising cell would not decelerate, then Newton’s second law of motion would be violated.
In adiabatic uplift the less dense rising cell does not decelerate.
Gases are ruled by the Gas Laws and not Newtonian physics.
SW wrote: “In adiabatic uplift the less dense rising cell does not decelerate.
Gases are ruled by the Gas Laws and not Newtonian physics.”
The laws that govern the motion of macroscopic air parcels also include laws of thermodynamics. They are consistent with the laws of mechanics and can’t conflict with them. At any moment in time, the acceleration of an air parcel relates to the sum total of the external forces that are acting on it in accordance with F = ma (where ‘F’ and ‘a’ are directed vectors).
Also, for sure the uplifted air parcel doesn’t decelerate at first. That’s just *because* the external buoyant force applied on the less dense parcel of air is larger than the weight of the parcel. (Though viscous forces also ought to be taken into account and, eventually, will equilibrate the two other forces such that the rising air parcel will reach a terminal velocity even if the buoyant force is constant, just like sky divers do.)
“only the second one (compression or expansion) yields a change in internal energy of the moving air parcel — and hence a change in average molecular kinetic energy.”
There is no change in internal energy from gravitational compression or decompression. There is only a transformation of energy between KE and PE.
Decompression converts KE to PE for a cooling effect.
Compression converts PE to KE for a warming effect.
Total internal energy (KE+PE) remains the same.
As per the Gas Laws.
“There is no change in internal energy from gravitational compression or decompression. There is only a transformation of energy between KE and PE.”
I said nothing about “gravitaitonal decompression” whatever that is. When the parcel expands adiabatically within its pressurized environment, then it performs work on its surrounding dW = PdV, and the law of conservation of energy ensures that the change in internal energy dU = -dW. This is also explained at the molecular level by the fact that molecules that bounce back from receding molecules on the periphery of the expanding mass of air bounce back with a lower velocity on average. The process has nothing to do with gravity.
If it does work on surrounding molecules such that there is a change in total internal energy (KE+PE) then that is diabatic and not adiabatic.
To be adiabatic it must do work against gravity.
SW: “To be adiabatic it must do work against gravity.”
You are making up definitions. The second stage of the Carnot cycle is a paradigmatic example of an adiabatic expansion process that performs work on the surrounding (the piston, in that case). A Carnot engine works just the same in the absence of gravity.
Pierre-Normand,
The sooner you withdraw from this line of discussion, the better. Stephen Wilde has been arguing his nonsense physics about the adiabatic process against a whole truckload of pretty hardcore sceptics on Tallbloke’s blog for a long time. He’s been shown a gazillion times exactly what the adiabatic process IS and is NOT, and still he simply refuses to listen, to read, completely and utterly tangled up in his own warped ideas of how the world supposedly functions …
Just a warming.
Hehe, warNing, not warming.
Pierre-Normand | December 2, 2014 at 11:31 am |
“A Carnot engine works just the same in the absence of gravity.”
Who cares? Convective cells in the earth’s atmosphere won’t work in the absence of gravity. Duh.
Pierre-Normand | December 2, 2014 at 11:31 am |
“A Carnot engine works just the same in the absence of gravity.”
Carnot defines “work” as “weight lifted through a height”.
What does something weigh in the absence of gravity?
“The sooner you withdraw from this line of discussion, the better. Stephen Wilde has been arguing his nonsense physics about the adiabatic process against a whole truckload of pretty hardcore sceptics on Tallbloke’s blog for a long time. ”
he’s a lawyer. Note you will never see a formula or quantitative statement from him that can be tested.
David Spinger,
This is completely beyond the point. SW is denying that adiabatic expansion of a rising parcel of air performs work of the surrounding. He rather believes the loss of internal energy of the gas to be converted into gravitational potential energy of the rising gas. That’s a crude misunderstanding of the work of adiabatic expansion (and it also is quantitatively wrong). Also, work isn’t defined as work against gravity. The definition of a Carnot cycle leave it completely open what the work perfomed by the adiabatically expanding gas on the walls of the expanding container (or piston) is converted into on the other side of the walls (or piston).
Kristian,
I am not arguing with people on discussion fora because I have a high expectation that they will change their minds anytime soon, if ever. Those are not private discussions.
Yes, I have the same approach. I’m just saying that this particular discussion with this particular person is particularly pointless. We ALL know what the adiabatic process is and is not. There is basically nothing to discuss. SW, however, adamantly asserts we’re ALL fundamentally wrong, even Carnot and Clausius themselves.
“We ALL know what the adiabatic process is and is not.”
“We” seems to include very few people on this blog.
Here is a brain teaser for you.
Consider a small heat source suspended high above the earth’s surface with a much higher temperature than the surrounding air. For example we could simply use a hot air balloon made of high emissivity material and carrying a heavy load.
Now take an IR spectrometer and measure the spectra emitted by the balloon from a fixed distance but at 3 different positions.
1. At the same heigh as the balloon
2. Directly above the balloon
3. Directly below the balloon
How the spectra differ if at all ?
Clivebest, is the gravitational red-(blue)-shift of the radiation relevant?
The interference with the earth’s IR radiation will complicate things. However the main point is that any difference between the up and down spectra would prove that there is a net radiative transfer upwards. All measurements made in any direction at the same height should give the same result.
Clivebest,
This is a calibration issue. Simply take a pyrgeometer, the temperature of the cell is part of the measurement. If the cell is at ambient temperature you will have three different flux measured, three different corrections and three identical results.
Is pressure broadening of GHGs absorption lines relevant?
There is no trick question here.
I would expect to see a BB spectrum at the balloon temperature, with pressure broadened absorption lines dependent on the viewing position.
From below you would see the largest absorption and from above you should see less absorption. However, in the horizontal you should see a perfect BB spectrum with no absorption at all !
This experiment should all be done at night of course and maybe also over a desert. Otherwise the background IR from the earth’s surface and atmosphere would wash everything out.
Clivebest “From below you would see the largest absorption and from above you should see less absorption. However, in the horizontal you should see a perfect BB spectrum with no absorption at all !”
Why is that? I was also expecting more broadening from below, just because the pressure of the air is larger. However, horizontally, the pressure of the air is intermediate in between the (average) pressures along the lines of sight from above and below. Why wouldn’t the GHG molecules absorb any IR from the warm black-body in the horizontal direction?
Clivebest,
OK, I think I see what you were driving at; bit there may have been an unwanted assumption in your setup. You said that the black-body is much *warmer* than the surrounding air! In that case I would expect abortion to occur in all three cases (though with variable amounts).
If, on the other hand, the black-body were at the *same* temperature as ambient air at that level, and there is a lapse rate, then one would see absorption in the GHG bands above, more emission in those bands below, and a pure unmodified BB spectrum horizontally.
It is not the pressure differential between the top and bottom of a hot air balloon that causes it to rise because that is offset by the gravitational field for a net zero effect.
It is the lower density of the air within the balloon that causes it to rise spontaneously.
Stephen Wilde, this is a false dichotomy. The balloon will begin to rise if and only if the net force is up. This net force is the sum of the weight of the balloon (down) and of the buoyant force (up). The pressure differential around the balloon determines the strength of the buoyant force. In conditions of hydrostatic equilibrium within the surrounding, it is equal to the weight of the displaced fluid. The expansion of the balloon increases the buoyant force because it then displaces more air around it. It doesn’t change the weight of the balloon. But just changing the external buoyant force thereby changes the net external force.
I found an aeronautics site which explained that the effect of the pressure differential between the top and the bottom of a balloon is negated by the pull of gravity on the balloon for a zero net effect.
That applies to solids such as the material that comprises the fabric of the balloon.
Gases are different so if you have a lower density of gas at a given temperature as compared to the surroundings then it will rise spontaneously towards a region of lower pressure.
The ballooon will rise only when the reduced density within it swings the balance between the pressure differential from top to bottom and the gravitation pull downwards.
The point is that:
Solids to not rise upward when heated. An external buoyancy force is needed.
Liquidfs do not rise up when heated. An external buoyancy force is needed.
Gases DO rise up when heated.An external buoyancy force is NOT needed.
Gases do that without any external buoyancy force pushing them up simply because warmer, lighter gases are inherently more buoyant than colder, heavier gases and will alter their position along the lapse rate slope spontaneously if they are not at the correct height for their temperatutre and density.
I can sense that you are unwilling to consider the possibility that it is so.
Stephen Wilde,
SW: “I found an aeronautics site which explained that the effect of the pressure differential between the top and the bottom of a balloon is negated by the pull of gravity on the balloon for a zero net effect.”
As I said earlier, under conditions of hydrostatic equilibrium, the buoyant force on a body (or air/liquid parcel) is equal and opposite to the weight of the displaced fluid. So, of course, when the density of the balloon is the same as the density of the ambient air, the two forces will be equal and cancel exactly.
When the density of the gas in the balloon is less than the density of the surrounding air, the the buoyant force is exactly the same (since it still is equal to the weight of the displaced outside air) but the weight of the gas is reduces, so the two forces don’t exactly cancel anymore.
“Gases DO rise up when heated.An external buoyancy force is NOT needed.”
The gas rises when heated because when it thermally expand the buoyant force increases as a result. That’s because the gas thereby displaces more surrounding fluid. The weight of the gas remains the same, and now the weight doesn’t cancel the buoyant force anymore. So, the net external force is up. Newton’s second law isn’t falsified.
Forget the buoyancy. Just assume there is a black body held at a fixed temperature like 350K suspended at say 4000 m.
Clivebest, I am just trying to address SW’s simple misconception that rising parcels of air exchange internal energy for gravitational potential energy.
Clivebest, sorry. I hadn’t noticed your brain teaser.
Pierre said
“The gas rises when heated because when it thermally expand the buoyant force increases as a result. That’s because the gas thereby displaces more surrounding fluid. The weight of the gas remains the same, and now the weight doesn’t cancel the buoyant force anymore. So, the net external force is up. Newton’s second law isn’t falsified.”
If the expanded gas displaces more surrounding fluid then the buoyant force is coming from the expanded gas and NOT from the surroundings.
Note that it is the expanded gas that was heated and not the surroundings that were cooled.
My point stands but I have long since forgotten why you thought it relevant anyway.
Didn’t I point out previously that such a semantic point made no difference to the existence or otherwise of the gravito thermal effect which requires a store of KE at the surface to sustain the continuing convective cycle without being radiated to space ?
In the case of Earth 33K above S-B
SW wrote: “If the expanded gas displaces more surrounding fluid then the buoyant force is coming from the expanded gas and NOT from the surroundings.”
This is like saying that when you sit on a table, the force that holds you up “is coming from” your making contact with the table and not from the table. Maybe that’s true in some sort of causal sense. From the point of view of Newtonian mechanics, it’s still an external force that holds you up against gravity. Likewise it’s still the pressure differential within the surrounding air that pushes the expanding air parcel up against gravity.
“Note that it is the expanded gas that was heated and not the surroundings that were cooled.”
Yes, in a sense, the expansion of the gas created the conditions whereby the net external force on the gas is directed up. It’s still the external force that does the mechanical work.
“My point stands but I have long since forgotten why you thought it relevant anyway.”
You also forgot the point of your own argument. Your point was to deny that the work that is responsible for the increase in gravitational potential of the rising air parcel comes from the surrounding (and ultimately, as I argued, from the gravitational potential energy lost by other parcels of air that are descending while the expanding parcel rises in their midst). That’s because you ultimately were arguing that the gain in potential gravitational energy of the rising parcel rather results from the conversion of (some of) the kinetic energy of the molecules of the air parcel. If this energy rather comes from descending parcels of air around it, your point doesn’t stand.
You were confusing two different processes: one that is responsible for the increase in gravitational potential energy (buoyancy), and a different process (adiabatic expansion) that is responsible for the decrease in internal energy. Since those processes have different energy sources, they need no be in balance with one another. There is no process of conversion of molecular kinetic energy into gravitational potential energy.
“the work that is responsible for the increase in gravitational potential of the rising air parcel comes from the surrounding (and ultimately, as I argued, from the gravitational potential energy lost by other parcels of air that are descending while the expanding parcel rises in their midst). ”
The surrounding is the gravitational field and not adjacent molecules.
The loss of GPE in the descending air becomes KE since the descending air warms.
The loss of GPE in the descending air does NOT become GPE in the ascending air.
At all times the total energy content of both parcels of air tremains constant and no energy passes between them.
Each parcel works against gravity, one against gravity as it rises and the other with gravity as it descends.
I think you are totally confused and wasting my time.
“the work that is responsible for the increase in gravitational potential of the rising air parcel comes from the surrounding (and ultimately, as I argued, from the gravitational potential energy lost by other parcels of air that are descending while the expanding parcel rises in their midst). ”
Totally confused and wasting
myeveryone’s time.Spooky potential energy exchanges at a distance. Now I’ve heard everything.
The standard model is missing yet another particle now… a particle that carries the force of gravity and a particle that carries the force of gravitational potential energy. ROFL
“Spooky potential energy exchanges at a distance. Now I’ve heard everything.”
That’s not spooky at all. If you forcefully sink a cork near the bottom of a bucket of water (pushing it down with a thin metal rod, say), this forces some of the water to rise in the bucket and thereby gain gravitational potential energy. Even after the cork is fully immersed, as it moves down, the average height of the water mass increases. If the cork is then allowed to rise again from the buoyant force alone, then the average height of the total mass of water will progressively diminish as the cork rises (even before it is begins to emerge at the surface). So the water will progressively lose gravitational potential energy at the exact same rate as the work that it perform through lifting the cork (some of which is converted in gravitational potential energy of the cork, some in kinetic energy, and some converted to heat through viscous dissipation). This potential gravitational energy loss of the surrounding fluid is the source of the work performed by the buoyant force.
“This is like saying that when you sit on a table, the force that holds you up “is coming from” your making contact with the table and not from the table.”
O…M…G that is one of the least informed things I’ve heard here in a while.
There is no “force” holding me up when I sit on a table. The muscles in my legs provided the force to lift my a$$ up to the table height. Energy isn’t expended to sit there once elevated and potential energy provided by my legs isn’t bleeding off.
And where I come from we sit on chairs not tables. And we don’t have to fuel our chairs so they have enough force to hold us off the ground indefinitely. ROFLMAO
David Springer, you are jumping on all my comment while ignoring what I am responding to. SW was claiming that the surrounding air can’t perform work on a buoyant air parcel just because the existence of force is caused by the expansion of the parcel. This is a non sequitur and my table sitting example merely illustrates why it is.
It appears that Climate Etc don’t uniformly appreciate these engineering facts:
http://images.the-scientist.com/content/figures/0890-3670-041011-32-1-1.jpg
• ultracentrifuge rotors spin in a vacuum, and
• the rotors themselves are not cooled in any way, and
• the drive-motors are cooled by an ordinary heatsink (no different from the heatsinks of an desktop computer).
Needless to say, the thousand-degree temperatures that the gravito-thermal effect (if it existed!) would generate in million-g untracentrifuges would swiftly destroy biological samples.
Observation This doesn’t happen.
Conclusion There just plain ain’t no such thing as a “gravito-thermal” effect!
Fan do you have a site for anyone that claimed the effect was huge?
AFOMD,
Surprise! I agree with you.
When using ultracentrifuges for uranium enrichment, external heat is required to obtain the required convection. Zippe centrifuges have been the subject of intense research, and there is a distinct lack of gravito-thermal effect in the peer reviewed literature, noted by users, or claimed by manufacturers.
Like the CO2 greenhouse effect, it purely doesn’t exist. Wishing will not make it so.
Live well and prosper,
Mike Flynn.
Dang, me and FOMD agree!! Stars collide, the sun rises in the west, this doesn’t happen often …
Nice example, FOMD, well done.
w.
FOND,
Thank you. You are clearly such a wise man.
What a pity you don’t contribute without all the silliness. I would not have seen the comment without Willis’s comment pointing to it.
Yeah – heating to Sun like temperatures doesn’t happen everyday in centrifuges.
Seriously – where is this energy meant to come from? Ambient temperatures? FOMBS as usual is not worth a first glance.
Note that during the very first convective cycle, whilst KE (equivalent to 33K) is being converted to PE and no PE is yet being returned to the near surface, the surface is losing energy by radiation to space AND to the first convective cycle via conduction.so the surface temperature will drop below 255K for a while.
When the first convective cycle completes and adiabatically warmed air is being returned to the surface at the same rate as surface warmth is being taken up adiabatically then the surface temperature rises to 288K because:
i) Incoming solar energy continues to arrive at a rate commensurate with a surface temperature of 255K AND
ii) Descending adiabatically warmed air is returning to the surface at a rate commensurate with surface warming of 33K AND
iii) The next convective cycle is simultaneously removing KE from the surface at a rate commensurate with surface warming of 33K thereby locking it away in PE which is not heat and does not radiate.
The net outcome is that the surface temperature of 288K is provided by 255K from the sun plus 33K from descending air but the surface cannot use that 33K for radiation to space because it is recycled into further convective uplift. Nevertheless the surface temperature will still be enhanced by 33K because the energy required by the ongoing convective cycle is still held at the surface.
The result is a surface temperature of 288K, 255K escaping via radiation to space and 33K continuing to support the weight of the atmosphere.
Some AGW proponents say that adiabatically descending air that has been warmed cannot heat the surface.
It doesn’t have to warm the surface directly. All it has to do is provide a less steep lapse rate which inhibits convection so that the surface warms from solar irradiation more than it otherwise would have done.
We see that all the time within atmospheric high pressure cells containing descending air and often they create an inversion which blocks convection altogether.
The irony is that reducing or blocking convection is what the glass in greenhouses does.
That descending adiabatically warmed air acts just like the glass on a greenhouse roof by reducing convection so it is mass acting via the adiabatic convective overturning cycle that is and always was the true greenhouse effect.
The term ‘Greenhouse Effect’ must have been originally coined by a meteorologist maybe 100 years or more ago who realised that adiabatically warmed air by virtue of being transparent and inhibiting convection would act exactly like a greenhouse roof.
The radiative chaps never learned that so they often say that the term is misleading.
The term might be misleading in terms of their attempt to use it in connection with their imagined radiative only scenario but it is spot on in terms of long established meteorology.
The thing is that meteorology was a very arcane subject in the 20th century and earlier.
Hardly anyone knew anything about it and a lot of the ways the laws of physics play out within an actual atmosphere are counterintuitive and hard to envisage such as the thorny concept of adiabatic processes.Everyone I discuss it with is oblivious to its true nature.
In the 1980s or thereabouts a bunch of astrophysicists thought they could take over climate science with no knowledge of basic meteorolgy and they have spread nothing but confusion in their wake.
Made them rich and famous though.
The Greenhouse Effect is perfectly described as a process that occurs as a result of a transparent layer of warm air that inhibits convection so as to allow the sun to warm the surface to above the S-B figure of 255K.
On average for the Earth as a whole the surface temperature enhancement for the mass induced ghreenhouse effect is 33K leaving no room for any contribution from radiative gases.
Believe it or not. Your choice :)
‘Needless to say, the thousand-degree temperatures that the gravito-thermal effect (if it existed!) would generate in million-g untracentrifuges would swiftly destroy biological samples.’
Temperatures created presumably by energy from quantum vacuum zero-point energy spontaneously emerging in this space/time as the rotor spins?
But it is potential energy of the atmosphere that I wanted to discuss briefly. The atmosphere has no potential energy as a whole – it is sitting in a gravity well and has no potential to flow anywhere by and large. Within the atmosphere there are multiple processes that change the height of individual molecules as some rise and some fall – but this doesn’t change the net zero of the PE of the atmosphere as a whole. The table sits on the floor – it has zero PE assuming it doesn’t collapse.
The processes for air movement are turbulence and convection – these change the bulk properties of specific regions of the atmosphere and these processes – extending down to high frequency micro-eddies – change the velocities of individual molecules as energies ebb and flow. .
The point is that simple Newtonian consideration of potential and kinetic energy at the molecular level do no begin to approach the complexities of the real atmosphere.
“The atmosphere has no potential energy as a whole – it is sitting in a gravity well and has no potential to flow anywhere by and large.”
It has potential energy relative both to the centre of gravity of the Earth and that of the Universe.
“Within the atmosphere there are multiple processes that change the height of individual molecules as some rise and some fall – but this doesn’t change the net zero of the PE of the atmosphere as a whole. ”
No it doesn’t but rising molecules gain more PE at the expense of KE and falling molecules gain more KE at the expense of PE. It may be a net zero process but it means that there is constant work being done and so to maintain the circulation a KE store (33K for Earth) needs to be present at the surface over and above the KE needed to radiate to space at 255K.
Interestingly enough, the Moon experiences higher surface temperatures than the Earth, even though it lacks significant atmosphere, and has less gravity than the Earth.
So it would appear that an atmosphere combined with higher gravity reduces the maximum surface temperature, devout belief to the contrary notwithstanding.
Gravito-thermal effect? Excellent for promoters of free energy, perpetual motion, or purveyors of tinfoil hats. Merely a source of mild amusement for the person of average intelligence, it would appear.
Live well and prosper,
Mike Flynn.
NASA gives the Bond albedo of the moon as 11% – and all energy is radiated from the surface. No convective because no water or atmosphere of course. This energy balance balance is what determines the temperature of the moon’s surface.
It is not of course relevant to the Fronsdal paper – which Mike understands perfectly he says. Perhaps you can fill us in on where he goes wrong Mike?
Rob Ellison,
I can’t figure what you are trying to say. Are you disputing the facts as I understand them?
I cannot understand the relevance of your first sentence, or the second, or the third.
I am not sure where I said I understood Fronsdal’s paper perfectly. you might care to provide a copy of my words, if you have them handy.
Are you really interested in understanding where Fronsdal’s reasoning is at fault? I will be happy to help, but first could you let me know why Fronsdal has been unable to obtain the use of an ultra centrifuge to perform his proposed experiment. He has been endeavouring to get someone to perform the experiment for at least 8 years that I am aware of. I suspect that like experimental verification of the greenhouse effect, attempts to show the existence of the gravity-thermal effect in fact show there is none.
I will defer to your superior knowledge, if you can back it up with some evidence.
Live well and prosper,
Mike Flynn.
Oh Mike – stop prevaricating. The situation of an atmosphere under gravity is obviously different to that of no atmosphere under a lesser gravity.
There are several other differences between the Earth and the Moon that seem quite obvious – but that I won’t labour.
I of course have no clue as to why an expensive piece of lab equipment modified for the specific needs of the experiment is not readily available – I will bow to your infinite wisdom here.
The first mention of the centrifuge experiment I am aware of was a 2010 arxiv.org paper. Perhaps you help me by linking this much earlier reference?
But you did say you understood the 2014 paper – complex and advanced math and physics that I struggle so hard with. So where did he go wrong? Don’t be shy – we all want to know.
Oh – and as to what you don’t remember claiming. I won’t bother with the thankless task of searching through comments in far flung post – well a couple of weeks at least.
I don’t know – perhaps we can ask P-N if he can refresh your memory. P-N was interested – seeing as you understand it so well – to have it explained to him as well.
Rob Ellison,
You obviously wouldn’t be able to understand my critique of Fronsdal’s paper, if you cannot understand the original. I don’t believe your demand is sincere, but I’m willing to change my mind.
Nice try. A fact or two would be appreciated.
I can’t help it if you have difficulty understanding reasonably straight forward concepts. Maybe your Warmist fervour exceeds your ability – what do you think?
Both the gravito-thermal effect and the CO2 greenhouse effect remain firmly ensconced on the same shelf as phlogiston, caloric, and the luminiferous aether, until demonstrated otherwise.
By the way, it might serve you better to cut and paste what I wrote, rather than baselessly assert what you wish I had written. This will help other readers to distinguish fact from fiction, I would hope.
Live well and prosper,
Mike Flynn.
I am sorry that you found the paper difficult. I did not. I disagree with some of the writer’s speculations. Indeed, he indicated he would be much more satisfied if experimental verification was possible. Alas, to date, no.
Live well and prosper,
Mike Flynn.
Pierre-Normand | October 21, 2014 at 12:35 am |
It’s been a while since I’ve studied thermo and GR at an undergraduate level and we covered nary anything at all of the interaction between those two fields in the GR course. So, if I get round to reading this paper, and encounter some problems, I possibly will rely on you for some help.
Emphasis mine. Happy to refresh you memory from all of a month or so ago.
By all means elucidate on these simple ideas. Which ‘speculations’ did you disagree with? In which specific aspect of the Lagrangian or the Hamiltonian did the error leading to the suggestion of a gravito-thermal effect enter the derivation? Please be assured that I have have reasonably level math skill and will attend with due diligence.
I await your words of wisdom with bated breath.
… reasonably (high) level…
Rob Ellison,
I am happy to indulge you – slightly, at least.
You wrote –
“It is not of course relevant to the Fronsdal paper – which Mike understands perfectly he says. Perhaps you can fill us in on where he goes wrong Mike?”
When I queried your assertion, you responded –
“Oh – and as to what you don’t remember claiming. I won’t bother with the thankless task of searching through comments in far flung post – well a couple of weeks at least.”
Apparently you had a change of heart, and decided to bother after all – and discovered that I had written –
“I am sorry that you found the paper difficult. I did not. I disagree with some of the writer’s speculations. Indeed, he indicated he would be much more satisfied if experimental verification was possible. Alas, to date, no.”
Of course, as usual, I have been provided with no reason to change my opinion. I point out that I never claimed perfect understanding, as you claimed.
I still disagree with some of Fronsdal’s speculations. Given the epithets and vituperative aspersions which you have tossed my way in the past, I assess your present desire that I provide you with knowledge which you lack, as somewhat insincere – I trust you understand why.
You have previously stated, as I recollect, that you ascribe precisely no value to anything I say. So be it. If you wish to ignore me, feel free. I promise I won’t burst into tears!
Live well and prosper,
Mike Flynn.
Well – you seemed to have had a lapse of memory and and insisted that I provide the quote or be found lacking in veracity. That’s 10 minutes I won’t get back – never mind. At least it will in your words help the onlooker to distinguish fact from fiction.
But I am quite disappointed that you – with your deep understanding of atmospheric physics – ‘CO2 has never warmed anything’ – and planetary energy dynamics – ‘the planet has been cooling for billions of years’ – do not give us the benefit of your insights into the Lagrangian and the Hamiltonian for the atmosphere under gravity – and not under gravity – in the Fronsdal paper. As P-N ans I at least am struggling with it and you find it so simple.
I am deeply wounded that you would think me insincere – and don’t answer my detailed questions. Believe me – I don’t ascribe your memory lapse to bad faith but to you having many other things of far greater import on your mind – despite being prompted not once but twice. But be assured that it was for your benefit that I spent the 10 minutes looking for your comment – because I just wanted to clear this up for you as it clearly didn’t ring a bell and P-N hadn’t turned up to confirm. It was clearly not fictionalised on my part – which not having a memory of such a recent claim seemed obviously to you to be a possibility. I hope this corrects the record and sets your mind at rest. .
You have not supplied me with the much earlier reference either. I suppose that’s out of the question too?
And please – far from ignoring you I will continue to benefit from your profound scholarship..
An atmosphere with gravity lowers the highs and raises the lows but overall raises the average.
The sun constantly pumps up the atmosphere against gravity (surface low pressure cells) and gravity constantly pulls it down again (surface high pressure cells).
The ongoing convective overturning needs a KE source at the surface over and above S-B to sustain it.
Basic meteorology, read some.
Can I ask something really simple.
We take an inert gas like helium.
We take a all wavelength transparent container filled with a 1 atmosphere of He at 285K, with the container walls at the same temperature.
What is the emission, W/m2, through the walls of our completely transparent container?
If we lower the pressure to 0.1, 0.01 and 0.001 atmospheres does the emission rate remain constant at the same temperature?
DocMartyn,
I’m not sure where you are heading with this, but the mass of He will reduce, as the pressure drops, assuming the container retains the same surface area.
As the mass drops, the concept of temperature as generally understood becomes somewhat less than useful.
Eventually, you could have a situation where the container encloses one atom of He. Assuming this atom has a temperature of 285K, the pressure will be very low, and the absorption and emission of the relevant photon will result in little average emission through the walls, although the concept of average emission is as useful as that of average anything in this case.
I extrapolate this situation to infer that as the pressure drops, the emissive power will drop in proportion to the mass of the enclosed matter, all else being held constant – which is probably unlikely!
I’m curious – what was your intent?
Live well and prosper,
Mike Flynn.
Perhaps Professor Flynn has had another memory lapse.
‘Emission spectra are produced when atoms of a dilute gas are `excited’ — in effect, heated — by an electrical current, ultraviolet radiation, or some other source of energy. Excited atoms have electrons in high orbits, and these emit photons with specific wavelengths when they jump back down to lower orbits.’ http://www.ifa.hawaii.edu/~barnes/ASTR110L_F05/spectralab.html
Dilute gases – unlike liquids, solids and compressed gases – do not emit a continuous Planck spectrum. An emissions spectra for helium is shown at the site above. Helium absorbs and emits at quite high energies – well above 285K. At lower temps – energy is transferred at the relative snails pace of particle velocities and collisions and the energy flux across Doc’s transparent walls depends on the temperature of the gas and the particle density. I suspect that the walls would emit in IR and the whole package cool down toot sweet.
We have to be a bit forbearing with Professor Flynn – he’s forgotten more than we ever knew.
Rob Ellison,
A helium balloon in a room containing air at 285K will also stabilise at a temperature of 285K. No cooler, no warmer. The balloon will be 285K. The helium will be at 285K. The string holding the balloon will be 285K.
If the air in the room is cooled to 273K, the balloon and its contents will cool to that temperature, unless you use magical Warmist helium which does not radiate light – EMR – and therefore does not fall in temperature.
Conversely, magical Warmist helium will not absorb EMR – light – and will not rise in temperature, for if it did, without being able to cool, it will keep increasing its temperature without pause or obvious limit. This is obviously nonsensical.
A gas cylinder of helium at a pressure of several hundred bars can be both warmed and cooled. The contents, not surprisingly, are likewise warmed or cooled, until they are the same temperature as the container. Helium at 1K, 100K, or 1000K emits radiation, the intensity of which is proportional to the fourth power of the absolute temperature.
However, if you choose to believe otherwise, that is your choice. If you believe that photons move at different speeds dependent upon their wavelength, I beg to disagree.
As I have said before, there seems to be some confusion relating to heat, energy, EMR, temperature, and related matters. All matter can absorb energy. All matter can radiate energy. The laws of thermodynamics – in all their disparate framings – do seem to endure.
Live well and prosper,
Mike Flynn.
As I am sure Professor Mike realises – in the atmosphere of the Earth nitrogen and oxygen are transparent to infrared radiation.
This doesn’t mean of course that the atmosphere doesn’t warm and cool – just that it occurs through molecular collisions. It is greenhouse gases that interact with photons at these frequencies.
That’s a good question. Helium doesn’t have any spectral line in the infrared region. Its least energetic line is at 667.815 nm. That’s well into the red visible spectrum. So, for gaseous helium to emit any photon at all at room temperature and 1atm would possibly require some sort of transient bound state from especially energetic collisions that may occur very seldom. This would be even less common at lower pressures. The emissions power must be extremely small (I would think).
“…would possibly require some sort of transient bound state…”
Maybe ‘transient interaction’ would sound less like an oxymoron.
Pierre-Normand,
With respect, DocMartyn stated that the He had a temperature of 285K. It is therefore emitting photons with the requisite energy appropriate to that temperature. Which is to say, unless my understanding is defective, exactly the same energy contained by photons emanating from any other matter at the same temperature.
A sample of any matter at 285K is just that. It doesn’t matter whether at that temperature said matter is gaseous, liquid, or solid. It is at 285K, and is indistinguishable by temperature from other matter at the same temperature. Helium breathed into the lungs and exhaled is the same temperature as the other exhaled gases.
Helium/oxygen filled dive cylinders will cool down if hotter than the surroundings, and heat up if cooler. The gas mixture is identical in temperature to cylinders of compressed air, or empty cylinders, if allowed to stand for a bit. The spectral absorption properties of the gas are irrelevant to the temperature.
Correct me if I’m wrong, but any gas at room temperature must be emitting photons. It is only at absolute zero (which is a practical impossibility if you think about it), that emission ceases. Hence, no temperature – otherwise known as absolute zero.
There is no such animal as a non radiative gas. All this talk of short wave, long wave, infrared, upwelling, downwelling, serves only to confuse the issue. Things heat up. Things cool down. The laws of thermodynamics don’t distinguish between oxygen, hydrogen, or Bombay Gin – at least at the macro level.
What do you think? Are my facts in error?
Live well and prosper,
Mike Flynn.
Mike Flynn: “With respect, DocMartyn stated that the He had a temperature of 285K. It is therefore emitting photons with the requisite energy appropriate to that temperature. Which is to say, unless my understanding is defective, exactly the same energy contained by photons emanating from any other matter at the same temperature.”
285°K just is 10°C. That’s not very warm. Gases at room temperature (or even colder) don’t glow in the visible spectrum. If a gas doesn’t have any bands in the infrared spectrum, then it will not emit more radiation in the visible light spectrum to compensate for this incapacity. It will emit exactly as much energy in its visible spectral bands as a black-body at the same temperature does at those very same frequencies. At a temperature of 10°C, this means it will emit almost nothing. Look up the Plank radiation curve (Plank’s law) as a function of temperature. The radiation power of a gas within its spectral bands is contained within the envelope of that curve.
http://en.wikipedia.org/wiki/Planck%27s_law
P-N wrote: “It will emit exactly as much energy in its visible spectral bands as a black-body at the same temperature does at those very same frequencies.”
That was incorrect. Replace “exactly as much” by “no more”. Only if the gas volume were very large would it approach the emission power of a solid black-body in those bands.
Mike Flynn I agree re the temp
in your example of 1 molecule it could not have a temperature of 285 K in any physical sense. It is in a vacuum and the concept of temperature becomes meaningless.
Pierre Normand
The gas is at 285 K , It has to emit energy if it is cooling down or staying at the same temperature due to incoming energy. It will emit that energy at some frequency that that degree of energy can provide. If not visible light, red light or some infra red light then infra red at a lower frequency. It has no choice.
Doc Martin, The spheres could also be of different sizes to account for the different pressures. To be at the same temperature the low pressure large sphere would have to have extremely fast moving particles. The surface areas for emissivity would be quite different.
Despite all this I guess Helium is helium because it has an unchanging signature and hence an unchanging rate of emission until one reaches very cold conditions.
Personally I expect the larger surface area (lowest pressure or thinner gas) would have to emit more heat as less of the emitted heat is reabsorbed by the gas in the container as there are less atoms in the way of the outgoing radiation but this effect would be minuscule.
angesh wrote: “If not visible light, red light or some infra red light then infra red at a lower frequency. It has no choice.”
Real helium gas in the laboratory still chooses not to emit any radiation at all in the infrared spectrum (or any lower frequency). Contrary to your expectation, helium atoms may be endowed with free will.
Pierre-Normand,
Real helium gas can absorb energy. It warms. If it radiates energy, it cools. If you have helium gas in a laboratory which radiates energy not at all, by definition it is at absolute zero. If it is above absolute zero, it is radiating energy at a wavelength dependent on temperature.
Neither helium nor any other gas refuses to emit photons if it is above absolute zero, in a laboratory or otherwise. Whether you agree or not, Nature doesn’t care. If something has a temperature, it is radiating energy.
As a side note, many people still view heat related phenomena in classical terms, which can lead to incorrect conclusions. Conduction is an example. As you know, I’m a CO2 warming non believer. The Warmists have to have non-radiating gases, perfectly opaque gases, an initially cold Earth, surfaces which radiate energy without a concomitant drop in temperature, and other similar strange things.
Luckily for me, Nature seems to be similarly inclined – at least at present.
Live well and prosper,
Mike Flynn.
Mike Flynn: “Real helium gas can absorb energy. It warms. If it radiates energy, it cools. If you have helium gas in a laboratory which radiates energy not at all, by definition it is at absolute zero. If it is above absolute zero, it is radiating energy at a wavelength dependent on temperature.”
Yes, it radiates energy at some definite frequencies. There just aren’t any such frequencies in the infrared spectrum in the case of gaseous helium. It doesn’t have any spectral line in that region. That’s an empirical fact that confirms quantum theoretical models of the helium atom. It can emit in the visible spectrum where it has some spectral bands. But those photons are much more energetic than infrared photons and hence require inter-molecular collisions that are more energetic than is typical for a helium gas at room temperature. Hence is emits such photons very seldom. It radiatively cools, but extremely slowly.
I may be missing something here, but wouldn’t a transparent container containing a transparent gas simply transmit whatever radiation entered from outside the container? The whole assembly will still be in local thermal equilibrium with its surroundings and a thermometer inside the container will read the same as one in the room outside of the container. Otherwise, you could have a perpetuum mobile.
Pochas, yes, it would transmit it. It would transmit it equally well whatever its temperature is. If radiation is the only kind of thermal interaction, then if the initial temperatures are different, it will possibly take centuries for thermal equilibrium to be attained between the helium in the container and its surrounding (maybe isolated though some vacuum) through the exchange of the odd photon energetic enough to interact with the gaseous helium.
Nitrogen cylinders are a frequent item of commerce, and I am unaware that they behave any differently than compressed air as they equilibrate to room temperature. At temperatures below 1000 F convection dominates and radiation is relatively unimportant. Radiatively “transparent” gasses convect like any other gas. The thing is, that thermodynamic temperature is related to the kinetic energy of the gas molecules, and not to radiation flux. In order for radiation to translate to temperature, a photon must be absorbed by an atom which kicks an electron to a higher orbital, then that electron decays to its ground state, and its energy can be released either by emitting another photon(s) of lower energy, or as kinetic (heat) energy and that second process results in an increase in temperature. Please forgive the lecture, but if we are to grasp anything at all about thermodynamics, we must understand these things.
As I’m sure Professor Mike meant to say – despite being being transparent the walls can be heated by particle collisions and will emit in IR even into a surrounding vacuum.
Pochas,
I was addressing DocMartyn’s question, which is specifically about radiation. Conduction and convection is something else. Nobody denies that it would be hard to prevent a compressed helium gas to conduct heat to the container. That’s besides the point. The question is about the amount of radiation from the helium gas at 385°C.
Speaking of greenhouses.
They warm up inside because the glass lets solar radiation in and then prevents convection.
Consider the atmosphere, in which air cools adiabatically as it rises and then warms adiabatically as it descends.
That adiabatically warmed descending air becomes largely transparent because it causes clouds to dissipate which is why surface high pressure cells are usually cloud free.
That adiabatically warmed descending air reduces the lapse rate slope and often reverses it in so called inversions and that inhibits or even blocks convection.
Convection being reduced or prevented, the solar heated surface is then able to rise 33K above S-B on Earth.
The term ‘Greenhouse Effect’ is a perfectly accurate description of the surface warming effect from descending adiabatically warmed air.
That must have been the original thought behind the first use of the term and it applies to up and down transport of mass within the atmosphere and not radiative fluxes.
The term ‘Greenhouse Effect’ has been hijacked by the radiative physics crowd and applied to an entirely different scenario. Enhanced radiation at the surface increases convection rather than reducing it so the term is wholly inappropriate for a radiative situation..
Hence all the confusion.
Stephen Wilde reminds me of someone who pretends to speak French.
To others who know no French, he might even sound convincing.
However those who speak French know its all gobbledygook.
They would advise Stephen to go and take some French lessons,but alas he will not
Its good that Stephen is interested in thermodynamics but well wishers would advise Stephen to read a good textbook on the subject.
LoL Mike Flynn, it’s mighty good that folks like you and Willis Eschenbach and even Peter Lang have all come to appreciate that ultracentrifuge evidence renders the gravito-thermal hypothesis dead as a dodo.
However, it’s not clear that Climate Etc folks (as yet) appreciate that, by the similar arguments of FOMD’s self-evaluation test of
thermodynamic and heat-transport intuition …
http://upload.wikimedia.org/wikipedia/commons/3/37/MultiLayerInsulationCloseup.jpg
… NASA’s hugely successful multilayer superinsulation technologies show plainly that the fundamental mechanism of CO2-amplified greenhouse physics is entirely correct, in that:.
• each increment of NASA-superinsulation increases the ability of a thermos-bottle to retain heat, and similarly
• each increment in CO2 concentration increases the ability of the earth to retain heat.
Of course, phenomena like lapse rates, aerosols, and circulation considerably enliven planetary physics relative to thermos-bottle physics … but the basic physical mechanism of the greenhouse effect still works.
Conclusion Good on `yah, NASA engineers and thermodynamicists … for showing the world plainly that the fundamental heat-transport mechanism that drives AGW ain’t rocket-science.
Oh wait … yes it is!
I suspect that star like temperatures don’t evolve in FOMBS centrifuge for good reason – the lack of zero point quantum energy perhaps.
But the essential atmospheric physics of the greenhouse effect is interaction with outgoing IR and subsequent emission in specific frequencies in random directions. The scattering effect can be observed from space using narrow aperture observing devices. The difference between 1970 and 1997 is shown here as an equivalent black body temperature.
https://watertechbyrie.files.wordpress.com/2014/12/harries-2001.png
Although we have it on impeccable authority – Professor Mike – that this is incapable of warming the surface through increased downward radiation – and that the Earth is in fact cooling from the core out. This beats heck out of zero point centrifuge energy – so suck eggs FOMBS.
Pekka, “I agree with Gibbs and Jaynes.”
I am glad, sorry I missed your other comments
Rob Ellison,
Any warmer body will emit radiation which if absorbed by a cooler body will result in both bodies being in thermal equilibrium, eventually, in the absence of changing external energy inputs.
If you are referring to the nonsensical CO2 warming concept, may I respectfully point out that energy emanating from the surface results in a lowering of surface temperature. Even if one hundred percent of the outgoing energy is absorbed by the atmosphere, and radiated back to the surface, the best that can happen is that the surface temperature does not fall.
Now the only thing that will return one hundred percent of the outgoing radiation is a perfect insulator, which by definition will allow no energy from the Sun to reach the surface. Of course, Warmists continue to ignore physics, and espouse the nonsense that arises from their ignorance. The fact that the CO2 warming effect, like the gravito-thermal effect, cannot be shown to exist, deters the Warmists not one jot.
In relation to the Earth having cooled since its creation in a molten state, you seem to dispute this being fact. I must admit to the assumption that the Earth’s surface was originally molten, and observe that currently it is not, and draw the inference that it has therefore cooled.
You may assume that the Earth was created at absolute zero or thereabouts, and due to the magical and mysterious effects of CO2, in combination with the distant Sun, heat has been absorbed to the point where the interior of the Earth is now molten, and the surface will continue to warm until it too, is molten. AFOMD appears to subscribe to this view, as does another commenter who proposes the mechanism of heat creep to overcome the inherent defects of the initial cold Earth theory.
I suppose I should ask if you believe that the Earth was created with a colder surface than is now the case, and if you believe that the core, if hotter than space surrounding the Earth, is either losing no energy at all, or accruing energy and heating up. I presume you can adduce some logic to support your contention, and if so, I would be most grateful to be apprised of same.
I suggest, once again, that you quote me directly, rather than ascribing to me words which you think or wish I uttered.
Live well and prosper,
Mike Flynn.
Dear Professor Mike
Any warmer body will emit radiation which if absorbed by a cooler body will result in both bodies being in thermal equilibrium, eventually, in the absence of changing external energy inputs.
Far be it for me to correct such a distinguished scholar of quantum mechanics. But dilute gases may not be a body in the sense of a fluid or a solid – and may not emit in a continuous spectrum.
If you are referring to the nonsensical CO2 warming concept, may I respectfully point out that energy emanating from the surface results in a lowering of surface temperature. Even if one hundred percent of the outgoing energy is absorbed by the atmosphere, and radiated back to the surface, the best that can happen is that the surface temperature does not fall.
Nonsensical? Right – got it. Added energy at the surface does not result in a temperature rise.
Now the only thing that will return one hundred percent of the outgoing radiation is a perfect insulator, which by definition will allow no energy from the Sun to reach the surface. Of course, Warmists continue to ignore physics, and espouse the nonsense that arises from their ignorance. The fact that the CO2 warming effect, like the gravito-thermal effect, cannot be shown to exist, deters the Warmists not one jot.
Right – the increase in IR interaction with gases in the atmosphere between 1970 and 1997 is not observational proof in the atmosphere of laboratory results.
https://watertechbyrie.files.wordpress.com/2014/12/harries-2001.png
Git it – sorry.
In relation to the Earth having cooled since its creation in a molten state, you seem to dispute this being fact. I must admit to the assumption that the Earth’s surface was originally molten, and observe that currently it is not, and draw the inference that it has therefore cooled.
You may assume that the Earth was created at absolute zero or thereabouts, and due to the magical and mysterious effects of CO2, in combination with the distant Sun, heat has been absorbed to the point where the interior of the Earth is now molten, and the surface will continue to warm until it too, is molten. AFOMD appears to subscribe to this view, as does another commenter who proposes the mechanism of heat creep to overcome the inherent defects of the initial cold Earth theory.
Obviously I had assumed heat transfers from the core and mantle at 0.05W/m2 was some 3000 times less than the 161W/m2 hitting the surface from the Sun – and even the changes in the energy flux – incoming and outgoing – were orders of magnitude greater then the core and mantle flux.
Sorry. Where would I be without Professor Mike.
I suppose I should ask if you believe that the Earth was created with a colder surface than is now the case, and if you believe that the core, if hotter than space surrounding the Earth, is either losing no energy at all, or accruing energy and heating up. I presume you can adduce some logic to support your contention, and if so, I would be most grateful to be apprised of same.
You have obviously forgotten again that we have discussed this – and I have gone into the various processes that create core and mantle heat.
I had thought that the surface warms and cools due to the transient difference between incoming and outgoing energy at a nominal top of atmosphere where all energy flux is radiative. This is obviously a fairly popular. I apologise for falling for it.
I suggest, once again, that you quote me directly, rather than ascribing to me words which you think or wish I uttered.
You may suggest again – but I did quote your comment of a month ago that I referenced twice – and which you had forgotten – despite being reluctant to search through the back issues for something that was clear in my memory. You then complained that I went searching through the back issues. As I said – you have many more important things on your mind than a throwaway comment that you were sorry that I was finding the paper difficult but that you understood it perfectly. I am disconcerted – what I claimed you said – was what you had said.
Equally my shortform versions – CO2 has never warmed anything by surrounding it – the Earth is cooling from the core out – seem quite accurate depictions of your positions on the topics.
Having memorized each and every one of your uniquely valuable contributions – I humbly suggest that this may be another – quite understandable – memory lapse and not bad faith at all.
.Rob Ellison,
I am pleased that you are in the process of abandoning the tenets of of the false prophets of Warmism, and moving towards the lights of logic and reason, not to mention science.
Now that you have accepted that the surface of the Earth has, indeed, cooled, and continues its remorseless and relentless slow cooling as evidenced by geophysical measurements by real scientists, you are well along the road to reality.
In relation to your attempt to claim that dilute gas cannot be treated the same as any other matter, I suggest you measure the temperature of the gaseous contents of a mercury vapour lamp as instanced in the common fluorescent lamp, when in the off, or unexcited, state.
Alternatively, radio valves of some types contain very dilute gas, or failing that, gas discharge tubes using noble gases such as neon, can be examined. The contents, after stabilising at 20C, will be found to be at 20C. If the surrounding temperature is reduced to 10C, the tube and its contents will be found to fall to 10C. You will notice that the dilute gas manages to achieve this as does all other matter, by emitting radiation in line with its temperature. No glowing, no emission spectra – it cools by the same mechanism as tube within which it is contained.
You may not like it, you may choose to avoid the fact by performing a lateral arabesque and then flying off at a tangent while whirling like a Dervish, but Nature cares even less than do I!
You mention falling for the TOA energy balance scam. No need to apologise, smarter people than either of us have been sucked into this one!
You have rather accurately summarised the facts of the Earth cooling, and the inability of CO2 to warm anything at all by increasing its energy content, merely by surrounding it. Hold fast to these truths!
I am pleased to be able to assist in your attempts to throw off the Warmist shackles. Many have escaped the cult, and subsequently resumed a normal life. Although some have found difficulty dealing with the ostracism and perverted attempts to reinculcate Warmist dogma, most feel a sense of relief at once more being able to exercise free will.
I sincerely hope you succeed in your endeavours. Remember I am always there to assist, if you need my help.
Live well and prosper,
Mike Flynn.
Professor Mike
I am pleased that you are in the process of abandoning the tenets of of the false prophets of Warmism, and moving towards the lights of logic and reason, not to mention science.
I am quite confident that there has never been any logic, reason or science to match it.
Now that you have accepted that the surface of the Earth has, indeed, cooled, and continues its remorseless and relentless slow cooling as evidenced by geophysical measurements by real scientists, you are well along the road to reality
I still find it quite difficult to get past data showing the Earth and oceans being warmed from the top down for several hundred metres. No doubt purely invented by false prophets. .
In relation to your attempt to claim that dilute gas cannot be treated the same as any other matter, I suggest you measure the temperature of the gaseous contents of a mercury vapour lamp as instanced in the common fluorescent lamp, when in the off, or unexcited, state.
We should probably consider luminesence, incandesence and the energies available in a maercury vapour lamp – not just a gas at 285K.
A heated gas in a tube – when turned of – will thermalise the walls through elastic collision and the walls will emit IR to cool the whole – even without emitting radiation directly from the gas. As I said before. However – I look forward to your instructions on this and other matters.
Alternatively, radio valves of some types contain very dilute gas, or failing that, gas discharge tubes using noble gases such as neon, can be examined. The contents, after stabilising at 20C, will be found to be at 20C. If the surrounding temperature is reduced to 10C, the tube and its contents will be found to fall to 10C. You will notice that the dilute gas manages to achieve this as does all other matter, by emitting radiation in line with its temperature. No glowing, no emission spectra – it cools by the same mechanism as tube within which it is contained.
It will cool off toot sweet – bot traditional quantum theory says gases absorb and emit emit in specific frequencies. This is no doubt another false prophecy. Thanks for clearing that up. Funny – we used to call them vacuum tubes and they got much hotter than that. I stand corrected.
You may not like it, you may choose to avoid the fact by performing a lateral arabesque and then flying off at a tangent while whirling like a Dervish, but Nature cares even less than do I!
You mention falling for the TOA energy balance scam. No need to apologise, smarter people than either of us have been sucked into this one!
You have rather accurately summarised the facts of the Earth cooling, and the inability of CO2 to warm anything at all by increasing its energy content, merely by surrounding it. Hold fast to these truths!
An arabeque involves standing on one leg while turning out the other leg and extending it behind – performed en point, demi pointe or a flat foot. But it is not clear to me what the mixed metaphor is intended to convey.
Hardly – what I have done is accept on your authority that increased energy at the surface does not result in a warming surface.
Climate Etc’s many students of thermodynamical climate-science are well-advised to heed the sage advice of the great Lev Landau:
Conclusion Nowadays, young researchers (especially) are well-advised to study thermodynamics the modern way … in the language of geometric dynamics … with particular care that every macroscopic thermodynamical assertion is solidly and explicitly grounded in statistical mechanics and (microscopic) Hamiltonian flows.
This unified program afford WONDERFUL levels of thermodynamical understanding!
Best wishes are extended to all Climate Etc readers, for continued enjoyment and success in appreciating thermodynamics and statistical mechanics and geometric dynamics in the modern style … as one unified subject!
Actually, the Loschmidt Paradox aka gravito-thermal effect is a bit of a statistical anomaly. The Maxwell-Boltzmann distribution assumes perfect chaos believe it or not, which is not really correct. Seems even chaos is not allowed to be perfect.
So while your centrifugal star equivalent heat generation is amusing, Gibbs entropy which allows for a more reasonable number of degrees of freedom and more likely phase space is the more accurate of the Gibbs versus Boltzmann entropies, at least according to Jaynes. But then entropy is an Anthropomorphic concept, not a property of a physical system which would make “equilibrium” a useful concept, but a property of an experiment, thought or otherwise, not a physical reality.
There is no second law violation using the Gibbs concept, but there can appear to be a second law violation using the Boltzmann concept. Since you are an absolute physics whiz I would have expected you resolve this little paradox quickly.
http://bayes.wustl.edu/etj/articles/gibbs.vs.boltzmann.pdf
CD,
A couple of my comments starting from this one
http://judithcurry.com/2014/11/27/open-thread-thanksgiving-edition/#comment-651077
seem to be directly related to the difference of Gibbs and Boltzmann H functions. I agree with Gibbs and Jaynes.
missed it by this much, Sorry I missed your other comments.
The other comments are a little further in the same thread, but what they add is related to the comments they respond to.
I tend to switch immediately to QM when I consider issues like interaction between molecules. Many concepts of statistical mechanics seem easier for me that way, but that cannot be true to everybody. Having lectured several courses of QM before lecturing thermodynamics for the first time must have something to do with my preference.
This may also be an issue that’s more obvious in Quantum Statistical Mechanics.
There are many paths to appreciating thermodynamics, statistical mechanics, and microscale (quantum) dynamics. Here is one such path … it’s optimized for fun learning AND practical applications.
—————
FOMD’s Thermodynamical Reading List
• Knuth’s “A=B” essay for overall philosophy (e.g. “Science is what we understand well enough to explain to a computer. Art is everything else we do.”)
• Zia et al on Legendre transform to make sure your mathematical foundations are tuned-up.
• Frenkel and Smith on classical simulation algorithms to get your feet wet, Knuth style.
• Onsager on entropy to define entropy the modern way … as a thermodynamic potential, whose hessian is specified by local fluctuations, from which all other potentials can be derived (per Zia et al.).
• Nielsen and Chuang on quantum dynamics to appreciate how quantum measurement back-action enters into the Third Law.
• Murcko’s video on quantum simulation agorithms to advance to the super-hip frontier of modern quantum simulation research.
————–
http://www.youtube.com/watch?v=wa59ZgflJD
Happy learning to all Climate Etc thermodynamicists!
@inbook{Knuth:1996it, Author = {Donald E.
Knuth}, Publisher = {A.~K.~Peters, Ltd.},
Title = {$A=B$}, Year = 1996}
@article{Zia:2009lr, Author = {Zia, R. K.
P. and Redish, Edward F. and McKay, Susan
R.}, Journal = {American Journal of
Physics}, Number = {7}, Pages = {614-622},
Title = {Making sense of the {L}egendre
transform}, Volume = {77}, Year = {2009}}
@book{Frenkel:1996ly, Address = {San
Diego}, Author = {Frenkel, Daan and Smit,
Berend}, Publisher = {Academic Press},
Title = {Understanding {M}olecular
{S}imulation: from {A}lgorithms to
{A}pplications}, Year = {1996}}
@article{Onsager:1953fk, Author = {Onsager,
L. and Machlup, S.}, Journal = {Physical
Review}, Pages = {1505 - 1512}, Title =
{Fluctuations and irreversible processes},
Volume = {91}, Year = {1953}}
@book{Nielsen:00, Address = {Cambridge},
Author = {Michael A. Nielsen and Isaac L.
Chuang}, Publisher = {Cambridge Univ{.}\
Press}, Title = {Quantum {C}omputation and
{Q}uantum {I}nformation}, Year = 2000}
@inproceedings{Murcko:2014aa, Author =
{Mark Murcko}, Booktitle = {Advances in
Drug Discovery and Development}, Month =
{24 September}, Organization = {Chemical
\&\ Engineering News (Virtual Symposium)},
Title = {Accelerating Drug Discovery:
The Accurate Prediction of Potency"},
Year = {2014}}
Hmmm … let’s try this link to
http://www.youtube.com/watch?v=wa59ZgflJD8
Mark Murcko’s Accelerating Drug Discovery: The Accurate Prediction of Potency
Note For reasons unknown, these simulation quantum algorithms work better than we expect them to.
Welcome to cutting-edge quantum simulation-science!
Physics is of interest but usually in climate is the uncountable in Einsteins bon mot. Mistaking arm waving at general principles – as I have said – for fundamental physical enlightenment is unlikely to be of much value in a large, complex and dynamic system. Of far greater relevance than quantum mechanics to the macro systems state is that third great idea in 20th century physics – after relativity and quantum mechanics.
I tend to read quite broadly in the Earth sciences – here’s a recent article fully referenced for instance – and fill in a picture from a wide variety of credible internet sources – including on physics.
http://watertechbyrie.com/2014/06/23/the-unstable-math-of-michael-ghils-climate-sensitivity/
Does FOMBS have a big picture – or is this merely vaguely waving at the barely relevant? Don’t bother answering – it’s a rhetorical question.
AFOMD,
Your NASA thermos-bottle contains no CO2 as insulation. It is known as a vacuum flask for good reason. NASA has more sense than to introduce CO2 into the vacuum of the thermos-bottle.
You may be unaware that Thermos is a trade name. I assume that NASA would prefer that you use the generic terms vacuum flask or Dewar flask to describe the insulated container.
In any case, NASA has not managed to produce any insulators with greater R values than previously known. Aerogels are vastly inferior to vacuum insulated panels, although more practical in many cases. In any case, not even NASA would be so foolish as to use CO2 in an aerogel – although they have some other strange things, and employed some odd people. If you are aware of any available insulator with better R values than a properly constructed Dewar flask, I would be most interested to hear from you.
NASA scientists and engineers have managed to overlook or ignore some basic principles which have resulted in avoidable deaths. This is rocket science in the real world, unfortunately.
It might behove you to use NASA as a reference more appropriately, if you wish to avoid being seen as desperately clutching at straws whilst attempting to remain erect in the absence of any legs on which to stand.
Phlogiston, CO2 warming effect, gravito-thermal – all shattered dreams, I fear.
Live well and prosper,
Mike Flynn.
Three simple points:
• Multi-layer insulation (MLI) ain’t aerogels (this video shows MLI being laid-down)
http://www.youtube.com/watch?v=vRh0Jkqd27Q
• Yes, MLI does supply far better insulation (typically 0.1 mW/m-K) than any solid insulation.
• In climate-science, CO2 plays the role of the heat-trapping mylar film (not the vacuum between the film).
It is a pleasure to help further increase your understanding of climate-science, Mike Flynn!
AFOMD,
MLI needs high vacuum between the layers presently – around 1×10^-4 Torr. Even at these pressures, perlite powder meets or exceeds MLI under almost all circumstances. No super insulation here. A vacuum is hardly a solid, so your comparison is specious.
Mylar film no more traps heat than CO2 does. If you can use Mylar film to trap some heat, maybe you can sell it to Siberians or Minnesotans during the winter. I’m only joking, of course. That’s probably a waste, because I suspect you are being serious. Ah, the sublime certainty of the Warmist faith, eh, AFOMD?
If you can produce any evidence that the study of averages derived from past weather events has any greater claim to being called a science than phrenology, please do so.
Strident self acclamations from purported Nobel Laureates such as Mike Mann, or the strangely bizarre Death Trains Hansen, are not evidence of anything except possibly shared delusional psychosis. You may not agree, but that’s life, I guess.
Live well and prosper,
Mike Flynn.
Uhhhh … mebbe yah overlooked the difference between “mW” and “W”? `Cuz NASA’s MLI insulation leaks heat at 0.1 lmW/m-K = 0.0001 W/m-K.
Perlite don’t compete!
Conclude It’s mighty good that NASA’s engineers are neither careless nor ignorant nor arrogant nor abusive, eh Climate Etc readers?
AFOMD,
I apologise. I inadvertently followed the Mannian procedure of reading the profile inverted. Test results indicate that up to 1 Torr, 60 layer MLI outperforms perlite K108. Past that point, perlite is better.
So no, I didn’t overlook the difference between mW and W. Sorry.
Your test results may differ.
As to the arrogance, ignorance, carelessness, or abusiveness of individual NASA employees, I make no particular comment. I suggest that perusing the testimony of various employees contained in the Rogers Commission report will provide the opportunity for readers to form their own opinion.
Richard Feynman, I believe, made the following comment –
“What is the cause of management’s fantastic faith in the machinery? .. It would appear that, for whatever purpose, be it for internal or external consumption, the management of NASA exaggerates the reliability of its product, to the point of fantasy.”
And people died as a result. So, was arrogance, ignorance, or carelessness involved? Or just bad luck? Repeated bad luck, perhaps?
In any case, wrapping CO2 around the Earth still cannot provide additional energy resulting in increased temperature. Neither the fantasies of NASA, AFOMD, or Rob Ellison can change the laws of physics. Good luck with trying!
Live well and prosper,
Mike Flynn.
A fan of *MORE* discourse, December 3, 2014 at 11:13 am:
“… NASA’s hugely successful multilayer superinsulation technologies show plainly that the fundamental mechanism of CO2-amplified greenhouse physics is entirely correct, in that:.
• each increment of NASA-superinsulation increases the ability of a thermos-bottle to retain heat, and similarly
• each increment in CO2 concentration increases the ability of the earth to retain heat.”
Which goes to show that AFOMD doesn’t understand the difference between Earth’s surface/atmosphere system and a blanket.
# Each increment of ANY insulating layer of ANY kind will reduce the ability of a body to shed its energy as heat to its surroundings. Any person who wears clothes and/or who prefers to sleep under a blanket knows this intuitively. The point of contention here is not with your first bullet point. It’s with the second one:
# Each incremental increase in atmospheric CO2 concentration will NOT reduce the ability of the body beneath the atmosphere, the solid surface, to shed its energy as heat.
First of all, notice how AFOMD in his first point above talk about the thermos bottle, the container inside the insulating layer, while in the second point, he moves his argument out to the outside of the insulating layer itself.
We’re talking about the solid/liquid surface here. The surface is the thermos bottle. The ToA is the outside of the insulating layer, the atmosphere.
Does more CO2 in the atmosphere manage to reduce the ability of the solid/liquid surface of the Earth to shed its energy as heat? Of course not. That ability is completely and utterly ruled by convection/evaporation. The only way more atmospheric CO2 could ever reduce general convective power would be by forcing the lapse rate (the temperature gradient away from the solar-heated surface), globally and on a permanent basis, to become less steep. It cannot possibly do this. It works the opposite way.
The main difference between the atmosphere and any other piece of insulation is that there is no solid, immovable top surface facing the bottom (solar-)heated one. If there’s a top layer acting as a rigid lid and which is warmed by the outgoing heat, then the temperature gradient down to the heated surface at the bottom will naturally reduce, and you get warming. This cannot and will not happen in the atmosphere.
The environmental lapse rate (ELR) is constrained by the tight interaction between radiation and convection to fluctuate around the average (gravity-based) adiabatic lapse rate (ALR), so that the mean global ELR finds a so-called ‘radiative-convective equilibrium’, equalling the globally averaged ALR (which is on the continuum between the dry ALR (DALR, ~10 K/km) and the saturated ALR (SALR, ~5 K/km), at 6.5 K/km).
The ‘radiative-convective equilibrium’ works like this:
The solar input heats the surface, which then in turn heats the lowermost layers of the troposphere, while the radiatively active gases (the so-called ‘GHGs’) cool the air masses to space through radiation from aloft in the troposphere. These more or less continuous radiative processes work towards STEEPENING the ELR above the ALR. This incites convection, which task it is to bring the original solar (radiative heat) energy from the heating end (low towards the surface) up to the cooling end (high towards the tropopause), LOWERING the ELR back down to (or below) the ALR in the process. At this point it stops. And the cycle can start again.
Radiation STEEPENS the ELR, convection brings it back DOWN.
CO2 is not convection.
‘Atmospheric and oceanic forcings are strongest at global equilibrium scales of 107 m and seasons to millennia. Fluid mixing and dissipation occur at microscales of 10^−3m and 10^−3s, and cloud particulate transformations happen at 10^−6m or smaller. Observed intrinsic variability is spectrally broad band across all intermediate scales. A full representation for all dynamical degrees of freedom in different quantities and scales is uncomputable even with optimistically foreseeable computer technology. No fundamentally reliable reduction of the size of the AOS dynamical system (i.e., a statistical mechanics analogous to the transition between molecular kinetics and fluid dynamics) is yet envisioned.
This reality in nature and computers has given rise to two pervasive AOS practices: (i) AOS solution fields are nonsmooth near the space–time discretization scales (i.e., the “resolution” of the model) imposed on the known governing principles expressed mostly as partial differential equations. (ii) AOS models contain essential parameterizations for unresolved or highly simplified processes whose specifications are not at a fundamental level of known governing principles.
Both practices are coping strategies to span as large a subrange as feasible for the uncomputably broad scale in the most fundamentally grounded fluid dynamical problem.’ James C. McWilliams – Louis B. Slichter Professor of Earth Sciences – UCLA Institute of Geophysics and Planetary Physics and Department of Atmospheric and Oceanic Sciences
There are statistical mechanical principles to do with pressure, temperature, energy states, etc. But we have a a large, dynamic and complex system that is not reducible by any equivalent statistical method and is more generally represented by set of hydrodynamic equations in which physical properties – mass and momentum – are conserved across grid boundaries. More or less smoothly.
There is a hierarchy of models – http://weather.unl.edu/RCM/IDB_Mexico/PDF/modelprelim.pdf – in which a Hamiltonian is one approach to low order models – http://www.nonlin-processes-geophys.net/13/125/2006/npg-13-125-2006.pdf
Each of these approaches has intrinsic limitations. There are emerging methods that may be of more fundamental interest at the systems level.
‘Considering index networks rather than raw three-dimensional climate fields is a relatively novel approach, with advantages of increased dynamical interpretability, increased signal-to-noise ratio, and enhanced statistical significance, albeit at the expense of phenomenological completeness. Climate indices represent distinct subsets of dynamical processes. One could consider these indices – the nodes of our network – to be climate oscillators, each node, by itself, an intrinsic, self-sustaining system. When coupled with other self-sustaining oscillators of the network, the collective choreography of interlinked nodes generates a hemispherically spanning, propagating teleconnection signal – our “stadium wave” – an atmospheric and lagged oceanic teleconnection sequence that communicates an Atlantic-born climate signal of multidecadal warming and cooling (superimposed upon longer-time-scale temperature trends) across the Northern Hemisphere. Significantly, a warm North Atlantic generates a decadal-scale lagged cooling hemispheric response; a cool Atlantic generates a warming one.’ Marcia Wyatt
The white dots cascading down the screen at this site – btw – seem to be real and not a visual hallucination. Let me know if they aren’t and I will make an appointment with a neurologist.
Although the warming and cooling signal is global originating at the both poles with a see-saw of atmospheric pressure driving ocean circulation.
Multi-decadal variability in the Pacific is defined as the Interdecadal Pacific Oscillation (e.g. Folland et al,2002, Meinke et al, 2005, Parker et al, 2007, Power et al, 1999) – a proliferation of oscillations it seems. The latest Pacific Ocean climate shift in 1998/2001 is linked to increased flow in the north (Di Lorenzo et al, 2008) and the south (Roemmich et al, 2007, Qiu, Bo et al 2006) Pacific Ocean gyres. Roemmich et al (2007) suggest that mid-latitude gyres in all of the oceans are influenced by decadal variability in the Southern and Northern Annular Modes (SAM and NAM respectively) as wind driven currents in baroclinic oceans (Sverdrup, 1947).
The systems approach to climate as suggested by complexity theory reveals a fundamentally different view of climate variability that cannot be approached by the reductionist methods of the Hamiltonian or any other technique.
‘Climate is ultimately complex. Complexity begs for reductionism. With reductionism, a puzzle is studied by way of its pieces. While this approach illuminates the climate system’s components, climate’s full picture remains elusive. Understanding the pieces does not ensure understanding the collection of pieces.’ Marcia Wyatt
… scales of 107 m = 10^7m
In the discussion above there is reference to planets in space with no nearby stars and just the cosmic background radiation. The planet is either atmosphere-less, has a non-GHG atmosphere or has a GHG atmosphere. It also has either a water surface or a rock surface.
What about an atmosphere-less planet (called Vulcan) that is both solid (rock) and translucent at the surface with an optical depth of 50 metres. It is a grey body with an emissivity of say 0.85. What is the surface temperature? Is it higher than the cosmic background temperature?
The planet Vulcan is not transparent and it is not opaque. It is made of a substance intermediate between black obsidian and transparent silica glass.
Now put the planet into our solar system at the orbital position of the Earth. What is the new surface temperature of Vulcan? Presumably it is not the standard SB temperature of 255 k. It must be significantly higher.
If the surface temperature is substantially greater than 255 k then this must reduce the approximate warming that can be attributed to the greenhouse effect on Earth. This is because the Earth has an ocean that is an analogue for the translucent obsidian. The Earth’s translucent ocean lifts the average surface temperature regardless of the presence or absence of greenhouse gases in the atmosphere, so long as its surface does not freeze over.
An argument is made in a previous comment that with a non-GHG atmosphere the Earth’s oceans would evaporate, condense, and fall to the surface as ice, thereby freezing all water at the surface. This does not apply to Vulcan. Nor does it actually apply to the real Earth as the real Earth always has an atmosphere. In other words the argument is a red-herring.
So on Earth how much of the observed greenhouse effect is caused by the the translucent nature of about 70% of its surface, given that most of the ocean surface is not frozen, and how much is caused by GHG in the atmosphere?
Rob R. “So on Earth how much of the observed greenhouse effect is caused by the the translucent nature of about 70% of its surface, given that most of the ocean surface is not frozen, and how much is caused by GHG in the atmosphere?”
In addition to the basic black body estimate of TSI/4 adjusted for albedo there is a sub surface temperature estimate of TSI/pi. TSI/pi gives an estimate of the sub surface assuming there is perfect insulation. To do it right, you would integrate over the entire liquid ocean surface considering the solar azimuth, elevation, seasonal variation, optical depth etc. to determine the actual input energy. This is what you would consider designing a solar gradient pond. Then you would have to consider all the heat loss. The heat loss estimates would include solar energy absorbed in all the atmospheric layers plus energy transferred from the sub surfaces, each layer of the atmosphere/ocean system. That is what the climate models try to do, but the ocean part is pretty difficult. Since the two “greenhouses” ocean subsurface and atmosphere are very tightly coupled, I don’t think you can completely separate the two. A rough estimate though is around 17% of the ocean part is not properly accounted for which is part of the reason the models tend to track on the hotter side of reality in addition to the cloud issues. That 17% is roughly what Guy Callendar listed as “other” in his paper on the GHE.
BTW, I am not a physicist, I just stayed at a Holiday Inn Express once.
It is a pleasure to oblige your curiosity Mike Flynn!
http://www.rossie.com/layer1x.jpg
Spacecraft engineers never orbit plain vacuum insulated dewars, because multi-layer insulation of cryogenic tanks reduces heat-leaks by further factors of (typically) hundreds to thousands.
Just as CO2 similarly increases the heat-trapping capabilities of the Earth’s atmosphere.
It is an ongoing pleasure to improve your aerospace, climate-science, and thermodynamical understanding, Mike Flynn!
Lol … Mike, yer joke conveys profound thermodynamic insight!
http://preparednessmama.com/wp-content/uploads/2012/11/finished-mylar-Collage.jpg
http://theopsdeck.com/img.prod.RC/PROD%20-%20RC%201034%20Polarshield%20Survival%20Sleeping%20Bag.snow.gif
Stay cozy, Climate Etc readers!
AFOMD,
So you cannot provide an R value for your MLI. This is understandable, as in a vacuum, each pair of highly reflective surfaces acts in the same manner as a single Dewar flask. Nesting Dewar flasks in similar fashion provides far greater insulation, but as NASA discovered, MLI suffers from serious defects in some aspects, which is why NASA used other forms of insulation in preference to, or in conjunction with MLI, depending on circumstances.
The matter is, in any case, moot. NASA seems to be using Russian rocket motors, or simply buys Russian tickets on Russian rockets. Invoking the name of NASA, third rate pseudo scientists, minority religious leaders, or a collection of assorted representatives of some 5% of the world’s population, doesn’t support the pseudo-science of Warmism terribly well.
Once again, you make the groundless assertion that the endless reexamination of averages derived from past weather events qualifies as a science. It doesn’t. Not according to me, anyway. I certainly wouldn’t have given Michael Mann a Nobel prize for any sort of science, but then neither did the Nobel Committee, so maybe I’m in good company.
Live well and prosper,
Mike Flynn.
AFOMD,
Wrapping a corpse in aluminised Mylar film provides no warmth, nor does CO2.
Wrapping a live human body in aluminised Mylar film, provides no warmth. It does, of course, retard the rate at which the body exchanges radiant energy with the external environment. However, a properly designed four seasons down filled sleeping bag will provide even better comfort. You won’t survive long sleeping in sub-zero temperatures clad only in a space blanket, NASA notwithstanding.
Surrounding a live human body with CO2 will achieve not much except bemused laughter from the onlookers, and agonised wonderment from the object of such lunacy. Maybe you might choose to volunteer to enter a blast freezer filled with CO2, clothed only in your dignity and suitable breathing equipment, or maybe not.
I would certainly pay a small fee to see your faith in the warming ability of CO2 evaporate in the face of freezing reality. When may we look forward to your demonstration?
Live well and prosper,
Mike Flynn.
Too much fun!
Rob Ellison refuses to accept that it was quite a long time before the oceans formed, and some time after that before the average water temperatures dropped below 50C. And so it goes. The Earth is warming – except that it isn’t. The surface radiates away energy – which causes it to warm.
The list goes on. I leave it to you, gentle reader.
Live well and prosper,
Mike Flynn.
Dear Professor Mike,
You know I believe religiously everything that you say. Including that the Earth was a pretty uncomfortable place to be during the early planet forming days.
But the question that presents itself – is what has it done for you lately? The core and the mantle continue to lose energy at a rate of 0.05W/m2 or so – and to gain energy at the surface at a rate of some 3000 times greater – warming the oceans and the ground to hundreds of metres depth at least. Even more at the place high above the planet where all energy flux is radiative sometimes called top of atmosphere for short – although i know you don’t like the term.
The problem is that this not a steady 3000+ plus times energy gain – but varies over time from snowball Earth to blue-green planet – repeatedly. So that the planet surface does appear to warm and cool and then warm again and cool again and so on. But I take it that you mean that the surface isn’t actually warming at the moment?
‘It is hypothesized that persistent and consistent trends among several climate modes act to ‘kick’ the climate state, altering the pattern and magnitude of air-sea interaction between the atmosphere and the underlying ocean. Figure 1 (middle) shows that these climate mode trend phases indeed behaved anomalously three times during the 20th century, immediately following the synchronization events of the 1910s, 1940s, and 1970s. This combination of the synchronization of these dynamical modes in the climate, followed immediately afterward by significant increase in the fraction of strong trends (coupling) without exception marked shifts in the 20th century climate state. These shifts were accompanied by breaks in the global mean temperature trend with respect to time, presumably associated with either discontinuities in the global radiative budget due to the global reorganization of clouds and water vapor or dramatic changes in the uptake of heat by the deep ocean. Similar behavior has been found in coupled ocean/atmosphere models, indicating such behavior may be a hallmark of terrestrial-like climate systems [Tsonis et al., 2007].’ http://onlinelibrary.wiley.com/doi/10.1029/2008GL037022/full
These synchronization events suggest that the Earth system is deterministically chaotic – and that the changes in the trajectory of surface temperature – around 1910, the mid 1940’s, the late 1970’s and 1998/2001 are quite natural changes in the system state involving abrupt changes in ocean and atmosphere circulation.
Clouds did seem to change about the right time.
https://watertechbyrie.files.wordpress.com/2014/06/earthshine.jpg
‘Earthshine changes in albedo shown in blue, ISCCP-FD shown in black and CERES in red. A climatologically significant change before CERES followed by a long period of insignificant change.’
But if anything the rate of ocean warming seemed to decline in Argo – although with great uncertainty.
As you have explained – this is a false prophecy and the gentle and cliched reader may cheerfully ignore the data on long term – and recent – climate change because it is clear from first principles that the planet surface is cooling at a steady rate. What would we do without Professor Mike? .
The Summary Judgment of Climate Etc Discourse
• The reality of the Gravito-Thermal Effect is denied by macroscopic thermodynamic theory, denied by microscopic dynamical theory, denied by observation of nature, and denied by laboratory experiment.
• The reality of the Greenhouse Effect is affirmed by macroscopic thermodynamic theory, affirmed by microscopic dynamical theory, affirmed by observation of nature, and affirmed by laboratory experiment.
That’s why the comments from Climate Etc’s denialists have distilled down to irrelevant quibbling, angry ranting, impotent frothing, and pointless abuse … eh Climate Etc readers?
Fan, it’s rare, so I’ll say it. I agree with you.
Have a good on ya day.
‘The equilibrium state of any ideal gas with a finite adiabatic index is essentially polytropic. Here, it is important to make precise what we mean by equilibrium. We use the term in the context of a mathematical model; it refers to a solution of the equations of motion with the property that all flows vanish and all the fields are time independent. Polytropic models of earthly and stellar atmospheres are very widely used, and the stationary configurations of such atmospheres are equilibria in this sense, although the physical configurations that they are meant to represent are not states of true thermodynamic equilibrium. An issue that we wish to understand is the precise role that is played by radiation. We should hope to develop an understanding of what would happen if the intensity of radiation were continuously reduced to zero. The possibility that the limit might turn out to be other than isothermal is not easy to accept, for it goes against one of the basic tenets of thermodynamics: Clausius’ statement of the second law (Section 3.7). The question is not entirely academic, but it has no direct bearing on the validity of our approach, for we apply it to the standard, polytropic atmospheres, just as has been done since the pioneering work of Lane (1870) [7].
It is important to incorporate the isothermal atmosphere into a dynamical framework; that is, to develop a system of equations of motion that predict the uniformity of the temperature at equilibrium. We suggest that the standard theory of polytropic atmospheres should incorporate a parameter or variable to represent the intensity of radiation and that would allow the effect of radiation to be reduced parametrically to zero, resulting in an isothermal equilibrium in the limit. In the event that an experiment should validate the isothermal atmosphere, the need to construct such a theory would become urgent.
There seems to be a dearth of experimental data. We study an ideal gas in a centrifuge and invoke the equivalence principle to relate this situation to atmospheres. Experiments are proposed. (Section 3.8).’
– See more at: http://www.mdpi.com/1099-4300/16/3/1515/htm#sthash.NZC7a5DJ.dpuf
As predicted – some hundreds of comments later – usually repeating the same arguments over and over – but failing to restrain scientific curiosity and the scientific method in a straitjacket of absurd and misguided gedankenexperiment
FOMBS lack of stellar like temperatures in a centrifuge is an especially extreme example of ideas gone feral. But then he has ulterior motives and science in this seems little more than cargo-cult science. Icons of a powerful and jealous God who will raise the believers on high. There is no solid basis in down in the dirt science – merely smoke and mirrors. Is this not obvious to everyone?
That’s why the comments from FOMBS has ‘distilled down to irrelevant quibbling, angry ranting, impotent frothing, and pointless abuse … eh Climate Etc readers?’ Is his purpose, practice and lack of substance not abundantly evident? Oh well.
In section 4.2 of his paper Frønsdal writes: “Suppose we start with a vertical column that, for one reason or another, is isentropic. At a certain moment, we turn off the incoming radiation and isolate the gas column from its environment. Assume that the column eventually becomes isothermal and that the dissipation of the temperature gradient is a slow process, during which the gas passes through a sequence of adiabatic equilibrium configurations. The question is this: what are those intermediary configurations, and what is the adiabatic dynamics around the ultimate equilibrium? Recent work by Fronsdal and Pathak (2011) [39] has attempted to answer this question, but this work may raise more questions than it set out to answer.”
I am unsure what an “adiabatic equilibrium configuration” means in this context. Maybe you have some suggestion. Frønsdal assumes the initial state to be “isentropic”. When the vertical temperature profile exactly matches the adiabatic lapse rate, then the gas not only is stable under convection (as it also is when the temperature gradient is smaller) but it also has a stationary temperature profile under convection. Adiabatic compression or expansion are isentropic processes. So it makes sense to say, as Frønsdal does, that the initial state (that exemplifies the adiabatic lapse rate) is isentropic since it is stationary under convection, both in respects of temperature, pressure and entropy. Though, this is only true in the case of an ideal gas, neglecting the effects of viscous dissipation that occur in all real gases, as Pekka notes.
Even more troubles arise when we consider the other configurations in the sequence. When the temperature profile doesn’t match the adiabatic lapse rate anymore, then it isn’t stationary under convection. So, what does it mean to say of such configurations that they are in “adiabatic equilibrium”? And the initial configuration itself only was stationary under convection, as we noted, under the assumption that there is no viscous dissipation.
Though the terminal isothermal profile *is* convectively stable and maximizes entropy, it isn’t stationary under convection. However, no convection occurs. Convective motions have been fully dissipated when the gas achieved that state, and it is stable. So, that’s not a problem. It’s the only true thermodynamic equilibrium state, so far as I can see.
I wrote rather misleadingly: “Convective motions have been fully dissipated when the gas achieved that state, and it is stable.”
Or it may be better to say that dissipation prevents convection to occur, or be maintained (without external energy input), as soon as the temperature profile reaches or drops below the adiabatic lapse rate, because of viscous dissipation. From then on, the evolution towards the isothermal profile occurs very slowly as a result of diffusion (conduction) only. It is convectively stable over that whole sequence, and thermodynamically stable at the end.
Wrong.
David, your idea that maximization of entropy entails, for a column of gas under gravity, that the average mechanical energy of the molecules be the same at all heights isn’t just simplistic and wrong, it is quite absurd. You clearly didn’t think it through.
If the temperature at the bottom of a tall column of air under gravitational acceleration g, at equilibrium, is 300°K, then the average kinetic energy of the molecules is about (3/2)kT, which is 6.21*10^-21J. This means that nitrogen molecules (mass = 4.65*10^-26 kg) that have this average kinetic energy, have speed
V = sqrt(2*KEavg/m) = 517m/s.
So, a N2 molecule that starts up at the bottom of the column with an upward trajectory, and the average kinetic energy, will rise to the height of h = 1/2g*t^2/2 (assuming g uniform for simplicity), where t = (517m/s)/g =
h = 6.8km.
This is the height at which a nitrogen molecule with the average kinetic energy at ground level has converted all this energy into gravitational potential energy. Now, according to you, it’s impossible for any nitrogen molecule (or any heavier molecule) to rise past this height h, at equilibrium, since else the average mechanical energy for the molecules at this higher level would be larger than the average at lower heights (which you deem to be constant). *All* the molecules at ground level that have a kinetic energy larger than average would somehow be prevented from rising any higher than the height h at which the molecules of that kind with the average kinetic energy are potentially capable of rising. By what magic would they be so prevented?
‘The equilibrium state of any ideal gas with a finite adiabatic index is essentially polytropic. Here, it is important to make precise what we mean by equilibrium. We use the term in the context of a mathematical model; it refers to a solution of the equations of motion with the property that all flows vanish and all the fields are time independent. Polytropic models of earthly and stellar atmospheres are very widely used, and the stationary configurations of such atmospheres are equilibria in this sense, although the physical configurations that they are meant to represent are not states of true thermodynamic equilibrium. An issue that we wish to understand is the precise role that is played by radiation. We should hope to develop an understanding of what would happen if the intensity of radiation were continuously reduced to zero. The possibility that the limit might turn out to be other than isothermal is not easy to accept, for it goes against one of the basic tenets of thermodynamics: Clausius’ statement of the second law (Section 3.7). The question is not entirely academic, but it has no direct bearing on the validity of our approach, for we apply it to the standard, polytropic atmospheres, just as has been done since the pioneering work of Lane (1870) [7].’
All I can do is quote the literature.
Rob Ellison (only) wrote: “All I can do is quote the literature.”
Agreed.
This was actually meant for somewhere else – but it obviously doesn’t stop smarmy little … feeling they can leave one line piles of utter goop behind. Something that is standard practice for CE it seems with nothing in the way of effective sanctions.
And although I do quote actual and relevant science a lot – as opposed to arm waving in the general direction of a scientific talisman – I am not known for not commenting at length in an erudite, informed, educated and urbane if somewhat and sometime abrasive style of someone not given to suffering fools willingly – and occasionally waxing humourous or lyrical – on a broad range of scientific, social, technological and economic issues. Waxing humorous or lyrical seems a sure fire way to generate snide and spiteful snark and is something else I have stopped indulging in here.
My position from the start on this paper was that here was an interesting but difficult paper that reached – via Lagrangian evolution of a Hamiltonian based on a Gibbs free energy action principle – some challenging conclusions.
That a conflation of twits futilely pontificating on many and varied less than convincing thought experiments doesn’t challenge my initial belief that I didn’t know enough to draw an informed opinion on the paper. My considered opinion after 100’s of comments is that there little light but at least in once case amusingly stellar like heat – and that discourse on advanced atmospheric physics topics at CE is energetic but naive, quite superficial and very frequently mind bogglingly misguided.
“[…] but it obviously doesn’t stop smarmy little … feeling they can leave one line piles of utter goop behind […]”
And you constantly complain about my being excessively verbose…
Pierre-Normand,
It took me a while to understand. Very clever. I often deride Warmist for one or two word dismissive declarations. Sorry.
I dips me lid to you, sirrah! I can only add – touché.
Live well and prosper,
Mike Flynn.
So not commenting is problematic as is commenting? This is a rather obvious ploy. I suppose if I shut up and went way – everything would be fine. My words however have nothing in common with P-N’s. I have actual word-smithing skills. I can be terse – I can be florid – I can layer meaning within meanings and sometimes amuse myself by saying something while implying the direct opposite in nested irony. As I did above. Or rollick in a Grand Guignol cascade of linguistic calamities. Right over his head of course. Every word has a place and a meaning in the ordinary English usage.
Have these people never read any of the great stylists of world literature? Fireworks exploding across a mindscape – diamond bright images illuminating to the depths of the soul. Or even within the utterly astonishing American tradition? Have your schools failed your population? Looking only at P-N and Maxy – grave fears would be held for the health of American culture. I cut my teeth on Henry Miller – a truly great American stylist.
“In the days to come, when it will seem as if I were entombed, when the very firmament threatens to come crashing down upon my head, I shall be forced to abandon everything except what these spirits implanted in me. I shall be crushed, debased, humiliated. I shall be frustrated in every fiber of my being. I shall even take to howling like a dog. But I shall not be utterly lost! Eventually a day is to dawn when, glancing over my own life as though it were a story or history, I can detect in it a form, a pattern, a meaning. From then on the word defeat becomes meaningless. It will be impossible ever to relapse.
For on that day I become and I remain one with my creation.
On another day, in a foreign land, there will appear before me a young man who, unaware of the change which has come over me, will dub me “The Happy Rock.” That is the moniker I shall tender when the great Cosmocrator demands-” Who art thou?”
Yes, beyond a doubt, I shall answer “The Happy Rock!”
And, if it be asked-“Didst thou enjoy thy stay on earth?”- I shall reply: “My life was one long rosy crucifixion.”
We may not aspire to poetry – but some fluidity and facility is the seasoning to the meat of reason and meaning.
There are 2 problems with P-N’s style. First the convoluted and impenetrable syntax consisting of physics like terms strung together in a way he fondly imagines is meaningful . It is not. The usual stricture applies. If you cant describe it simply you don’t understand it – and if you don’t understand it you can’t explain it at all. Visualisation process is the key to understanding both poetry and physics.
‘Visualization in some form or other is a vital part of my thinking…half-assed kind of vague, mixed with symbols. It is very difficult to explain, because it is not clear. My atom, for example, when I think of an electron, I see an atom and I see a vector and a y written somewhere, sort of, or mixed with it somehow, and an amplitude all mixed up with x’s … it is very visual … a mixture of a mathematical expression wrapped into and around, in a vague way, around the object. So I see all the time visual things associated with what I am trying to do.’ Feynmann
Kip Thorne commented on Stephen Hawing.
‘As Stephen gradually lost the use of his hands, he had to start developing geometrical arguments that he could do pictorially in his head. He developed a powerful set of tools, you may develop other tools, and the new tools are amenable to different kinds of problems than the old tools. And if you are the only master in the world of these new tools, that means there are certain kinds of problems you can solve and nobody else can.’
Einstein said that the ‘words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought. The psychical entities which seem to serve as elements in thought are certain signs and more or less clear images which can be “voluntarily” reproduced and combined. There is, of course, a certain connection between those elements and relevant logical concepts. It is also clear that the desire to arrive finally at logically connected concepts is the emotional basis of this rather vague play with the above-mentioned elements. But taken from a psychological viewpoint, this combinatory play seems to be the essential feature in productive thought–before there is any connection with logical construction in words or other kinds of signs which can be communicated to others.’
The 2nd problem is simply reproducing the same arguments hundreds of times in a post. A little excessive. This latter combines with the former in what I call extreme verbiage. Sadly – a mess of pottage sans any literary seasoning or precise yet simple explication of whatever it is he is on about.
Oddly – my trying to help him out here is not being greeted in the spirit it is offered.
Einstein also said:
“In the interest of clearness, it appeared to me inevitable that I should repeat myself frequently, without paying the slightest attention to the elegance of the presentation. I adhered scrupulously to the precept of that brilliant theoretical physicist, L. Boltzmann, according to whom matters of elegance ought to be left to the tailor and to the cobbler.”
‘Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.’ Bertrand Russell
The theory of relativity has a sparing and simple elegance that unfolds in the mind for decades.
Is P-N comparing his prolix prose to that of Einstein? No contest there.
Albert Einstein — ‘If you can’t explain it to a six year old, you don’t understand it yourself.’
Following Let’s follow Donald Knuth’s advice
It was Knuth who inspired FOMD to take one further step … explaining gas-column physics to a symbolic programming language!
‘Everything that can be counted does not necessarily count; everything that counts cannot necessarily be counted.’ Albert Einstein
‘Sensitive dependence and structural instability are humbling twin properties for chaotic dynamical systems, indicating limits about which kinds of questions are theoretically answerable. They echo other famous limitations on scientist’s expectations, namely the undecidability of some propositions within axiomatic mathematical systems (Gödel’s theorem) and the uncomputability of some algorithms due to excessive size of the calculation.’ James McWilliams
‘In sum, a strategy must recognise what is possible. In climate research and modelling, we should recognise that we are dealing with a coupled non-linear chaotic system, and therefore that the long-term prediction of future climate states is not possible.’ IPCC
FOMBS has explained everything mathematically? One of the first things we learn in engineering is the sanity check. I take it we have gotten past not getting stellar like temperatures in a centrifuge then?
Per requests:
————————-
Assignment Demonstrate that the maximum entropy principle, for a vertical gas-column in a gravitational field, implies that the temperature of the gas-column is uniform, such that there is *NO* gravito-thermal effect. Show all work explicitly.
Showing the work Here we derive temperature-uniformity solely from the assumption of maximum entropy, (using the symbolic programming language Mathematica to avoid sign-errors).
To anticipate, here is the output of the code (which will follow in a separate comment).
Implications of the Sackur-Tetrode entropy function
***************************************************
ideal gas law: T -> (2*U)/(3*k*N)
ideal gas law: P -> (2*U)/(3*V)
Verified: P*V == N*k*T
ideal-gas law: \[Epsilon] -> (3*P)/2
ideal-gas law: \[Rho] -> (m*P)/(k*T)
maximum-entropy gas-column: T -> T0
maximum-entropy gas-column: P -> P0/E^((g*m*z)/(k*T0))
*******************************************************
Verified: the maximum-entropy equilibrium is isothermal
(i.e., there is no gravito-thermal effect)
Result The maximum-entropy state of an ideal gas-column in a gravitational field has uniform temperature, such that there is *NO* gravito-thermal effect.
Assignment Demonstrate that the maximum entropy principle, for a vertical gas-column in a gravitational field, implies that the temperature of the gas-column is uniform, such that there is *NO* gravito-thermal effect. Show all work explicitly.
Appendix: Working Code
Just paste-and-run in Mathematica (hopefully).
(* *********************************** *)
"\<\
Implications of the Sackur-Tetrode entropy function
***************************************************\>"//
Print;
(* begin with the Wikipedia definition
of the Sackur-Tetrode entropy *)
U::usage = "kinetic energy of the gas (units J/m^3)";
V::usage = "volume of the gas (units m^3)";
N::usage = "number of particles in the gas";
h::usage = "the Plank constant";
m::usage = "the mass of a gas particle";
k::usage = "Boltzmann constant";
(* define intrinsic thermodynamical variables *)
z::usage = "vertical gas-column spatial coordinate";
g::usage = "gravitational acceleration (units m/s^2)";
\[Rho]::usage = "mass-density of the gas: \[Rho] \[Congruent] N*m/V";
\[Epsilon]::usage = "kinetic energy-density of the gas: \[Epsilon] \[Congruent] U/V";
\[ScriptCapitalE]::usage = "total energy-density of the gas: \[ScriptCapitalE] = \[Epsilon]+\[Rho]*g*z";
(* **************************** *)
(* specify the entropy function *)
(* **************************** *)
Sfun$UVN::usage = "Sackur-Tetrode entropy function";
Sfun$UVN[U_,V_,N_] = k*N*Log[(V/N)(U/N)^(3/2)] +
(3/2)*k*N*(5/3 + Log[(4 Pi m)/(3 h^2)]);
(* ************************ *)
(* derive the ideal gas law *)
(* ************************ *)
T$UVN::usage = "temperature of the gas";
P$UVN::usage = "pressure of the gas";
T$UVN = {1/(T) == D[Sfun$UVN[U,V,N],U]}//
Solve[#,T]&//Flatten//
ReplaceAll[T,#]&;
Print["ideal gas law: T -> ",T$UVN//InputForm];
P$UVN = D[Sfun$UVN[U-P*\[Delta]V,V+\[Delta]V,N],\[Delta]V]//
Limit[#,\[Delta]V->0]&//Solve[#==0,P]&//Flatten//
ReplaceAll[P,#]&;
Print["ideal gas law: P -> ",P$UVN//InputForm];
(* verify that ideal gas law is satisfied *)
P*V == N*k*T//
ReplaceAll[#,{T->T$UVN,P->P$UVN}]&//
If[#//TrueQ,
Print["Verified: P*V == N*k*T"];
,
Print["Invalidation: P*V != N*k*T, yikes!"];
Throw["Invalidation"];
]&;
(* derive rules for change of variables *)
toPVrules = {T == T$UVN,P == P$UVN}//
ReplaceAll[#,{U->\[Epsilon]*V,N->\[Rho]*V/m}]&//
Solve[#,{\[Epsilon],\[Rho]}]&//Flatten;
Map[Print["ideal-gas law: ",#//InputForm]&,toPVrules];
(* ******************************* *)
(* find gas-column maximum entropy *)
(* ******************************* *)
(* compute the equilibrium equations *)
\[Lambda]1::usage = "Lagrance multiplier for energy-conservation";
\[Lambda]2::usage = "Lagrance multiplier for mass-conservation";
equilibriumEquations = (Sfun$UVN[U,V,N]/V + \[Lambda]1*\[ScriptCapitalE] + \[Lambda]2*\[Rho])//
ReplaceRepeated[#,{
U->V*(\[ScriptCapitalE]-\[Rho]*g*z),
N->V*\[Rho]/m
}]&//{D[#,\[ScriptCapitalE]],D[#,\[Rho]]}&//
ReplaceRepeated[#,{\[ScriptCapitalE]->\[Epsilon]+\[Rho]*g*z}~Join~toPVrules]&//
Simplify//PowerExpand//Simplify//
Map[#==0&,#]&;
(* it is simpler to verify the equilibrium solution
as an ansatz than to construct it ab initio (although
the ab initio construction is entirely feasible) *)
equilibriumSolutionAnsatz = {
T -> T0, (* NOTE: *no* gravito-thermal effect *)
P -> P0 Exp[-g*m*z/(k T0)]
};
equilibriumSolutionAnsatz//
Map[Print["maximum-entropy gas-column: ",#//InputForm]&,#]&;
equilibriumEquations//
ReplaceAll[#,equilibriumSolutionAnsatz]&//
PowerExpand//Solve[#,{\[Lambda]1,\[Lambda]2}]&//Flatten//
FreeQ[#,z]&//
If[#//TrueQ,
Print["\<\
*******************************************************
Verified: the maximum-entropy equilibrium is isothermal
(i.e., there is no gravito-thermal effect)\>"];
,
Print["Invalidation: isothermal disequilibrium, yikes!"];
Throw["Error"];
]&;
This is an example of why we lawyers think science is too important to be left to scientists. Scientists too often think they’ve proved a conclusion when in fact they’ve assumed the conclusion to begin with. There are circles in which this is known as begging the question.
Renowned legal scholars like Roberto Mangabeira Unger certainly lend weight to your opinion!
https://www.youtube.com/watch?v=KmZXUDEocxA
Good on `yah, Joe Born, for helping to inspire Climate Etc readers to inquire more deeply and learn more broadly!
Jesus Joe.
You lawyers dont even understand that science isnt about proof.
you dont prove anything in science.
A) you explain.
B) you predict.
There are some areas of science where you cannot predict, or cases where you can predict, but testing is practically not feasible. In these areas science is limited to explanation. explanation is “making sense” of observables with the most parsimonious set of rules.
Proof belongs to math and logic and geometry. Science is explanation and prediction. You dont prove you are right. you show that your explanation accounts for observables and that it makes predictions that are in principle testable, even though you may not be able to explicitly test them.
No amount of experimentation can ever prove me right; a single experiment can prove me wrong. – Albert Einstein
FOMBS treats science and maths as a talisman. It doesn’t seem at all practical.
‘1. An object marked with magic signs and believed to confer on its bearer supernatural powers or protection.
2. Something that apparently has magic power.’
Pretty much the antithesis of science.
Steven Mosher, “You lawyers don’t even understand that science isn’t about proof. You don’t prove anything in science.”
That is so true. I think Joe though was commenting more on how Fan presents his science than how science is supposed to be.
Fan is assuming that the maximum entropy principle as it applies to ideal monoatomic gases accurately demonstrates that an isolated atmosphere under the influence of gravity will be “perfectly” isothermal. The way Fan presents his “demonstration” has more of a “proof” feel to it than a more scientific “feeling” argument that includes limits of his model and potential sources of uncertainty etc. etc.. Sackur-Tetrode entropy is generally recognized a being less than ideal at lower temperatures, ie lower molecular velocities, where real gases tend to behave less like ideal monoatomic gases, though it is close enough in the majority of cases.
For Fans case though, covering the Earth with his Mylar MLI could produce an equilibrium temperature in the low thousands of degrees which would pretty much ensure an isothermal equilibrium. Unfortunately, that might inspire some of the Sky Dragon types to believe Fans Demonstration of *no* gravito-thermal effect is actually a demonstration “of” the gravito-thermal effect. I think it has something to do with the assumption that there is Zero potential energy at the lowest level of the atmosphere due to gravity when the mass of the entire volume actually creates the gravitational potential. Kind of a chicken or egg thing as I understand it.
Joan Baez, the physicist not the singer, believes he has a solution but I don’t think he has published it.
This does not imply anything about temperatures in the column. These two simple equations – Sackur–Tetrode and the ideal gas equation are statistical expressions of the system state. We get a number for entropy – which is maximum for the equilibrium state and for pressure-volume-temperature relationships. So knowing pressure and volume we can determine temperature of the gas – for instance – and use it to calculate entropy for the equilibrium state.
To imagine that the solution to these equations – if that is in fact what happens – lacking assumptions for pressure and volume – or a coherent approach to the logic of progression in these simple equations – is a mathematical proof of anything at all is a complete sham or utter insanity. Take your pick.
AFOMD,
As you probably know, I don’t follow your links.
However, I can see a representation of a sign which might lead one to believe that Buddhism is a religion. I might disagree, but would you mind expressing your personal definition of religion?
Just curious. I have no intention of arguing – it is of course personal to you. I don’t follow your links, I’m interested in your personal opinion.
Feel free to ignore me if you think it’s a bit personal. I understand.
Live well and prosper,
Mike Flynn.
A respectful and sincere question surely deserves a respectful and sincere reply.
Two words: continuing revelation.
https://www.youtube.com/watch?v=ouiGjndtTrw
Caveat Everyday experience, and history too, remind us that God and the Devil alike reside “in the details” … the details everyday life … and that the line between good and evil “runs down the middle of every human heart.”
Most everyone who responded to FOMD’s Mathematica calculation seem to overlook that it is a valuable contribution since it purports to prove (I haven’t checked) that for an ideal gas under gravity, the state that maximized entropy is isothermal. Since this result flatly contradicts the expectations of many advocates of a gravito-thermal gradient (such as David Springer, Doug C and probably also Christian Frønsdal) also regarding ideal gases, it is a valuable contribution to the debate. A valuable response to it would be to verify the soundness of the proof (under the assumption that the gas is ideal) or pointing out any error.
Rob Ellison: “This does not imply anything about temperatures in the column.”
Yes, looking more closely at the code — for how little I understand — it seems to me Rob might be right. I don’t see how FOMD allows for various vertical temperature profiles (with T an explicit function of z) and select for the profile that has the maximum entropy. This may need more work.
Technical Note Physically, an ideal gas column is specified physically by the temperature of the column and the pressure at its base; mathematically the gas column is specified by the thermodynamic potentials
and 
, which enter in the Mathematica code as Lagrange multipliers.
In thermodynamical lingo,
is the “inverse temperature” of the gas-column; 
is the “chemical potential” of the gas-column; and *BOTH* are spatially uniform.
In engineering practice, temperature and pressure are the preferred variables for the pragmatic reason that they are easy to measure, even though they are *NOT* as mathematically natural as the potentials
and 
.
http://thumbs.dreamstime.com/x/curvy-road-ahead-19074876.jpg
Thorough understanding of thermodynamics requires familiarity with *BOTH* sets of variables.
————
P-N, there are two groups that any “solution” needs to address. One group, Sky Dragons and fans of perpetual motion, are literally looking at the limits of Maxwell-Boltzmann statistics and the ideal gas laws thinking that the G-T effect is “significant” enough to patent and another group that would like to fine tune “equilibrium” to include things like relativistic effects. It would probably be better to address the more sane of the two instead of rehashing “Ideal” gases and “Ideal” definitions of equilibrium.
The second group could be onto something by the way, at least in my opinion.
Pierre-Normand: “A valuable response to it would be to verify the soundness of the proof (under the assumption that the gas is ideal) or pointing out any error.”
My sell-by date is too imminent to spend enough time slogging through the Mathematica code and learn the physics arcana, so I’ll have to decline that invitation.
I did look “Sackur-Tetrode” up here: http://en.wikipedia.org/wiki/Gibbs_paradox, though, and at least at first blush its derivation appears to assume the absence of gravity: the phase space is said to be the surface of a hypercylinder, not a hypercone.
As I said above in a previous comment, that smells a lot like begging the question. Again, though, I have not waded through the whole thing.
Joe Born,
A hypercone would be a better choice but I think the “Idealists” would still defend their concept to the ultimate heat death.
Joe Born wrote: “I did look “Sackur-Tetrode” up here: […], and at least at first blush its derivation appears to assume the absence of gravity: the phase space is said to be the surface of a hypercylinder, not a hypercone. As I said above in a previous comment, that smells a lot like begging the question.”
Good point. There is a discussion of and ideal gas in a gravitational field in the following link where they adapt the S-T formula to account for gravity, though the isothermal profile is assumed (which as they seem to imply goes hand in hand with the assumption that diffusive equilibrium is achieved and that therefore the chemical potential doesn’t vary with altitude — see also the last paragraph of Pekka’s note) and the density gradient is derived.
http://www.physics.usu.edu/torre/3700_spring_2013/lectures/04.pdf
Let’s see of FOMD can run his code with the adapted S-T formula or show why the result ought not to change. Meanwhile, have a look at the more complete discussion that I linked to earlier:
http://journals.ametsoc.org/doi/pdf/10.1175/1520-0469%282004%29061%3C0931%3AOMEP%3E2.0.CO%3B2
There seems not to be any question begging in this treatment of our problem,
Pierre-Normand: “Meanwhile, have a look at the more complete discussion that I linked to earlier”
Thanks for the link, but it’s something I had looked at before and found unsatisfying. Possibly it was just that I was leery of the what assumptions may go into the concept of potential temperature. (I’m a layman–e.g, before I looked it up yesterday I would have thought Sackur Tetrode was some kind of vacuum tube–and it takes me some time to think these things through.)
My interest in this issue is not so much whether at equilibrium a gas column is isothermal but rather how much we layman should accept when we hear that “scientists say” such and such. Even in their particular areas of expertise, and where there actually is a known solution, the discussion above shows scientists are likely to be unaware of the tacit assumptions they are making. Particularly when humanity’s welfare depends on it and there is no known solution, we laymen should challenge their opinions.
I also think the Roman et al. and Velasco et al. papers are the ones that make the fewest assumptions (except for ignoring quantum mechanics). They don’t speak explicitly in terms of maximizing entropy, but they do compute the probability density of a particle’s having a particular altitude and speed, and assigning distribution in accordance with that density should, I think, maximize entropy. So far, therefore, I think Roman et al. and Velasco et al. together provide the best treatment. And, as you say, they find isothermality to within the limit of thermodynamics’ applicability.
Joe Born wrote: “So far, therefore, I think Roman et al. and Velasco et al. together provide the best treatment. And, as you say, they find isothermality to within the limit of thermodynamics’ applicability.”
Indeed, and their mathematical treatment at the level of partition functions of mechanical states simply vindicates what can be found independently from entropy consideration in classical thermodynamics. This corroborate the sound statistical mechanical foundation of classical thermodynamics and explains why Verkley and Gerkema find results consistent with those from kinetic theory. That’s no accident.
CD wrote: “Joan Baez, the physicist not the singer, believes he has a solution but I don’t think he has published it.”
That would be John Baez
FOMD: “By abstracting and extending the methods of the Sackur-Tetrode example, show that […] at the maximum-entropy equilibrium *ALL* of the thermodynamic potentials are spatially uniform.”
Yes, that would be valuable as an *supplementation* (not just an extension) of your result. If I understand correctly, it would amount to a demonstration of the fact that lambda_1, the inverse temperature (and hence also T), is spatially uniform. However, as your previous demonstration stood, this was simply assumed, right?
No. In the example, the unique entropy-maximizing state has uniform temperature. It’s true that we guessed this as an ansatz … which is not the same thing as assuming it … for the simple reason that we might have discovered that the uniform-temperature ansatz failed!
FOMD: “No. In the example, the unique entropy-maximizing state has uniform temperature. It’s true that we guessed this as an ansatz … which is not the same thing as assuming it … for the simple reason that we might have discovered that the uniform-temperature ansatz failed!”
OK, I think I am getting it now. So, T is a function of z, after all, and you are making use of a variational principle to check that the the isothermal solution yields an extermum for entropy, correct? That would indeed be valid and a special case of your general statement about uniformity thermodynamic potentials being a consequence of entropy maximization.
“extermum (sic)” …extremum…
That is exactly correct!
http://www.casinocashjourney.com/images/Slot%20Machine.jpg
Further reading Here is an excellent (and recent) discussion of the Legendre transforms that go back-and-forth between conserved densities and their thermodynamic potentials.
@article{Zia:2009lr, Author = {Zia, R. K.
P. and Redish, Edward F. and McKay, Susan
R.}, Journal = {American Journal of
Physics}, Number = {7}, Pages = {614-622},
Title = {Making sense of the {L}egendre
transform}, Volume = {77}, Year = {2009}}
Very nice reference, FOMD. Thanks. It’s available at arxiv:
http://arxiv.org/pdf/0806.1147.pdf
The American Journal of Physics (published by the American Association of Physics Teachers) is simply awesome. As an undergraduate student, 20 years ago, I would spend whole afternoons at the library perusing old issues to find fun puzzles about QM and the theory of relativity. I also spent way too much time doing this shortly before my exams.
So we have morphed from a Lagrance (sic) multiplier to the Legendre Transform?
‘The Legendre Transform (LT) is a commonly used
mathematical tool in upper division and graduate physics
courses, especially in Classical Mechanics (CM) [1], Statistical Mechanics (SM) and thermodynamics. [2]
Most physics majors are exposed to the LT first in CM,
where it provides the connection between the Lagrangian
L(q) and the Hamiltonian H(p), and then in SM where
it creates relations between the internal energy, E and
the various thermodynamic potentials, e.g., S, G, H
and A.’
Let me know when you get past hand waving at 100 year old equations.
There is no “morphing” of anything into something else. The method of Lagrange multipliers was used to find extrema of equations subject to equality constraints (such as follow from conservation energy, and of mass). Discussion of the Legendre transform just was relevant to the definition of the dimensionless thermodynamic potentials. (Read a bit more of the paper). They’re two independent topics, though both are relevant to explaining FOMD’s calculation.
P-N: “They’re two independent topics, though both are relevant to explaining FOMD’s calculation.”…
Though the latter isn’t necessary to validate the result, it explains how thermodynamics potentials relate to conserved quantities. See specially the two subsection entitled: “The route of physics: interpretation of the
equilibrium condition” and “How does the Legendre transform enter into
thermodynamics?”
You may believe anything you like P-N. I am certainly not falling for the saga of using a Lagrange multiplier to determine equilibrium entropy in Sackur-Tetrode. Utter BS. Nor am I inclined to wonder what a Legendre transform means for the potentials in this utterly mad riff on Sackur-Tetrode and the ideal gas equation.
Let’s keep it at basics. What can we possibly know from these 2 simple equations? Anything more – and there has been a great deal more said with much fanfare and little to no substance – and it is all BS.
“Nor am I inclined to wonder what a Legendre transform means […]”
Yes, I know.
The thermodynamic potential is explicit in the formula. All the rest is crazy talk. You have to have something with a modicum of relevance – not simply arm wave at a paper. Or simply arm wave if you find it interesting – but not claim relevance in some context in which it is simply bafflegab.
Rob Ellison wrote: “The thermodynamic potential is explicit in the formula.”
Indeed it is. The Langrange multiplier method just is used to check that the isothermal profile, together with the vertical barometric density profile, jointly realize an extremal entropy state (and it’s obviously not a minimum). Any continuous deviation from this profile, either in density or temperature, would therefore reduce entropy. It is therefore an equilibrium state.
You can now forget about the Legendre transform paper if you aren’t interested to learn more about its applications to classical thermodynamics and statistical mechanics. FOMD’s calculation doesn’t depend on it.
For people who unlike Rob aren’t completely incurious about the direct relevance of Legendre transforms to entropy maximization (and the dual principle of energy minimization), for simplifying calculations with the use of thermodynamic potentials, there is also this neat online presentation:
http://casey.brown.edu/research/crp/Edu/Documents/00_Chem201/6_thermodyn_pot/6-thermodyn_pot-frames.htm
Sorry we have the Sackur-Tetrope expression.
http://www.wolframalpha.com/input/?i=Sackur-Tetrode+equation
And the ideal gas equatuion.
http://www.ajdesigner.com/idealgas/
Do you really expect that the rest of the apocryphal bafflegab holds any meaning at all? Such mendacious and empty verbiage from the acolyte of extreme verbiage. I always hope for a higher standard of personal integrity – but am never bothered when it doesn’t eventuate.
None of the recent links in this thread mentions gravity confinement thus there is no analysis applicable to gravito-thermal effect. One must first accept the fact that potential energy and kinetic energy are freely interchangeable in gravitational confinement. The sum of PE and KE is called mechanical energy. ME is of highly practical concern to engineers who build things in gravity wells i.e. engineers living on the planet earth. Like duh. From there we merely consider what is the state of maximum entropy in a non-convecting atmosphere. It cannot possibly be isothermal IMO because PE at altitude will give a mole of atmosphere more usable energy than a mole of atmosphere at no altitude if both moles have the same kinetic temperature.
No one has ever disproven this since Loschmidt described the gravito-thermal effect 150 years ago in the golden age of physics. No amount of blog banter from undistinguished physicists who can’t even rise to having their opinion on the matter placed in the peer reviewed literature. It’s a comedy of inferiors thinking they don’t need experimental physics because they have the world perfectly modeled inside their pointy little heads like much of the rest of warmist dingbats whose failure to predict what happens in the real world is legendary. Hiding the decline in temperature is a knee jerk reaction among that crowd whether it comes to paleo-temperatures from tree rings, meausured temperatures in the southern hemisphere, the Little Ice Age, the missing tropospheric hot spot, and now a lapse rate in a non-convecting atmosphere that is demanded by maximum entropy considerations in free mechanical energy.
Technical Note Physically an ideal gas column is naturally specified by the temperature
of the column and the pressure 
at its base; mathematically the gas column is naturally specified by the thermodynamic potentials 
and 
(which enter in the Mathematica code as Lagrange multipliers).
In thermodynamical lingo,
is the “inverse temperature” of the gas-column; 
is the “chemical potential” of the gas-column; and *BOTH* are spatially uniform.
In engineering practice, temperature and pressure are much-preferred variables — even though they are *NOT* as mathematically natural as the potentials
and 
— for the pragmatic reason that they are easy to measure.
Pierre-Normand, this is precisely correct!
However, the result is *not* limited to ideal gases only, or to the Sackur-Tetrode entropy function in particular.
Advanced exercise By abstracting and extending the methods of the Sackur-Tetrode example, show that for any convex entropy function whatsoever, for any number of conserved quantities whatsoever, subject to any spatially-varying fields whatsoever, in any (possibly non-euclidean) geometry whatsoever, in any number of spatial dimensions whatsoever: at the maximum-entropy equilibrium *ALL* of the thermodynamic potentials are spatially uniform.
http://www.greaterbostonsuburbs.com/funny%20road%20sign.jpg
Happy thermodynamical computing, Climate Etc readers!
FOMD: “In thermodynamical lingo, \lambda_1 is the “inverse temperature” of the gas-column; \lambda_2 is the “chemical potential” of the gas-column; and *BOTH* are spatially uniform.”
This may most likely be the case, but just assuming it seems to be the question begging against someone who would insist that lambda_1 might not be uniform if there is a gravito-thermal effect.
What the calculation demonstrates is a special case of this general theorem:
Theorem Given any state with non-uniform thermodynamic potentials, there is a state having (1) the same globally conserved quantities, and (2) spatially uniform thermodynamical potentials, and (3) higher entropy.
Indeed, from both a physical and mathematical point of view, thermodynamical potentials are defined in terms of the entropy function, precisely so as to ensure that this theorem holds!
For the common case that energy is the sole conserved quantity, this potential-uniformity theorem is equivalent to the Zeroth Law of Thermodynamics
Really? The usual sanity check is to cite literature along these lines. But of course there is none. Nothing remotely bears any resemblance to this utterly mishmash of physics madness in support of an ‘antatz’.
I have never seen such horrifying triple plus blogospheric unscience. Is there a taint of lunacy here – an immensely over the top Bose-Einstein meltdown – or is merely a cynical duping of the gullible. I can’t imagine any rational purpose for the latter.
CD wrote: “P-N, there are two groups that any “solution” needs to address. One group, Sky Dragons and fans of perpetual motion, are literally looking at the limits of Maxwell-Boltzmann statistics and the ideal gas laws thinking that the G-T effect is “significant” enough to patent and another group that would like to fine tune “equilibrium” to include things like relativistic effects. It would probably be better to address the more sane of the two instead of rehashing “Ideal” gases and “Ideal” definitions of equilibrium.”
Some people I choose not to argue with at all. When I choose to argue with someone, I try refrain from pigeonholing him/her. You yourself seemed to endorse “the basic premise of the gravito-thermal effect as [you] understand it”. This ‘basic premise’ actually is an *argument* that can be applied with no modification to an ideal gas at equilibrium in a box. So long as you don’t acknowledge the flaw in this basic argument, you are pigeonholing yourself into the same box as the Sky Dragon Slayers, and David Springer; at least on that issue. It’s difficult to move forward to examining more complex cases, or more subtle arguments, when this simple misunderstanding isn’t acknowledged and corrected.
P-N, Interesting. So it is like your “ideal” against the world. Sounds like a religious thing. Since my position is that no ideal model is ever truly ideal, I am a heathen.
btw, in the newest paper you linked comparing isothermal to isentropic the author finds a value of alpha equal to 1.6868. There is a whole new group of “deniers” out their that would likely find the ratio to be this
http://upload.wikimedia.org/math/7/d/a/7dae50ded3e335e34196ed67dc8dc49e.png
That particular group is into Self-Organizing Criticality. They may be considered the Zen group that believes there is no true equilibrium only preferred states of relative balance in nature :)
Pierre, you don’t know enough to distinguish my position from the dragon slayers. I would be most happy though if you didn’t waste my time by responding to me in the future as you’re too uninformed to engage in any productive dialog with me. You’re a warmist troll and you might better find a blog with more of your kind on it to engage in mutual back patting and congratulatory activities that is your only source of self-esteem.
“P-N, Interesting. So it is like your “ideal” against the world. Sounds like a religious thing.”
CD, for the Nth time, most of your fellow gravito-thermalists — including yourself! — practice the same religion since your “basic premise” applies to ideal gases. If the premise is correct, then there ought to be a temperature gradient in an *ideal* gas column *at equilibrium* because it requires no extra assumption regarding deviations from ideality or equilibrium. Else the premise is flawed and must be abandoned. You can’t have you cake (endorse the ‘basic premise’) and eat it too (claim that the premise is consistent with the absence of a temperature gradient for an ideal gas under gravity at equilibrium).
DS: “Pierre, you don’t know enough to distinguish my position from the dragon slayers.”
It’s not my goal to distinguish or compare you with them. You misread my post. I said to CD that he can’t dissociate himself from the slayers on the issue of the G-T effect when he (and yourself) endorses basically the same “basic argument” about constancy of mechanical energy as a function of height, and is seemingly unaware (as you are) of the flaw in this argument. If you don’t want to lose time with me, and are unwilling to respond to some criticisms or your arguments… don’t respond.
P-N, “Else the premise is flawed and must be abandoned.”
Spoken like a true authoritarian :) Ideal Gas Theory is a valiant attempt to force nature to be a linear as humanly possible. T is related to E by 5.67e-8*T^4 +/- a touch. So as T linearly decreases E, exponential decreases. When you pick a range where the relationship between T and E can be assumed linear or more accurately more predictable, your model that you are assuming the universe obeys is more accurate.
When you get down in the ballpark of 184K degrees, about 65 Wm-2 with CO2 in the mix, there are interesting coincidences. When you get to around 273K with water there are interesting coincidences. So assuming a fixed enthalpy and a predictable relationship between T and E gets more complicated.
Now if you assume away those issues, you would predict the temperature change between the Earth’s Stratopause and the Turbopause to be one thing, but when you include those coincidences you get a lapse rate from 273K to 184K over approximately 50 kilometers. Which is about 1.78K/km
You can pick another planet with another mixture of gases and find another lapse rate in some portion of its atmosphere that behaves “oddly”. In my experience with dealing with water vapor, assuming a “fixed” enthalpy is nutso cuckoo. So I am completely convinced that someone looking hard enough can find a special case.
Joe Born,
Regarding a topic that interests both of us, I found the discussion in the following paper, regarding the point of making use of different partition functions such as the canonical, grand canonical or microcanonical ensembles (there are more; there even exists a grand microcanonical partition function!), for the study of systems under gravity to be illuminating.
P. H. Chavanis, ‘Gravitational instability of isothermal and polytropic spheres’
http://cds.cern.ch/record/566951/files/0207080.pdf
Thank you. (I hope to be able to comprehend it.)
This is easily shown to be wrong for the simple reason that if a vertical column of gas were isothermal in a gravitational field then there would obviously be unbalanced energy potentials because molecules at the top would have more gravitational potential energy whilst still having the same kinetic energy. And if you have unbalanced energy potentials then you do not have maximum entropy.
Dr Alex Hamilton,
That’s a common misunderstanding. The following post by Pekka addresses your question:
http://judithcurry.com/2014/12/01/gravito-thermal-discussion-thread/#comment-653688
See also the following post:
http://judithcurry.com/2014/12/01/gravito-thermal-discussion-thread/#comment-653483
Consider also that it just doesn’t make sense for a column of a weakly interacting ideal gas at equilibrium to have balanced potentials in the way you conceive. This would mean that the average internal energy of the molecules at the bottom of the gravity well determine a maximum height above which the average kinetic energy would be negative. Any level above this maximum height would be thus be forbidden. This would be the height H where the potential gravitational energy of a molecules m*g*H would be equal to the average internal energy of a molecule at the bottom of the column ((3/2)kT for a monatomic gas). But clearly, since this is an average, half the molecules at the bottom have enough kinetic energy to climb above that height (provided they are suitably oriented).
I just found another relevant paper:
Verkley and Gerkema, ‘On Maximum Entropy Profiles’, Journal of Atmospheric Science, 2004
http://journals.ametsoc.org/doi/pdf/10.1175/1520-0469%282004%29061%3C0931%3AOMEP%3E2.0.CO%3B2
From the abstract: “[…] what vertical temperature profile maximizes the total entropy of the column? Using an elementary variational calculation, it is shown how the result depends on what is kept fixed in the maximization process. If one assumes that there is no net heat exchange between the column and its surroundings—implying that the vertical integral of the absolute temperature remains constant—an isothermal profile is obtained in accordance with classical thermodynamics and the kinetic theory of gases. If instead the vertical integral of the potential temperature is kept fixed—as argued by several authors to be appropriate in the case of convective mixing—an isentropic profile results”
The second response contains the phrase “constant potential temperature”
which I think is perfectly suited in that it’s a concise and apt summation of my opinion on the equilibrium state of a non-convecting atmosphere. I wish I coined the term myself. The wiki entry http://en.wikipedia.org/wiki/Potential_temperature should also be read and understood. The atmosphere isn’t a box and air isn’t an ideal gas. Insisting that these idealized states are reflective of and predictive of the real non-ideal world can lead to significant mistakes. Climate science in particular, not being amenable to experimental science to confirm postulates, is rife with such mistakes.
http://www.phys-l.org/archives/2012/1_2012/msg00075.html
http://en.wikipedia.org/wiki/Potential_temperature
“Since parcels with the same potential temperature can be exchanged without work or heating being required, lines of constant potential temperature are natural flow pathways.”
Implied is that non-constant potential temperature in a planetary atmosphere requires expenditure of energy (work or heating) to maintain. In an isolated non-convecting atmosphere the equilibrium state is constant potential temperature i.e. a constant mechanical energy gradient such that no work can be accomplished across the gradient.
The resistance of dogmatic (warmist) individuals is indicative of their lack of critical thinking skills and almost total reliance on concepts supported by the ad populum fallacy. Such thinking characterizes a pernicious philosophy of science that stunts progress.
“Implied is that non-constant potential temperature in a planetary atmosphere requires expenditure of energy (work or heating) to maintain.”
Since the assumption is that the convective process is *adiabatic*, heat conduction (from molecular diffusion) is neglected. Viscous heat dissipation from the relative movement of adjacent convective cells also is neglected. This is why the isentropic temperature profile doesn’t represent a state of thermodynamic equilibrium for a real gas. An external energy source is required to maintain convection.
“In an isolated non-convecting atmosphere the equilibrium state is constant potential temperature i.e. a constant mechanical energy gradient such that no work can be accomplished across the gradient.”
On the contrary, the paper argues that the profile is isothermal in non-convecting atmospheres (at equilibrium) and tends to approach an isentropic profile when conviction is large enough such that effects from dissipation and diffusion can be neglected. Actual convection, or the absence thereof, is the criterion that separates the isothermal from the isentropic cases.
In any case, the isentropic solution exhibits a barometric density profile together with an the adiabatic lapse rate, so it is quite different from the strange ‘iso-mechanical-energetic’ profile that you were defending. The profile that you are defending has a cut-off height where all the mechanical energy is transformed into potential gravitational, and molecules can’t rise any further, rather than the density dropping exponentially (with a temperature dependence of the exponential function).
Maximum entropy is attained when mechanical energy in a mole of atmosphere at any given elevation is equal to a mole of mechanical energy at any other elevation. No work can be extracted from that state. Potential and kinetic energy are freely interchangeable so nothing exists to prohibit an isolated non-convecting atmosphere from reaching this maximum entropy state. Your argument simply doesn’t hold water, Pierre. It is disputed by basic statistical mechanics.
“Maximum entropy is attained when mechanical energy in a mole of atmosphere at any given elevation is equal to a mole of mechanical energy at any other elevation. No work can be extracted from that state.”
(Let me first pick a nit: when a gas loses internal energy through performing adiabatic expansion work on the surrounding, radiating, or conducting heat away, then some of the energy is lost from internal rotational and vibrational states of di- and polyatomic molecules, not just from (translational) kinetic energy. But let us ignore this and imagine that ‘air’ is constituted of monatomic molecules for simplicity, and all the internal energy is therefore kinetic. (Hence Uavg = KEavg = (3/2)kT). I also had overlooked this in a previous commentary.)
If a mole of air at ground level on Earth has a temperature of 300°K, then, assuming thermodynamic equilibrium as you conceive it, then *all* its molecular kinetic energy is converted into gravitational potential energy at a height of 5.8km. This would entail (again, ignoring internal rotational states of diatomic molecules, etc.) that the kinetic temperature of one mole of air at that height would be 0°K. This is also the height potentially reached by a molecule that has the *average* kinetic energy at ground level and that is initially moving straight up. You view is that there aren’t any molecules that can rise any higher than 5.8km at equilibrium. For if some definite proportion did, then the total mechanical energy of one mole of air at this higher level would be larger than it is at ground level — since it can’t be any lower than the total gravitational potential energy at this level. Right?
Pierre-Normand | December 6, 2014 at 8:34 am |
” I said to CD that he can’t dissociate himself from the slayers on the issue of the G-T effect when he (and yourself) endorses basically the same “basic argument” about constancy of mechanical energy as a function of height, and is seemingly unaware (as you are) of the flaw in this argument. If you don’t want to lose time with me, and are unwilling to respond to some criticisms or your arguments… don’t respond.”
That is not an accurate description of the dragon-slayer argument. Unsurprisingly you aren’t familiar with that either. The dragon-slayer argument is that the bottom of the atmosphere is warmer than it would be in the absence of gravity. That is not my argument nor that of Loschmidt. You bring nothing to this dialog arguing against straw men. Your lack of ability to describe the arguments presented in opposition smacks of religious zealotry rather than informed argument. Please stop wasting our time.
Pierre-Normand | December 6, 2014 at 8:34 am |
DS: “Pierre, you don’t know enough to distinguish my position from the dragon slayers.”
It’s not my goal to distinguish or compare you with them.
—————————————————————————–
It’s not your goal to understand the arguments in opposition to your own. That is certainly a revealing statement. You’re right and what anyone else thinks simply doesn’t matter and isn’t worth your time. LOL
Obviously, I wan’t to distinguish your *argument* from their’s, just no *you* personally who I want to compare. I thought I had made that clear in the post that first provoked your ire. I said that I try not to pigeon hole people who I choose to respond to. It just so happen that your argument about the alleged invariance of total molar mechanical energy density with height is flawed for the same reason CD’s ‘basic premise’ and the slayers make the same error.
P-N, Excuse me, my basic premise is that is that in a real gas the range of potential velocities would produce a range of inter-molecular interactions that cannot be properly considered in an “ideal gas” model. In other words, there are complex enthalpy considerations that would impact entropy estimations. I believe that is in the e^-(H-TS)/kT Gibbs free energy. That would make equilibrium, temperature dependent though it is actually energy dependent with T used as a sometimes limited proxy for energy, i.e. kinematic temperature versus a more robust thermodynamic temperature.
In a *real* atmosphere the temperature and composition would matter. On the whole, “meh, it is insignificant in a real atmosphere.” is my *position* statement. Now what you *think* my position is could differ, but using circular logic isn’t going to firm up whatever your position is.
I think Rob has already compared this to the Bose-Einstein fiasco. The object of physics is to describe nature not force nature to bend to your will.
Again with the straw men, Pierre. I said nothing about energy density with height. It’s not hard to quote me accurately unless doing so weakens your own argument the maybe it would be hard for someone who is convinced of their own infallibility. I said in an insolated non-convecting atmosphere the equilibrium state is that a mole of air at the bottom has the same mechanical energy as a mole of air at the top. Please stop arguing with straw men. It’s a waste of everyone’s time and mechanical energy.
David Springer: “I said in an insolated non-convecting atmosphere the equilibrium state is that a mole of air at the bottom has the same mechanical energy as a mole of air at the top.”
That’s exactly what I understood you to have said. A mole has the same mechanical energy at any height. I paraphrased your position thus: “the alleged invariance of total *molar* mechanical energy density with height” (added emphasis). That means the same thing. When parcels of air have the same total mechanical energy per mole at any height, then the molar mechanical energy density is invariant with height. Those are two equivalent ways to say the same thing. And my arguments have been targeting exactly this invariance claims of yours, also seemingly supported by your beliefs that entropy maximization entails it, and that thermodynamic equilibrium entails an isentropic profile.
David Springer, December 6, 2014 at 10:44 am:
“It’s not your [Pierre-Normand’s] goal to understand the arguments in opposition to your own. That is certainly a revealing statement. You’re right and what anyone else thinks simply doesn’t matter and isn’t worth your time. LOL”
I very much agree with this observation. Very much to the point. Thanks :)
It seems obvious to me that this idea has merit. Imagining the same planet with a non-radiative atmosphere that Willis imagined above, the self-evident truths would seem to me to be:
1) without an atmosphere; radiation in would equal radiation out, and it would radiate in accordance with its temperature^4.
2) add the atmosphere, and the gas in contact with the surface would attain that temperature through conduction.
3) Hot air rises, gravity pulls it down again. New colder gas replaces the warmed gas; convection & lapse rate
4) Until equilibrium was reached the energy in would be less than energy out. Radiation is still occuring from the surface
5) Once the atmosphere had reached the temperature of the surface, then equilibrium is restored and enery in = energy out once again.
6) We are left with a planet with a warmer atmosphere than before.
If, it seems to me that people are suggesting that non-radiative gasses can’t heat up, can I suggest they do an experiment by filling a pressure cooker with a non radiative gas, closing off the pressure valve and putting it on the stove-top on full, and going out for the evening. Take your time. Have that second bottle. dessert. If they’d be happy doing that – I’d be convinced. :-D
Oops.. 4) should obviously be:
4) Until equilibrium was reached the energy OUT would be less than energy IN. Radiation is still occuring from the surface