Guest Post by Willis Eschenbach
Since at least the days of Da Vinci, people have been fascinated by perpetual motion machines. One such “perpetuum mobile” designed around the time of the civil war is shown below. It wasn’t until the development of the science of thermodynamics that it could be proven that all such mechanisms are impossible. For such machines to work, they’d have to create energy, and energy cannot be either created or destroyed, only transformed.
I bring this up for a curious reason. I was reading the Jelbring hypothesis this afternoon, which claims that greenhouse gases (GHGs) are not the cause of the warming of the earth above the theoretical temperature it would have without an atmosphere. Jelbring’s hypothesis is one of several “gravito-thermal” theories which say the heating of the planet comes from gravity rather than (or in some theories in addition to) the greenhouse effect. His thought experiment is a planet with an atmosphere. The planet is isolated from the universe by an impervious thermally insulating shell that completely surrounds it, and which prevents any energy exchange with the universe outside. Inside the shell, Jelbring says that gravity makes the upper atmosphere colder and the lower atmosphere warmer. Back around 2004, I had a long discussion on the “climateskeptics” mailing list with Hans Jelbring. I said then that his theory was nothing but a perpetual motion machine, but at the time I didn’t understand why his theory was wrong. Now I do.
Dr. Robert Brown has an fascinating post on WUWT called “Earth’s baseline black-body model – a damn hard problem“. On that thread, I had said that I thought that if there was air in a tall container in a gravity field, the temperature of the air would be highest at the bottom, and lowest at the top. I said that I thought it would follow the “dry adiabatic lapse rate”, the rate at which the temperature of dry air drops with altitude in the earth’s atmosphere.
Dr. Brown said no. He said that at equilibrium, a tall container of air in a gravity field would be the same temperature everywhere—in other words, isothermal.
I couldn’t understand why. I asked Dr. Brown the following question:
Thanks, Robert, With great trepidation, I must disagree with you.
Consider a gas in a kilometre-tall sealed container. You say it will have no lapse rate, so suppose (per your assumption) that it starts out at an even temperature top to bottom.
Now, consider a collision between two of the gas molecules that knocks one molecule straight upwards, and the other straight downwards. The molecule going downwards will accelerate due to gravity, while the one going upwards will slow due to gravity. So the upper one will have less kinetic energy, and the lower one will have more kinetic energy.
After a million such collisions, are you really claiming that the average kinetic energy of the molecules at the top and the bottom of the tall container are going to be the same?
I say no. I say after a million collisions the molecules will sort themselves so that the TOTAL energy at the top and bottom of the container will be the same. In other words, it is the action of gravity on the molecules themselves that creates the lapse rate.
Dr. Brown gave an answer that I couldn’t wrap my head around, and he recommended that I study the excellent paper of Caballero for further insight. Caballero discusses the question in Section 2.17. Thanks to Dr. Browns answer plus Caballero, I finally got the answer to my question. I wrote to Dr. Brown on his thread as follows:
Dr. Brown, thank you so much. After following your suggestion and after much beating of my head against Caballero, I finally got it.
At equilibrium, as you stated, the temperature is indeed uniform. I was totally wrong to state it followed the dry adiabatic lapse rate.
I had asked the following question:
Now, consider a collision between two of the gas molecules that knocks one molecule straight upwards, and the other straight downwards. The molecule going downwards will accelerate due to gravity, while the one going upwards will slow due to gravity. So the upper one will have less kinetic energy, and the lower one will have more kinetic energy.
After a million such collisions, are you really claiming that the average kinetic energy of the molecules at the top and the bottom of the tall container are going to be the same?
What I failed to consider is that there are fewer molecules at altitude because the pressure is lower. When the temperature is uniform from top to bottom, the individual molecules at the top have more total energy (KE + PE) than those at the bottom. I said that led to an uneven distribution in the total energy.
But by exactly the same measure, there are fewer molecules at the top than at the bottom. As a result, the isothermal situation does in fact have the energy evenly distributed. More total energy per molecules times fewer molecules at the top exactly equals less energy per molecule times more molecules at the bottom. Very neat.
Finally, before I posted my reply, Dr. Brown had answered a second time and I hadn’t seen it. His answer follows a very different (and interesting) logical argument to arrive at the same answer. He said in part:
Imagine a plane surface in the gas. In a thin slice of the gas right above the surface, the molecules have some temperature. Right below it, they have some other temperature. Let’s imagine the gas to be monoatomic (no loss of generality) and ideal (ditto). In each layer, the gravitational potential energy is constant. Bear in mind that only changes in potential energy are associated with changes in kinetic energy (work energy theorem), and that temperature only describes the average internal kinetic energy in the gas.
Here’s the tricky part. In equilibrium, the density of the upper and lower layers, while not equal, cannot vary. Right? Which means that however many molecules move from the lower slice to the upper slice, exactly the same number of molecules must move from the upper slice to the lower slice. They have to have exactly the same velocity distribution moving in either direction. If the molecules below had a higher temperature, they’d have a different MB [Maxwell-Boltzmann] distribution, with more molecules moving faster. Some of those faster moving molecules would have the right trajectory to rise to the interface (slowing, sure) and carry energy from the lower slice to the upper. The upper slice (lower temperature) has fewer molecules moving faster — the entire MB distribution is shifted to the left a bit. There are therefore fewer molecules that move the other way at the speeds that the molecules from the lower slice deliver (allowing for gravity). This increases the number of fast moving molecules in the upper slice and decreases it in the lower slice until the MB distributions are the same in the two slices and one accomplishes detailed balance across the interface. On average, just as many molecules move up, with exactly the same velocity/kinetic energy profile, as move down, with zero energy transport, zero mass transport, and zero alteration of the MB profiles above and below, only when the two slices have the same temperature. Otherwise heat will flow from the hotter (right-shifted MB distribution) to the colder (left-shifted MB distribution) slice until the temperatures are equal.
It’s an interesting argument. Here’s my elevator speech version.
• Suppose we have an isolated container of air which is warmer at the bottom and cooler at the top. Any random movement of air from above to below a horizontal slice through the container must be matched by an equal amount going the other way.
• On average, that exchange equalizes temperature, moving slightly warmer air up and slightly cooler air down.
• Eventually this gradual exchange must lead to an isothermal condition.
I encourage people to read the rest of his comment.
Now, I see where I went wrong. Following the logic of my question to Dr. Brown, I incorrectly thought the final equilibrium arrangement would be where the average energy per molecule was evenly spread out from top to bottom, with the molecules having the same average total energy everywhere. This leads to warmer temperature at the bottom and colder temperature at elevation. Instead, at thermal equilibrium, the average energy per volume is the same from top to bottom, with every cubic metre having the same total energy. To do that, the gas needs to be isothermal, with the same temperature in every part.
Yesterday, I read the Jelbring hypothesis again. As I was reading it, I wondered by what logic Jelbring had come to the conclusion that the atmosphere would not be isothermal. I noticed the following sentence in Section 2.2 C (emphasis mine):
The energy content in the model atmosphere is fixed and constant since no energy can enter or leave the closed space. Nature will redistribute the contained atmospheric energy (using both convective and radiative processes) until each molecule, in an average sense, will have the same total energy. In this situation the atmosphere has reached energetic equilibrium.
He goes on to describe the atmosphere in that situation as taking up the dry adiabatic lapse rate temperature profile, warm on the bottom, cold on top. I had to laugh. Jelbring made the exact same dang mistake I made. He thinks total energy evenly distributed per molecule is the final state of energetic equilibrium, whereas the equilibrium state is when the energy is evenly distributed per volume and not per molecule. This is the isothermal state. In Jelbrings thought experiment, contrary to what he claims, the entire atmosphere of the planet would end up at the same temperature.
In any case, there’s another way to show that the Jelbring hypothesis violates conservation of energy. Again it is a proof by contradiction, and it is the same argument that I presented to Jelbring years ago. At that time, I couldn’t say why his “gravito-thermal” hypothesis didn’t work … but I knew that it couldn’t work. Now, I can see why, for the reasons adduced above. In addition, in his thread Dr. Brown independently used the same argument in his discussion of the Jelbring hypothesis. The proof by contradiction goes like this:
Suppose Jelbring is right, and the temperature in the atmosphere inside the shell is warmer at the bottom and cooler at the top. Then the people living in the stygian darkness inside that impervious shell could use that temperature difference to drive a heat engine. Power from the heat engine could light up the dark, and provide electricity for cities and farms. The good news for perpetual motion fans is that as fast as the operation of the heat engine would warm the upper atmosphere and cool the lower atmosphere, gravity would re-arrange the molecules once again so the prior temperature profile would be restored, warm on the bottom and cold on the top, and the machine would produce light for the good citizens of Stygia … forever.
As this is a clear violation of conservation of energy, the proof by contradiction that the Jelbring hypothesis violates the conservation of energy is complete.
Let me close by giving my elevator speech about the Jelbring hypothesis. Hans vigorously argues that no such speech is possible, saying
There certainly are no “Elevator version” of my paper which is based on first principal physics. It means that what I have written is either true or false. There is nothing inbetween.
Another “gravito-thermal” theorist, Ned Nikolov, says the same thing:
About the ‘elevator speech’ – that was given in our first paper! However, you apparently did not get it. So, it will take far more explanation to convey the basic idea, which we will try to do in Part 2 of our reply.
I don’t have an elevator speech for the Nikolov & Zeller theory (here, rebuttal here) yet, because I can’t understand it. My elevator speech for the Jelbring hypothesis, however, goes like this:
• If left undisturbed in a gravity field, a tall container of air will stratify vertically, with the coolest air at the top and the warmest air at the bottom.
• This also is happening with the Earth’s atmosphere.
• Since the top of the atmosphere cannot be below a certain temperature, and the lower atmosphere must be a certain amount warmer than the upper, this warms the lower atmosphere and thus the planetary surface to a much higher temperature than it would be in the absence of the atmosphere.
• This is the cause of what we erroneously refer to as the “greenhouse effect”
Now, was that so hard? It may not be the best, I’m happy to have someone improve on it, but it covers all the main points. The claim that “gravito-thermal” theories are too complex for a simple “elevator speech” explanation doesn’t hold water.
But you can see why such an elevator speech is like garlic to a vampire, it is anathema to the “gravito-thermal” theorists—it makes spotting their mistakes far too easy.
w.
Bryan says:
Bryan:
You seem to have a problem understanding that context is important for a discussion. For the discussion we are having here, about the errors that render the N&Z paper nonsense, the debate over the temperature of the moon is a distraction.
Also, you will note that when we discussed the temperature of the moon in Halpern et al., we noted that the moon has wide temperature swings and for the most part avoided trying to define a single average temperature for a celestial object with such a wide temperature variation, noting only that a ballpark “average” that you get from taking the mid point of the mean day and night temperatures is somewhere in the range of what you expect, i.e., between the extreme of what would be predicted if the temperature just followed the local insolation and the other extreme of what would be predicted for the case of a uniform temperature.
We did not spend a lot of time arguing about exactly what that average temperature was. Hence, this actually shows a strong consistency in our position regarding getting bogged down in gory details of exactly what the “average temperature” is for a celestial object that has an extremely broad temperature distribution.
Paul Birch;
we have no way of knowing how many other forms they tried before coming across one that seemed to work. Given that there are only about six planets being fitted (excluding airless bodies) information theory tells us that such an empirical fit is wholly unconvincing. They do give what I suppose is intended as a physics justification for their model, but this I find incomprehensible – probably because it’s complete nonsense.>>>
I agree. Anything that I don’t understand is clearly nonense. For example, I don’t understand how gravity works, so it must be nonsense.
You’re essentially accusing them of curve fitting and noting that there are “only” six planets being fitted. “Only” six? They found ONE curve and it fits SIX planets.
Seems like a pretty good curve to me.
O H Dahlsveen says:
January 23, 2012 at 1:35 pm
Clueless. Got a link?
w.
davidmhoffer says:
January 23, 2012 at 6:07 pm
David … I truly don’t know what to say about this comment.
1. Paul didn’t say he didn’t believe equation 8 because he didn’t understand it. In fact, he doesn’t believe it because he does understand it. As a result, your attempt at satire is meaningless.
2. I’m not “essentially” accusing them of curve fitting, I am saying flat out that they fitted the curve … as they freely admit.
3. I’m sure it does seem like a “pretty good curve” to you, David … I’m sure it does.
w.
Smokey says:
January 23, 2012 at 4:41 pm
[my emphasis]
That would be the boxes were insulated with cotton around the outside. If the boxes had been filled with cotton that would have been packed with cotton. Also the boxes had been constructed with the window attached before cotton was mentioned. Also, there wouldn’t be much point in painting the inside of the box black and then filling it with white cotton. Are greenhouses filled with cotton? Not hardly. Vaughan Pratt’s boxes were insulated with 0.5″ thick foamed polystyrene art board (polystyrene foam with paper covering on both sides). My boxes (work in progress and the weather has been terrible here lately) are insulated with R-30 fiberglass batting inside a box made of 0.75″ foamed polystyrene board. I get an increase over ambient of on the order of 100C for a box with a polyethylene film window and 20-30C higher than that for a box with a glass window. The bottom surface of a triple layer IR opaque windowed box reached 170C. Wood only got up to 60C with a higher ambient temperature.
Why would Abbot replicate identically an obviously flawed experiment? Wood only achieved a temperature of 65C. Abbot’s experiment reached 118C, 102C above ambient. Wood didn’t even mention the ambient temperature. Wood’s results disagreed with both previous results and with theory. It was dismissed as irrelevant at the time. It wasn’t resurrected until 1990 by people who apparently didn’t bother to look at the complete story.
I think I know what Wood’s mistake was, but, as I said, the weather has been uncooperative so I haven’t been able to prove it. I’ve only had about 2 hours of clear sky in the last two weeks.
thepompousgit says:
January 23, 2012 at 3:40 pm
You’re not trying for maximum temperature. It would kill the plants. Any device that is intended to operate at a temperature different from ambient must be insulated first, like an oven or a refrigerator or your house or like a planet is insulated by the vacuum of space. Most people use polyethylene film for greenhouses because it’s cheap and easily replaced if it gets damaged by the weather and it’s good enough.
But some applications need better performance which can be provided by low-E glass ( http://www.florianproducts.com/low-e.html ). If Wood were correct, then low-E glass that is now standard in high quality double glazed windows would be a colossal scam. But he was wrong and it isn’t.
thepompousgit says:
January 23, 2012 at 3:40 pm
Most people use polyethylene film for greenhouses because it’s cheap and good enough. If you’re trying to demonstrate the greenhouse effect, though, you have to try harder.
There is a market for greenhouses constructed of high performance low emissivity glass like PPG Solarban80. If Wood was correct the entire low emissivity glass industry is a colossal scam. But he wasn’t and it isn’t.
thepompousgit says:
January 23, 2012 at 3:40 pm
My replies keep getting lost. Perhaps they’re getting bounced because I mention the trade name of a commercial product.
Anyway. Most people use polyethylene film for greenhouses because it’s cheap and good enough. But Wood was trying to demonstrate that even under what he thought were ideal circumstances, the IR transmission characteristics of the window made no difference. He was wrong and it’s not difficult to prove it.
Willis Eschenbach;
3. I’m sure it does seem like a “pretty good curve” to you, David … I’m sure it does.>>>
I once sat in a calculus class where the professor proposed a problem involving a case of beer at some unkown temperature being immersed in a lake of known temperature and the temperature of the case of beer being taken at a couple of points in time after the beer had been immersed. It was a long time ago, there may have been other factors, but that was the essence of the problem. The professer asked for equations to determine the temperature of the case of beer at various times in the future. I got the answer via three pages of calculus, as did much of the rest of the class.
The guy beside me however pulled out a sheet of natural log paper, plotted what little data we’d been given, struck a line through it, and got almost exactly the same answer.
That’s a pretty good curve.
Now if you can set your sarcasm aside for a moment, please help me understand this. There is in fact a curve, is there not? Yes, N&Z may have erred in how they determined the curve. I haven’t gone back through the math to make any judgment. There are those far more versed than me in both the calculus and the physics, both of which were a very long time ago for me. And, even if they erred, I refuse to throw the babay out with the bath water. They are correct on a number of points, including the fact that straightforward averaging of P and T arrives at conclusions regarding GHE and other issues that are unsound. The effective blackbody T of earth is not 255, it is less, a lot less. By moving energy from the tropics to higher latitudes, the energy balance can be completely undisturbed, yet yield a higher average temperature, without GHG effects to do it. They got a lot more right than they got wrong, and they got some things wrong for the right reasons. I think they erred in useing surface pressure for example, I think they should have focused on density. The higher the density, the more efficient processes such as conductance and convection are at moving energy from low to high latitudes, which in turn results in a higher average temperature though not a higher average radiance, and this relievs their theory of needing to account for higher temperatures derives from compression of gas. I maintain that the driving factor is the efficiency with which energy ismoved from low to high altitdues, and the higher that efficiency, the more uniform the temperature of the planet, and from that, the higher the average T though effective T via SB Law remains unchanged and no violation of laws of thermodynamics occurs.
But at days end, either there is a curve, or there isn’t. If I was intent on refuting N&Z, I’d start with the empircal data. What are the surface pressures of those planets and what are there temperatures? Does that yield a curve suggestive of a mathematical relationship or not? If the curve plot zig zags across the page, not. If it follows a smoothly curved line of some sort, then I have only one question.
What defines the curve?
If N&Z arrived at the right curve via the wrong means, there still remains a curve to be explained.
DeWitt Payne said @ur momisugly January 23, 2012 at 8:18 pm
Lost posts: Sometimes they get stuck in the spam filter & get released by different mods. I find it helps to send a message to the mods to delete the “extras”. Sometimes the message really doesn’t get through. As a matter of course these days, I copy the post to the clipboard, or Notepad just in case.
Greenhouse cladding: I looked up the difference between IR treated polythene and ordinary. The treated gives between up to 1.5 C above ambient at night. On really cold nights it is next to useless so not much use in a greenhouse. I suspect that it might pay for itself in a hothouse when you are paying for fuel. I am familiar with LoE glass as we used double-glazed LoE when building The House of Steel. Gits like their comfort 🙂
I find most people haven’t read the historical research papers they so freely “quote”. Historians & philosophers read them; they are usually very instructive 🙂 I might have a look at those early experiments and have a play; I certainly have enough scrap materials lying around. First I have to build The Finished Greenhouse. The experimental one works, but the FG will be equipped with automated venting (thermal wax operated) and will be productive over a slightly longer season. SWMBO tends to frown if I play when there’s “real” work to be done.
I’d appreciate sharing what you come up with in regards to your experiment. My email is jonathan at sturmsoft dot com. Cheers…
I fear that lay readers visiting this site are going to conclude that a large portion of the physics community have taken leave of their senses.
Whatever the convoluted quibbles about the N & Z workings everyone knows that air above heated ground gets warmer than it would above unheated ground.
That means ALL the air not just any GHGs within it. And that the degree of warmth acquired will be density related
The primary mechanism is conduction and convection. The presence of GHGs might help the conduction and convection process by spreading upward longwave around more efficiently between adjoining non GHG molecules but equally it helps the conversion of conducted and convected energy back to outward longwave so the effect is pretty much neutral.
Arguing against the general principle is frankly an embarrassment to all.
Then all that N & Z did was to look at improved data for planetary surface temperaure, adjust for an apparent error in the previous application of the S – B equations and point out that in the real world the simple relationship betwen pressure and solar input comes remarkably close to matching actual surface temperatures without considering atmospheric composition at all.
In the process they find that the extra kinetic energy needed to explain surface warmth beneath an atmosphere cannot possibly be accounted for by the presence of GHGs alone.
So, chaps, instead of bleating that it isn’t possible and inventing all sorts of imaginative ‘flaws’ in the N & Z work (that do not address the essential point) I think a period of quiet reflection is called for on the part of the most assertive contributors here.
Willis Eschenbach says:
January 23, 2012 at 12:38 am
“Actually the facts we have do allow us to draw some conclusions. Let me define the “theoretical S-B temperature” as the temperature of a blackbody with a uniform surface temperature corresponding to the amount of incoming radiation. Here’s what we know.
1. For a given incoming radiation, any variation in surface temperature from the isothermal state will lower the mean surface temperature.
2. An atmosphere, with or without greenhouse gases, can reduce the temperature drop from variations in temperature. It does this by reducing the amount of day / night ∆T and equator / polar ∆T.
3. A transparent GHG-free atmosphere cannot warm the surface above the isothermal state of the theoretical S-B temperature.
Therefore: at a minimum, the greenhouse effect of GHGs and clouds must be responsible for at least the thirty degrees C that the earth is above the theoretical S-B temperature.
In addition, since the greenhouse effect undoubtedly reduces the day/night temperature swings, some additional amount of the warming beyond the 33°C is also due to the greenhouse effect.”
I strongly disagree. Fact is If insolation was uniform the passive solar water heating system could not even make it to the average local ambient temperature for the same reason I disagree with your conclusions.
Thus your conclusion that it would have to be 30 degrees warmer is no doubt wrong. There is not the slightest doubt in my mind that heat storage in the atmosphere is part of the greenhouse effect, if not all of it.
The only reason passive solar water heating technology works is because of the diurnal cycle of insolation. Otherwise the system would produce exactly what underground pipes produce now without a system namely water at your local average climate temperature which also happens to be about the temperature of the soil that the pipes run through.
The fact is simple physics ensures that at least a major portion of the “GHE” is due to atmospheric warming by the diurnal cycle.
Air is an excellent insulator and the GHE is really more like 16K because probably the correct way of measuring it is by taking its “average” throughout the layers of the atmosphere from the surface to that notion of TOA where 240 watts is emitted to the sky and since the lapse rate is linear the average should be half what is measured at the surface.
I have built a few water systems and would not be surprised that 16K is an average you can achieve.
Probably the only reason to not today rely exclusively on them is the fact that you can have extended periods of very heavy clouds that limit their potential on certain days in certain locations so you have to a back up system to deal with that.
But that is something even the greenhouse effect has no answer for.either!
Bryan:”In the derivation of the ideal gas laws the molecules are said to make perfectly elastic collisions with the container walls.
“In reality the walls are ‘sticky’.”
However that may be, the question before the house is what the temperature distribution would be in the ideal case.
A brief review of the bidding:
Jelbring says that at equilibrium a thermally isolated ideal-monatomic-gas column in a gravitational field will assume a configuration that exhibits the dry adiabatic lapse rate, and I believe he’s saying this is the maximum-entropy state. I won’t attempt to characterize his rationale.
Robert Brown disagrees. He says that the maximum-entropy configuration is isothermal. Unfortunately, his analysis is appallingly superficial for a physics professor. For all that is apparent in his responses, he remembers nothing more than the result that heat flows from hot to cold and apparently doesn’t recall the assumptions by which that result was reached. This appears to be the general level of understanding of the other physicists on this site, too. I’m embarrassed for Duke and, since it is one of the most well-regarded universities in the United States, for my country’s educational establishment.
To me it appears that neither Jelbring nor Brown is correct. Based on the result stated in the Velasco et al. paper, my impression is that the maximum-entropy configuration does have a non-zero temperature lapse rate, but one that is less than the dry adiabatic lapse rate for any significant number of molecules. But there are steps in Velasco et al. paper I was struggling with, and I had hoped that there was enough intellectual curiosity at this site that I would get help with that from the physicists here.
Unfortunately, none of the physicists engaged meaningfully, and the only two participants here who have engaged have been big disappointments. Willis Eschenbach claimed actually to have read Velasco et al.’s equations and found that they didn’t say what I contend they do. Since Equation 8 so clearly does yield a non-zero lapse rate, I briefly harbored bad thoughts about Willis’s veracity. After seeing him flail about with the math on another thread, though, I’m willing to accept that he actually had read the equations but just was not equal to the math. Be that as it may, it’s clear he’ll be no help.
Finally, Paul Birch weighed in on the single-molecule thought experiment to which I applied Equation 8, but he, too, appears able only to parrot rules he’s heard. I’ve been reduced to trying Socratically to lead him to the correct answer, but it’s tough sledding. And, in any event, it doesn’t seem likely that he’ll be equal to helping derive Equation 8 from Equations 5 and 6.
So my question to you is, Can you perform that derivation?
I take your kilometer’s tall cylinder of atmosphere in thermal equilibrium and flip it over, like flipping an hour glass. It involved no input of work as its height did not change, so the column’s energy remains constant. But now the gas at temp T that was at the top has been wildly compressed, making it much, much hotter, while the gas at temp T that was at the bottom has been expanded, making it much, much colder. If you let it get anywhere close to thermal equilibrium I’m going to flip it over again, and since I’m not putting in any work, I can do this all day, continuously forcing your air column back to the dry adiabatic lapse rate as I sip a margarita.
I love doing jobs that don’t involve an input of work and constantly overturn an idealized thermal equilibrium, because it’s just that easy.
You must be very strong, because the density of air in the column in thermal equilibrium is much greater at the bottom than the top. In fact, you did a rather lot of work, if the cylinder in question is very high. All the air in your cylinder will then fall back to the bottom and inelastically collide with it. Because the column is adiabatic (well insulated) and you’ve input work, the air will have more energy and will be at a higher temperature in equilibrium. If you keep doing this, it will get very hot indeed, and I suspect that you will get tired. If you’re planning on restoring your lost metabolic energy with margaritas, plan on getting a really, really big pitcher.
rgb
Joe Born says:
January 23, 2012 at 4:17 pm
Paul Birch: “Every time it hits the surface it bounces back with a different energy, sometimes higher, sometimes lower.”
Joe: “What “surface” did you mean? Actually, let’s just concentrate on the surface off which the molecule bounces at the bottom of the column.”
OK. (In Jelbring and Willis’s set-ups there’s also the lid and side surfaces, but by all means let’s ignore them, since in the absence of collisions it’s obvious that the horizontal components of the molecule’s momentum keep the same “temperature”).
“At that surface its potential energy is zero, right?”
Zero or an arbitrary constant, yes.
“So the “different energy”.you must be talking about is all kinetic energy? If the potential energy is zero, and the kinetic energy is “sometimes higher, sometimes lower,” then the total energy is changing?”
Correct. The molecule is in thermal equilibrium with the surface, so at that surface its vertical velocity at each bounce is drawn from the Maxwell Distribution, which goes as exp(-p**2/kT), positive velocity on its way up, negative half on its way down. Energy is being swapped between surface and gas molecule on each bounce, but there is no net transfer over time. So the height the molecule can reach is different each bounce; thus, averaged over time, there is an probability density falling off exponentially with height. When you see the molecule high up, this is inevitably a highly selected outlier from the distribution – a bounce with an unusually high upwards velocity when it left the surface far below.
In my opinion, this is one case in which taking the extreme Knudsen case (single molecule, or gas too rarefied to have collisions) doesn’t actually make it any easier to understand what is going on – particularly since the gas is in thermal equilibrium and has a corresponding distribution of velocities.
Trick says:
January 23, 2012 at 4:50 pm
Paul Birch says: “Even your one-molecule system doesn’t have the same energy all the time.”
Trick: “It does if you mean total energy”
Not when it is in thermal equilibrium with a surface. It has an energy drawn randomly from the underlying Maxwell distribution. See my reply to Joe.
Joe Born you say;
“Based on the result stated in the Velasco et al. paper, my impression is that the maximum-entropy configuration does have a non-zero temperature lapse rate, but one that is less than the dry adiabatic lapse rate for any significant number of molecules. ”
If you post a link to the paper I will read it.
davidmhoffer says:
January 23, 2012 at 9:27 pm
“… a case of beer at some unkown temperature being immersed in a lake of known temperature and the temperature of the case of beer being taken at a couple of points in time after the beer had been immersed….The guy beside me however pulled out a sheet of natural log paper, plotted what little data we’d been given, struck a line through it, and got almost exactly the same answer.”
That is because the physics is trivial and he only needed the time constant. One free parameter and a known equation. So far as I can see, N&Z have no sound physics behind their equation and use at least four free parameters to fit no more than six inaccurate data points. That’s not a “good curve”. It’s worthless rubbish. I don’t even need to rework the fit, as Joel has done, to know it’s worthless. Common sense, my scientific intuition, and information theory alike all tell me so. Note that this doesn’t imply that N&Z’s hypothesis is necessarily wrong; what it says is that their purported evidence is meaningless; it doesn’t prove a thing (except perhaps that N&Z don’t seem to have a clue how physics works).
Robert Brown disagrees. He says that the maximum-entropy configuration is isothermal. Unfortunately, his analysis is appallingly superficial for a physics professor. For all that is apparent in his responses, he remembers nothing more than the result that heat flows from hot to cold and apparently doesn’t recall the assumptions by which that result was reached. This appears to be the general level of understanding of the other physicists on this site, too. I’m embarrassed for Duke and, since it is one of the most well-regarded universities in the United States, for my country’s educational establishment.
I’m sorry you find my analysis superficial. Perhaps you’ll find my top post on the issue (pending) more convincing. Also bear in mind that the only question I’m addressing is whether or not the adiabatic lapse rate is static thermal equilibrium as asserted by Jelbring. The adiabatic lapse rate completely ignores the mechanism of conduction and relies entirely on convection (the basis of adiabatic lapse).
I’m perfectly happy to look at an actual statistical mechanical computation that purports to examine the issue, as long as it is done in accordance with the axioms and methods of stat mech, that is to say, use a partition function or examine the density of states properly. Jelbring does none of that and his argument is absurd and wrong.
It is also certainly the case that — as my next top post will demonstrate pretty clearly — that including any sort of channel for heat conduction will either reduce any observed lapse rate to zero or cause a most peculiar flow of energy. I’d be interested in hearing your response to it.
The nice thing about the laws of thermodynamics is that they pretty much always hold. It requires very special circumstances for them not to hold — very small systems, open systems, strongly constrained systems. Analyzing a large systems in thermal equilibrium (not open) leaves only strong constraints, and those require very careful arguments and experimental support for experts to accept — the knee-jerk assumption is that equilibrium is isothermal and the first and second laws hold, built right in to the axioms of stat mech, detailed balance, the partition function. In the meantime, Caballero leaves it as a textbook exercise in detailed balance to show that there is no thermal lapse in equilibrium in the vertical direction in a uniform gravitational field.
I’ve already offered a verbal version of the argument (in another thread, IIRC) — the only way to achieve detailed balance across a vertical surface between neighboring differential slices of gas is if the distribution of velocities above and below the slices are the same, because they have to exchange equal numbers of particles going in the opposite directions. If the MB distributions are the same above and below, the two slices have the same temperature. If they have different temperatures, the peaks are shifted and detailed balance is impossible.
The point is that detailed balance is perfectly satisfied if — and I would argue only if, but I’m willing to listen to a counter argument — the MB distribution of molecular velocities is the same throughout the fluid. That goes without question, as a simple and obvious identity. It is trivial to balance forces with an isothermal distribution. So whether or not there is another solution, as you assert, there is absolutely no doubt that a stationary solution to both the static force balance and the requirement for detailed balance in energy flow is an isothermal column of fluid with the textbook expression for the pressure as a function of height. At any instant in such a fluid, the density will not change and the velocity distribution will not change, because equal numbers of particles will move up and down across any vertical surface and will have the same velocity as they do. Note that arguing that “gravity” speeds them up or slows them down ignores the fact that gravity does no net work in this system, and that the mean free path is much smaller than the distance for secular changes in the velocity due to gravity. Gravity heats things only when there are inelastic processes going on — dropping a big rock onto the Earth as a one time event. It is a bit difficult for me to see how gravity is going to move a system from detailed balance isothermal pressures to a distribution with a lapse and then maintain the lapse against the inexorable process of heat conduction the other way.
Perhaps there is an order of taking limits that is physically reasonable that permits this to happen, but surely the onus of proof is on the person making the assertion that it does to do a good job of proving it, as it is a most unusual and unexpected result. Jelbring’s E&E paper contains nothing of the sort, and it is what we are discussing, although feel free to top post about some other paper that proposes a lapse once we finish with Jelbring (later today) and N&Z (where I “finished” their empirical curve fitting T_s for the planets earlier this morning, demonstrating that the curve is completely meaningless, an artifact of the functional forms they used to fit with truly absurd physical numbers). That isn’t to say all of N&Z’s work is useless — I think their approach to computing a better approximate initial (pre-greenhouse) warming is fine and have proposed it myself on other threads, although their description and computation are not necessarily done “right”, yet. They are at least reasonable. I can’t assess their remarks on thermal lapse rates because they haven’t really explained them, or connected them in any way with the numbers in their “miracle” fit with its 54 Kbar and 202 bar reference pressures.
But when we finish with those two papers (and all of the attention they have attracted from confirmation biased skeptics who appear literally desperate to find some physics that shows that the GHE itself doesn’t exist, which is frankly absurd given top-of-atmosphere IR spectroscopy but go figure) I’d be happy to look at a paper that purports to derive a nonzero lapse rate with an open mind, especially if that lapse rate is almost vanishingly small, small enough to be a small correction to isothermal but nowhere near the observed adiabatic lapse rate that is clearly nowhere near a static thermal equilibrium.
In addition, I personally would be a whole lot happier for it to be experimentally verified. I already described a simple tabletop experiment to test the hypothesis — set up a horizontal dewar filled with e.g. Xenon as a centrifuge, place recording thermometers at both ends, and spin up the tube to 100-1000g, recording a long time series of the end temperatures. I’d expect the outer end to heat rapidly as you spin it up, and then relax to a uniform temperature throughout the tube, but I’d be happy to be experimentally shown to be wrong under controlled circumstances as long as the experimental run time exceeds the time required for conduction to thermalize the system and as long as the gas near the top/inside of the dewar never gets too thin for thermodynamics to work to describe it (in part because the mean free path gets so large that it is not in thermal equilibrium in the classical sense). I’d say spinning it up so that the top pressure is around what it is at the top of the troposphere (and the bottom is whatever, starting from 1 bar throughout) would be enough to see if there is a measurable lapse in equilibrium.
Perhaps that will be enough to restore your love and respect, to make my remarks and efforts to bring some small level of compliance with the actual laws of physics reflect well on Duke once again and stop embarrassing not only Duke, but all the physics departments in the United States. But somehow, I doubt it.
Sigh.
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Correct. The molecule is in thermal equilibrium with the surface, so at that surface its vertical velocity at each bounce is drawn from the Maxwell Distribution, which goes as exp(-p**2/kT), positive velocity on its way up, negative half on its way down. Energy is being swapped between surface and gas molecule on each bounce, but there is no net transfer over time. So the height the molecule can reach is different each bounce; thus, averaged over time, there is an probability density falling off exponentially with height. When you see the molecule high up, this is inevitably a highly selected outlier from the distribution – a bounce with an unusually high upwards velocity when it left the surface far below.
In my opinion, this is one case in which taking the extreme Knudsen case (single molecule, or gas too rarefied to have collisions) doesn’t actually make it any easier to understand what is going on – particularly since the gas is in thermal equilibrium and has a corresponding distribution of velocities.
And I completely agree. Detailed balance. People are conflating increasing particle density and hence energy density with temperature, which is a measure of average energy per particle. Each particle on average doesn’t rise or fall in equilibrium, so gravity is completely irrelevant to its temperature. Where gravity matters is in establishing the pressure profile of the gas. Where the two get tied together is — only — in the density of an ideal gas as a function of its temperature.
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Joe Born
One thing I did notice recently when looking at the graphs of density against altitude for air is that in the real atmosphere(adiabatic) the density does not decrease as fast as a proposed isothermic solution.
For 10Km the USA standard atmosphere gives 0.41Kg/m3.
A formula used for an isothermal atmosphere at the same altitude gives 0.34Kg/m3.
This means that if a column of air was suddenly made thermally isolated the centre of mass would gradually drop.
This means that gravitational potential energy would be lost and must therefore be turned into kinetic energy.
In other words as well as the gas becoming isothermal it also increases its average temperature.
So it seems that the isothermal option has increased its entropy.
Joe Born says:
January 24, 2012 at 2:09 am
“Finally, Paul Birch weighed in on the single-molecule thought experiment to which I applied Equation 8, but he, too, appears able only to parrot rules he’s heard. I’ve been reduced to trying Socratically to lead him to the correct answer, but it’s tough sledding.”
Have a bit of patience! I don’t sit at this computer 24 hours a day, and you’re no Socrates! As an admitted non-physicist you seem to be of the opinion that this Velasco et al (whoever they may be) have proved that there is a non-zero lapse rate at equilibrium. You will pardon me if I suspect that you are simply misunderstanding what they say (unless they’re not physicists either, in which case they’re probably just wrong – or even if they are physicists, it’s a lot more likely that they’ve made a slip-up than that they’ve overthrown the principles of thermodynamics). So if you want physicists here to check out the paper, post a (non-paywalled) link where we can read it.
Paul Birch: “So if you want physicists here to check out the paper, post a (non-paywalled) link where we can read it.”
Links to the Velasco et al. and related papers are provide at http://tallbloke.wordpress.com/2012/01/04/the-loschmidt-gravito-thermal-effect-old-controversy-new-relevance/.
Bryan: “So it seems that the isothermal option has increased its entropy.”
Yes, it does seem so, and I believe it would. I’m actually making only a very modest claim. I’m sure that going from a significant lapse rate s large as the dry adiabatic lapse rate to isothermality would increase entropy. But going from such a lapse rate to the (very small) lapse rate Velasco et al prescribe would increase it more if Velasco et al. are right.
Robert Brown: “Perhaps that will be enough to restore your love and respect, to make my remarks and efforts to bring some small level of compliance with the actual laws of physics reflect well on Duke once again and stop embarrassing not only Duke, but all the physics departments in the United States. But somehow, I doubt it.”
I apologize that in a moment of exasperation I went over the top, although I must say I have indeed been taken aback by how unwilling the disputants here have been to consider the bases for their beliefs.
I would indeed welcome a chance to have people who do this stuff for a living vet Velasco et al. and Roman et al. But I’m guessing experimental proof will be hard to come by in view of the low lapse rate Velasco et al. dictate for any reasonable amount of gas.
By the way, I’m getting to this only after having moved my argument to your own thread, to which I suggest we all transfer this discussion.