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.
“DeWitt Payne says:
January 21, 2012 at 5:02 pm
You didn’t pay close attention to the specification of my device.”
You are wasting your time DeWitt.
It is clear that Tallbloke is no longer in a rational thinking mode.
He is in fullblown ‘La La La’ denial mode.
He has invested so much of his standing and prestige in this position that any evidence that contradicts his position is just going to induce the ‘La La La’ response.
We have seen what happens on the ‘other’ side of the CAGW debate. First they get defensive, then they get angry and then they start censoring and then they stop listening.
Sad really!
Alan
Why are you all wasting time on inconsequentials? The problem is solved.
Scot Allen,
Calculated. The heat capacity of a monatomic gas is nearly independent of the atomic weight on a per mole basis and is equal to about 21 J/K^-1 mole^-1. But Cp must be in the form J kg^-1 K^-1 to calculate the lapse rate. So take g and divide by Cp on a per mole basis and multiply by the atomic weight expressed as kg/mole. That’s 0.004 for helium and 0.13129 for xenon.
Tim, the reasoning of your post is fine … except for the final conclusion follow “and thus” … which (upon careful atom-counting and energy accounting) turns out to be incorrect, per a previous post titled “a WUWT Puzzler”.
As often happens in thermodynamics and statistical mechanics, careful counting and accounting lead us to surprising conclusions!
Bart,
Might I suggest you do yourself a favor and not name Physical Laws after yourself. It is bad form, first you have to PROVE your law and then others have to acknowledge that you are in fact correct. Sorry, but that’s the way it works.
This comes from someone who has not had the high honor of having a LAW named for me, perhaps someday I might have that honor. But, frankly it is not very high on my “bucket list”.
Is there a specific point in my hypothesis (it was clearly enumerated if I recall correctly) that you dispute ?
Cheers, Kevin.
Alan Millar,
With respect to Tallbloke, I’m quite aware that it’s futile. I have the same problem with Nasif Nahle when he insists that partial pressure is identical to partial pressure times path length. That causes him to think that the emissivity of CO2 in the atmosphere is low. It’s impossible to convince him otherwise because he has invested too much of his reputation in his hypothesis. Note that Tallbloke seems to think Nasif is a reliable source.
But I’m retired so I have the time. And I refine my own understanding by having to use different explanations and examples. Also, for people lurking on this thread, I think it’s important to not leave false statements unanswered.
Scot Allen says:
January 21, 2012 at 5:14 pm
And we’re back to perpetual motion again. What you’re saying is that a 100 m vertical insulated silver rod will have the same difference in temperature from top to bottom as a 100 m insulated column of air. That could only be true if the two are isothermal. Otherwise, the lapse rate of a silver rod must be less than a column of air and you can extract energy from the system.
“Scot Allen says:
January 21, 2012 at 5:14 pm
Robert’s silver rod does not show that. The atoms in the silver rod are affected by gravity in the same way molecules of air are affected. Hotter silver atoms at the bottom deliver their energy to those above, and those to more atoms above and so on during conduction. Each tiny temporary displacement carries kinetic energy, but some of that energy is converted to gravitational potential energy. This stored potential energy can’t be conducted. It is converted back to kinetic energy as the atoms displace downward. These differences in kinetic energies between layers must create a temperature gradient.”
So what are you are trying to indicate here? That two connected heat sources can be prevented from exchanging heat?
If no, then Jelbring’s hypothesis is a bust. If yes, then publish with evidence and/or mathematics and get your Nobel prize.
Which is it going to be?
Alan
An isothermal atmosphere has a vertical gradient of total energy since enthalpy plus potential energy increases upwards (enthalpy is proportional to T). As such, if left to itself, there is a downward (downgradient) flux of energy, which is only sustainable if you drain the excess from the bottom and add it at the top. If you impose top and bottom insulated boundaries that don’t allow an energy flux, it ends up warming the bottom and cooling the top towards an isentropic state that has no energy flux because, in this adiabatic state, enthalpy plus potential energy is a constant.. So an isothermal state is only sustainable with the correct flux boundary conditions.
There is another basis for saying that in the absence of all energy sources, a column of gas must be isothermal, with or without gravity. A temperature gradient necessarily creates entropy, continuously. It takes energy (and heat pumping) to counter this and maintain a steady state gradient. I’ve blogged about this here.
DeWitt Payne says at 1/21 at 10:21:
“If gravity then re-establishes the DALR, we can run the heat engine again, and again, and again. When the DALR is re-established, the heat that was moved from the helium to the xenon will move back again. The total energy content of the two cylinders won’t change.”
If I get this, you have taken the cv of interest which is Willis’ GHG-free tall gas column in presence of inexplicable gravity and modified the bottom of his cv so it can touch to a simulated earth, in particular with xenon canister. Now heat can flow out/in of Willis’ original 1 system premise, things have changed. This is fair of course and a logical extension of the adiabatic original discourse. Not adiabatic anymore.
To begin, let me just discuss the one DeWitt cylinder on top as the 1st system.
My view would be DeWitt top system immediately starts with helium T stratified. Physical plate at bottom touches to enable heat flow out of helium in order to equilibrate with the 2nd xenon system at lower T. This heat flow lowers the DeWitt top system internal P & internal T field but keeps first (helium) system V and n unchanged.
Equilibrium with bottom cylinder is reached and top DeWitt cylinder is disconnected (untouched). We are back to Willis’ original cv except ideal gas PV=nRT is lower at every h. Since KE is lower each molecule is speeding around less fast. The system stratifies as before but molecules total energy have lower KE (since P is lower, V constant) with same PE above the h=0 gravity field ref. point.
Don’t see how you can write “the total energy content of the top cylinder won’t change.” Fill me in. Maybe I didn’t get it.
KevinK says:
January 21, 2012 at 5:49 pm
“Might I suggest you do yourself a favor and not name Physical Laws after yourself. “
I haven’t. Figure out that riddle – it’s an easy one.
“Is there a specific point in my hypothesis … that you dispute ?”
Yes. I have disputed it. I am not going to discuss it anymore. I have an actually physically viable hypothesis I am trying to get people to notice and start thinking about.
A physicist says “Tim, the reasoning of your post is fine … except for the final conclusion follow “and thus” … which (upon careful atom-counting and energy accounting) turns out to be incorrect”
I am a bit confused, since I think we both came to the same conclusion — that the second camp (who believe the declining temperature profile is the equilibrium condition) are wrong. My post actually follows the same line of reasoning that yours did. I stated specifically that “it is clear the “lose KE and lose temperature” argument has a huge hole in it. ”
I just said it much later in the thread after missing your post earlier. 🙂
I think I see a logic here with convecting air. The relationship with kinetic energy and temperature has been confusing to say the least.
Perhaps the problem is in the way its been explained.
OK so as a gas rises it does not lose kinetic energy thats whats been said about the adiabatic “process”.
But at the same time we are told it loses temperature.
One logic would be the kinetic energy always equates to a certain temperature in a single kind of material.
And when air rises it also mixes with other air. The mixing lowers the average temperature of the mixed gas, which is all we can read with measuring devices; but it takes a while for the kinetic energy of individual molecules to come to equilibrium as you need collisions or radiation or something of that nature for them to dump their kinetic energy.
If I can adopt that idea then I can see my way through this morass a bit more easily.
Here I can see an isothermal atmosphere and a lapse rate created by the fact the convection/conduction system fails to keep up.
It really fails to keep up during the cooling cycle as it might require a lot of years for conduction to work its way through the atmosphere. Convection on the other hand might only take a few days or a week or so to catch up (though that last nth of a degree could be long extended as convection slows to a crawl so slow a snail looks like a speeding bullet.)
So since this equalization in effect is in fact determined by a combination of gravity and atmosphere mass that makes Jelbring basics right (just his equilibrium is wrong). And to prove Jelbring was wrong about the equilibrium, his critics were required to resort to an argument that proved the essence of this theory was right that convection and conduction would eventually catch up and equalize the temperature of the atmosphere. (or at least I can think of no other means for the surface to be normal temperature and have a need for it to be the source of warming the upper atmosphere. So in the end Jelbring’s model proves beautifully useful.
Now one more step! If the reason we have a lapse rate is this delay in equalization of the atmosphere it follows that the longer the delay the hotter the surface and the cooler the upper atmosphere and viola we are back in business with a lapse rate and an explanation for why the surface is warmer than its expected blackbody temperature. Or at a minimum we have a concrete theory it at least partially explains it. Then the correlations across planets with disregard to GHG begins to explain why it might be a very large part of it.
I am feeling pretty comfortable with that. Does somebody have a pin to puncture my balloon?
Tim Folkerts says 1/21 at 5:15pm:
“..but for different trips, the value is different (ie the boltzman distribution).”
Tim – if you mean Maxwell-Boltzmann, double check a couple thermo texts or ref.s on that – I find a main assumption for M-B distrib. to hold is no external forces (electrostatic, gravity) on the molecules.
Willis’ cv of interet has inexplicable gravity field which is an external force on the molecules – it introduces the PE (ngh) into molecular total energy term that M-B doesn’t consider (M-B KE = total molecule energy for M-B). Maybe find a ref. that does consider PE in modified M-B and fill us in. There might be a cool answer in this line of reasoning.
“DeWitt Payne says:
January 21, 2012 at 5:52 pm
But I’m retired so I have the time. And I refine my own understanding by having to use different explanations and examples. Also, for people lurking on this thread, I think it’s important to not leave false statements unanswered.”
Ahh… I see, we must be of a similar age. I am semi-retired and got my first job as a scientist in the late 1960’s. Changed career path though, subsequently.
I now try to contribute to these sort of blogs in logical layman terms. One, because I think that is what is best for the general readership and two, because I don’t fancy having to brush up on my Mathematics after nearly 40 years!
Alan
Bart’s Law:
It follows that surface temperature sensitivity to the addition of radiative gases is negative: the addition of more IR radiative gases will tend to lower the surface temperature. This is a sensitivity – it does not preclude the possibility of feedback from other processes tending to resist the change, e.g., cloud albedo effects.
Bart’s Law is justified by the following line of reasoning:
The foregoing is, I think eminently reasonable and appealing. The following is my current thinking about how it all fits together:
Convergence is initially superlinear, because the more you bite into the areas of the tails, the faster you increase the back-radiation and hence surface temperature. Eventually, you reach the peak of the emissions spectrum and you can go no higher, because each additional increment of surface temperature produces too little extra back-radiation to sustain it in equilibrium with SB.
The other frequencies outside the limiting emissions spread will still attempt to reach the higher temperature emissions levels, but they are constrained by a requirement of continuity in the total emissions, and the dominant emissions spectrum constrains them. The result is a “pincushion” spectrum at TOA which dips in the region of the dominant emissions spectrum.
“…Eventually, you reach the peak of the emissions spectrum and you can go no higher…”
Or, maybe you can go a little higher, at any rate until the rate of increase in back radiation is insufficient to sustain the surface temperature above the SB equilibrium limit.
The way I see this ‘gravity’ theory explained in the comments is-
1/ gravity can be easily made to work. eg hydroelectric plants convert gravity into electricity.
2/ atmospheric pressure is caused by the weight of the air. ie gravity working on the atmospheric mass to pin it to the source of the gravity, earth. other gravitational fields also alter this eg tides. this pressure is the expression of the gravitational force.
3/ the earths surface is warmed directly by sw radiation from the sun. the surface temperature will be higher than space as long as the atmosphere has mass. a temperature gradient is created.
4/ the portion of sw radiation converted to lw radiation by the blackbody earth will come across no absorbers or few, so will pass freely to space.
5/ air (not classed as a greenhouse gas, but capable of retaining heat.. just!) is a very poor thermal conductor, but with time will eventually form a gradient due to the fact that both ends remain at constant temperatures.
to add bits that have been mentioned further-
6/ one end of the gradient changes within a 12hr period. ground and air cools at night.
7/ changes in gravity from various tides also change/shift pressure.
the way i see it though is that while conduction and convection surpass the radiative factor at the lower altitudes, where the gas is thin in the upper atmosphere the radiative exchange becomes more important.
About the the WUWT puzzler : http://wattsupwiththat.com/2012/01/19/perpetuum-mobile/#comment-870583
If the shells have the same speed at all altitude but there are fewer of them at higher altitude. Then the sum of momentum is lower at high altitude. So the gas analogy would give us a lower temperature at a higher altitude.
You are entirely correct Tim — and also, my post should have been more clear that were agreeing (for which confusion I hereby apologize)
By the way, it’s fun to see that folks actually care about the GHE, and are following (and contributing to) the discussion. And it is mighty impressive to see how closely the discussion here on WUWT have evolved in parallel with the historical evolution of GHE theory.
These ideas most definitely are *NOT* simple or trivial. One wonders, at what point can it be fairly said, that among skeptics and nonskeptics alike, a consensus is emerging that the GHE is real?
Willis, you reply to me with this DUMB statement and some other nonsense:
“First, I fear that what happens on other planets is of little interest to me. The planets are so different from the Earth, and we understand our own climate so poorly even though we live in it, that what is happening on Jupiter or Venus can provide little insight, falsification, or support for theories about the Earth.”
Willis, we are kindred spirits in many ways, and I really, really respect you and enjoy your posts, but I’m concerned that you are putting your head under the sand here! Just because you have “no interest” in something has nothing to do with the truth and science, no? STRAWOMAN??? Your statements are nothing but a total denial of FACTS, sir! You HAVE NOT ADDRESSED THE EMPIRICAL EVIDENCE THAT CHALLENGES YOUR THEORY, WILLIS!!!! IN FACT, YOU CONTINUE TO IGNORE ALL THE EMPIRICAL EVIDENCE!!* Are you afraid of the empirical evidence?
Until you address these concerns, I remain unconvinced of some magic “radiative GHE effect.
And the current average global temps are not helping you, either, sir.
[SNIP: Swearing at the moderators and calling them bad names is bad form and makes them cry. -REP]
Willis Eschenbach says:
davidmhoffer says:
Ackk! Now, you guys are both getting me confused because you are confusing the terms “parameters” and “variables”. What bothers me is not so much the variables as the free parameters. To define N_TE in terms of P_S, there are 4 free parameters…Those numbers in Equation (7). How do we know they are “free parameters”. Well, for one reason, they say, “However, we discovered that NTE was strongly related to total surface pressure through a nearly perfect regression fit via the following nonlinear function” which tells you that they did a fit; the other is that the numbers are not simple values like 1 or 2 or 3…They are clearly numbers that were obtained through a fitting procedure.
Now, to write T_S in terms of N_TE, there are two further numbers, although I think one can argue that those are not “free parameters” at least once their definition of T_gb is chosen (and one is just to correct for the 3 deg background of space…which is numerically irrelevant anyway). However, even discounting these, to express T_S in terms of P_S (and S_0 and T_gb), there are 4 free parameters…the ones that appear in Equation (7).
So, like I said, their fit involves 4 free parameters, plus some freedom in their choice of T_sb. And, given the different values that are floating around for the average temperature of the moon and, I imagine might be similarly true for the other nearly airless bodies, there may have even been some “play” in the data itself.
It takes an amazing absence of skepticism to look at their fit and be that impressed by it. Nobody who does so can seriously call himself a “skeptic” in anything but a very Orwellian sense of the word! In fact, nobody who takes their paper seriously at all after the sort of gargantuan errors we have found can by called “skeptics”. It is simply a ridiculous use of the word.
…at any rate until the additional increment in back radiation is insufficient to sustain the additional increment in surface temperature above the SB no-atmosphere equilibrium limit.
Robert Brown,
I have been following your posts both here and at Tallbloke’s blog. Unfortunately I have not read all of the posts here at WUWT (although I have covered a lot of them) so I hope what I say is not a repeat of what others may have said.
First, you talk extensively about “equilibrium” and “thermal equilibrium”. But I believe we should be talking specifically about “thermodynamic equilibrium”. Thermal equilibrium is but a subset of thermodynamic equilibrium. A system is in “thermodynamic equilibrium” when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium and chemical equilibrium. Thermodynamic equilibrium equals thermal equilibrium only when a system’s internal energy can be described by
U = CvT (1)
In this case the system’s internal energy is thermal energy and thermal equilibrium is all that matters. Your statement “Thermal equilibrium is isothermal, period” only applies to such a system. But that is not the system of a planetary atmosphere under the influence of a gravitational field.
Second, we need to better define where the classical laws of thermodynamics and equilibrium are valid. They are valid with a homogeneous system where all the locally defined intensive (e.g., per unit mass) variables are spatially invariant. But a system is not homogeneous if it is also affected by a time invariant externally imposed field of force, such as gravity. Thus in a gravitational field the laws of thermodynamics have to be applied in a manner that reflects the external field. This is a paradigm buster in itself.
Third, the thermodynamics of an atmosphere cannot be described wholly through considerations of heat transfer only (Trenberth diagram, anyone?). The atmosphere must be treated as a system undergoing both heat and mass transfer. Mass transfer is the reason that gravity is so important in understanding atmospheric thermodynamics. This gets to the mechanical equilibrium part of thermodynamic equilibrium.
Fourth, chemical equilibrium is also very important in atmospheric thermodynamics. But if you assume uniform molecular diffusivity in a horizontal layer (gravitational potential energy handles the vertical diffusion) we are left with latent heat and that is beyond our discussion here.
Thus, as I explained in a previous Tallbloke post,
http://tallbloke.wordpress.com/2012/01/16/the-gravity-of-some-matter/#comment-14236
the proper formulation of the first law of thermodynamics for a “dry” atmosphere under the influence of a gravitational field is:
dU = CvdT +gdz – PdV (2)
The first energy term, CvdT, is the only variable that deals with thermal energy (temperature). The other two energy terms, gdz (gravitational potential energy) and PdV (mechanical work energy), deal with mass transfer. Thus temperature reflects only one variable in the energy composition of the atmosphere. As Tallbloke has pointed out, for the first law to apply energy can be transformed from one form of energy to another, but total energy content must remain constant (dU = 0). The temperature profile through the atmosphere is dependent on the mix of energies at any given point.
The temperature profile resulting from a dry adiabatic lapse rate is covered in my previous post above. And that profile reflects an isentropic system in steady state dynamic equilibrium described by:
CpdT + gdz = 0 (3)
The same system in static equilibrium can be described by the equation of state:
CpT + gz = constant (4)
But for an isothermal temperature profile to exist in an atmosphere in a gravitational field both CpT and gz must increase with altitude. Thus internal energy (U) is not a constant but must also increase with altitude. That violates the first law. The only way that could be achieved is if work is being done to the system. And such a system would not be in thermodynamic equilibrium.
The zeroth law only applies to a homogeneous system and the atmosphere under the influence of a gravitational field is not a homogeneous thermodynamic system (as defined above). And equation (3) does not violate the second law since the process equation reflects an isentropic (constant entropy) process.
The Jelbring hypothesis holds up perfectly from a thermodynamics standpoint.
Your insertion of an insulated silver wire into the discussion makes for an interesting mental exercise, but it has nothing to do with the thermodynamics of a planetary atmosphere. You have just added a non-existent subsystem to the existing system. And the wire cannot be a metaphor for conduction since vertical conduction is almost non-existent in a gaseous system in a gravitational field.
As for the N&Z hypothesis, I too have no firm opinion as yet. I am awaiting Part 2 of their submission that deals with the detailed thermodynamics. But if that is based on a premise similar to the Jelbring hypothesis, I will be pleased.
I would like to provide one quote from Thomas Kuhn’s book “The Structure of Scientific Revolutions” to wrap things up:
“Because the unit of scientific achievement is the solved problem and because the group knows well which problems have been solved, few scientists will easily be persuaded to adopt a viewpoint that again opens to question many problems that have previously been solved.” (Page 169)
Bill