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.
Willis – you just described a solar powered version of the gas refrigerator.
http://home.howstuffworks.com/refrigerator5.htm
KevinK – Think about it for a second, there are lots of very obscure physical effects that have practical applications. For example, the Bernoulli effect is what makes a plane fly..
~~~
Most of the upward thrust comes from the downward deflection of air particles by the wing. That is why stunt planes can fly upside down:
http://www.cap-ny153.org/forceslift.htm
Robert Clemenzi says:
January 21, 2012 at 10:43 pm
Average speed of N2 at surface is 500m/s.
It has kinetic energy (ignoring rotational energy)
1/2 * 28 * 1.66 x 10^-27 kg * (500 m/s)^2 = 5.81×10^-21 J.
Average distance between molecules at surface is 10^-5 cm.
28 * 1.66 x 10^-27 kg * (9.8 m/(s^2)) * 10^-5 cm = 4.56×10^-32 J of kinetic energy change over 10^-5 cm.
Seems small, but a molecule at the bottom of the atmosphere transferring energy to another above and so on up to 10km gives 4.56×10^-21 J KE to PE change. That’s significant.
I think it doesn’t matter to the base gravity/mass theory if the atmosphere at equilibrium isothermic or stablizes with a lapse rate.
But I think Jelbring’s theory is cleaner and more intuitive if the atmosphere does stabilize at an isothermic condition.
If incoming and outgoing radiation is prohibited from the model world that means the equalizing of the atmosphere has to be internal. Thus the lower atmosphere has to be the source of warming the upper atmosphere proving that at equilibrium the lower atmosphere would be cooler.
Thus gravity and atmosphere mass are the main functions. The delayed response to equilibrium that breaks down the lapse rate via taking heat from a cooling lower atmosphere to a warming upper atmosphere provides the mechanism that gravity uses to raise the surface temperature.
The isothermic delay claimed by the isothermal crowd is evidence for the gravity/mass/friction relationship that pegs the lapse rate as its signature when the atmosphere is in motion. When you remove the external inputs it becomes apparent. The fact that conduction and convection are behind schedule is evidence of this relationship.
Jelbring’s model is ideal for teasing this out whether or not the atmosphere stabilizes at the lapse rate or continues on to isothermic equilibrium. If it just abruptly stopped you would have hopeless continuous perpetual motion mouth movement and perhaps its deserved. But when it continues to via an allegedly well understood physical process to an equilibrium the mechanism has not changed it just continues to work to obtain the equilibrium the physicists claim as fact. So convection and conduction continues its work albiet at a greatly lower rate of change now that the big 174 petawatt driver has been unplugged so it can catch up on its homework.
Tim Folkerts says:
January 21, 2012 at 5:15 pm
There are really only two possibilities.
1) The second law works and thus the temperature must be uniform.
2) KE + PE is constant, so the particles cool as they go up, and thus the temperature drops.
The laws of thermodynamics have been stated in terms of energy rather than heat for over a hundred years. The news hasn’t reached Duke University it seems.
I can give the “elevator speech” for why #2 is suspect. For any given trip, the KE + PE is indeed constant, but for different trips, the value is different (ie the boltzman distribution). If you look near the top, the “low energy tail” never gets that high, so you are only looking at self-selected particles that started in the high energy tail. These originally-high-energy-particles have indeed lost some KE on the way up, but they started with extra on average. This can (and does) leave this SUBSET of particle with the right average energy to be at the same temperature as the WHOLE set was at the bottom.”
I think this is wrong because of the very short mean free path length between collisions. Maxwell did a fair bit of work on that when he was considering the collisions and distributions of various sized gravel (analogous to differing KE in molecules) in the rings of Saturn (also sorted by gravity) and this is what led him to develop Clausius’ statistical mechanics. I’ve been reading up on this at the library in my University and will be writing an article sometime in the next few weeks.
I certainly haven’t proven this rigorously in this non-mathematical paragraph. However, it is clear the “lose KE and lose temperature” argument has a huge hole in it. Those who want to pursue this line of reasoning IN THE FACE OF STRONG COUNTER-ARGUMENTS, would need to determine the distribution of energies of particles at any altitude, and show that those remaining particles are indeed lower KE then the whole set was at the bottom. I am sure they can’t do this because I am sure they are wrong.
Well, do the maths and see if you get the same answer as Joe Born and Valesco. I’m certainly willing to concede the possibility that the gravito-thermal effect we are outlining might not account for the whole of the dry adiabatic lapse rate, but a substantial part of it. There may be some room in there for radiative effects too. It’s current ongoing work. Real science in real time.
I have to say I’m a bit surprised to see you using categorical statements like “This can (and does)” when you haven’t done the maths. Mind you, you are not alone…
Remember the path lengths when you get around to it. It’s important. Maxwell knew that. It may be why he never attempted a mathematical refutation of Loschmidt, but appealed to his own second law formulation. Boltzmann did attempt it, but never got a satifactory result. The controversy continues.
Willis,
Thanks a lot for your reply to this particular bozo. You say:
“I don’t know what mechanism Jelbring thinks will restore the initial heat differential, but he definitely thinks it will be restored.”
That’s the money quote. If Jelbring wants to contradict that, I’m all ears. Otherwise, I lean to the view (we non-physicists can only lean! :-)) that he is effectively proposing a perpetual motion machine is possible.
Sorry that you replied that way, Willis.
I think that if you put the two-sided Albedo up as a post, the ruckus following “Perpetuum Mobile” will be a “tempest in a teapot” compared to “Two-sided Albedo”.
In all seriousness, I think there are significant issues regarding reflectance from the cloud layers that deal with solar and reflected (converted) spectrums. That is why “A” is not necessarily equal to “a”?
And why does the backpacking liquid oxygen generator not work? (Yes! I know why it doesn’t, but what are we doing differently when we say the ground receives 240 W/m^2 ?)
Willis, I think your answer was just to a higher (google) authority. Hence, there is value in a separate discussion on a “Two Sided Albedo” to marshal the facts.
Re: Willis 12:17am. Stephen, the measured albedo of the planet is about 0.3. Because this is a measured figure, perforce it includes all “double reflections”. “Perforce?”
Do to the math, Willis! You will always measure from satelite 340 W/m^2 for any value of “a”. But I can drive the energy trapped in a ground-cloud wave guide to a lot of different levels based upon different values of “a”. I’m not even excluding “a” might be greater than “A” when you take into account converted spectrum from visible light into more infrared energy. I do not know what “a” is, but I have no reason to believe it is zero.
Surely the potential energy of the gas in the bottom is contained in pressure? Take gas from the top, lots of PE due to gravity, no pressure. Take an enclosed sample from the bottom, take it to a vacuum, and you can get work from its expansion, even though its start temperature is the same as the gas from the top. No temp difference required, and the energy sums the same.
DeWitt Payne says:
January 21, 2012 at 5:52 pm
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.
Thanks for the mind reading DeWitt.
I’m painfully aware that since the near fatal accident I was in I often get things wrong, and I’m less able to do complex algebra than I used to be. So instead I now concentrate my efforts on providing a platform for others to have their ideas discussed. Nasif’s idea was discussed. It was strongly criticised by John Eggert, who knows a thing or two, though no doubt you have your disagreements with him too. That’s science.
As an engineer, I was taught thermodynamics from a kinetics and molecular mechanics point of view. It seems Robert Brown is more a heat is work kinda guy. Nikolov and Zeller, Bill Gilbert and Joe Born do the maths. As a historian of science, I record their output and act as librarian ferreting out relevant old papers. As a blogger, I decide how to hold my space in the way I see best. No doubt there is subjectivity and personal bias involved, but I do my best to strike the balance I want to in the partisan atmosphere of the climate debating blogosphere. Sometimes I find myself in agreement with the direction WUWT thrusts in, sometimes not. Same goes for other science blogs.
Let the chips fall where they may, and the best science win.
Robert Clemenzi: “The DALR and the gravitationally induced lapse rate are created via totally different mechanisms. As a result, their magnitudes are not even close.”
If you put numbers into Velasco et al.’s Equation 8 for mean single-molecule kinetic energy as a function of altitude, the magnitude of the (non-zero) lapse rate there implied is indeed much less than the dry adiabatic lapse rate if the number of molecules is on the order of those we usually encounter.
Robert Clemenzi says:
January 21, 2012 at 10:43 pm
tallbloke says:
January 21, 2012 at 3:59 pm
Total energy = KE+PE.
I partly agree. There is also rotational and vibrational energy.
However, thermal conduction from warm to cold means that energy will move from one block of atmosphere to another. As a result, the actual lapse rate will be much closer to zero than it is to the DALR. The question is – How much closer?
Let’s assume that the average speed of a molecule is extremely high. When a molecule moves either toward or away from the center of the Earth, it will undergo an acceleration for some time (dt). If the change in velocity due to gravity is a significant part of the average speed, then there should be a measurable induced lapse rate. However, I suspect (I have not computed this) that the gravitationally induced change in velocity will be at least nine orders of magnitude less than the average velocity (mainly because dt is extremely small). As a result, the gravitationally induced lapse rate will not be significant with respect to the current models. In other words, it would be indistinguishable from zero. (Of course, when the pressure gets low enough, dt increases and the lapse rate should become noticeable.)
Thank you Robert Clemenzi.
I agree that as path lengths get longer, the effect will increase. However I disagree that conduction would take place at equilibrium for the reason I gave Robert Brown. In the Jelbring model at energetic equilibrium the proposed thermal gradient will not produce a flow of heat between contiguous air packets because the gradient passes through those air packets. Therefore the upper ‘surface’ of the lower packet will be at the same temperature (Same KE+PE) as the lower ‘surface’ (arbitrarily chosen measuring point) of the air packet above it. The two packets would have different average temperatures commensurate with the g/Cp relationship, but since the adjacent ‘surfaces’ are at the same temperature, no heat will flow because energy is in equilibrium.
in the real atmosphere, the input from the Sun leads to energetic heat transfer, conduction, convection and radiation. However, the underlying gravitational pressure gradient induced thermal effect means the dry adiabatic lapse rate will tend towards the gravity-pressure induced apse rate. This is indeed what observational evidence shows.
Robert Brown says
“Well done, but way too much work. The easiest PPM2 one can build is a simple thermocouple that lights a light bulb or turns an electrical motor. Place the upper contact in the supposedly cold air at the top of the static column. Place the lower contact in the warm air at the bottom. Insulate the heat transfer medium (e.g. silver) all the way down to the actual junction, so that heat is conducted from the hot bottom to the cold top, through the thermoelectric junction.”
Using DALR of 9.8K/km work out the figures for a real thermocouple connected by real copper leads using real resistance and heat loss figures and you will see why this proposed experiment is imposible.
If there is no outside influence on the planet, and no internal heat source, all atoms would reach absolute zero, so there would be no heat no matter where in the atmosphere atoms were situated, and therefore no difference in temperature top to bottom.
If there is a source of heat -the sun or from the planet core, the pressure of atoms would make temperatures higher at the bottom, fueling circulation which equalizes temperatures, but never quite gets there.
In the last case a heat engine would be possible, but in reality fueled by the heat source. So no perpetuum mobile.
Robert Brown:
If I understand your position, it’s that at equilibrium the laws of thermodynamics require heat to flow from hot to cold no matter how low the ratio of temperature gradient to potential gradient is. To me that is not a self-evident result of those laws. Maybe it is a result. But you have not demonstrated that it is. You have just argued as if the result were itself the law.
In contrast, Velasco et al. have provided a mathematical proof that it is not. They may be wrong, but at least they showed their reasoning, whereas you have not. Perhaps you don’t have the time. Fine. But know that this leaves the intelligent layman no choice but to credit Velasco et al., at least until he can find the error in that proof on his own.
Willis, your comment about supercritical gasses does not negate compressive heating which occurs in liquids and solids. It is certain that the liquid outer core of our planet is liquid due in part by compressive heating, the bulk heat is from radioactive decay of potassium, thorium and uranium in order of importance, and the lithosphere has areas of compressive melting at subduction zones that produce granite It is compressive adiabatic heat that enables Jupiter to radiate more heat than it receives despite the atmosphere being hydrogen and helium mix not known for their GHG credentials. This is not a PMM but a natural process gaining heat energy from gravitic work done. (water on the high pressure side of a pump is warmer than that in the low pressure side and water is ‘incompressible’).
As far as Venus is concerned there is such a violent atmosphere that mixing might change the supercritical properties of the mainly CO2 atmosphere. But compressive heating will still occur and more severely due to the high surface atmospheric pressure. If it were not for the presence of water on Earth we would have an atmosphere with similar properties to Venus. But this is the subject of a different discussion completely.
William Gilbert says:
January 21, 2012 at 9:27 pm
The best discussion of the perpetual motion paradox that I have seen on this thread is the one by Robany here:
http://wattsupwiththat.com/2012/01/19/perpetuum-mobile/#comment-871446
But I did not see any responses to him. Anyone have any comments?
Personally, I am having a lot of trouble with the whole PM concept for the Jelbring system. Gravity is a time invariant externally imposed field of force acting on mass. When did Newton’s second law of motion become a perpetual mobile of any kind?
Bill
====
I hadn’t read it, my eyes glaze over fairly rapidly trying to read this thread, but it is what I was trying to say (not a scientist) about the gravity not being perpetual motion as energy being taken out of a natural cycle as we have it is bound to affect the cycle (and if this changes the component gases it could impact on the gravity field by changing it, by changing the potential gravitational energy available, say – can the enclosed system be scaled down?
Willis Eschenbach says:
January 21, 2012 at 9:26 pm
As an example of the arbitrary nature of the N&Z choice of values for surface pressure in their paper, they say the pressure of the earth is 98,888.20 pascals. I particularly liked the fact that it is allegedly accurate to the nearest hundredth of a pascal….
Finally, whenever you see parameters given to seven significant figures, and the earth’s surface pressure given to two decimals, you know you are dealing with amateurs. That kind of fake precision is a big red flag at any time.
At least they are using their arms to operate calculators instead of waving them around furiously.
Joel Shore says:
January 21, 2012 at 9:25 pm
These “theories” really have revealed some very embarrassing things about the AGW-skeptic movement…which, to their credit, some skeptical folks like Willis, Robert Brown, and Roy Spencer are trying desperately to correct, although it makes it all the more amazing that such crazy nonsense continues in light of their best efforts to squelch it.
Classic Joel Shore.
When you can’t successfully refute the theory, smear the proponents.
We know who is trying to squelch what Joel.
Independent of the question about the effect of gravity on temperature, N&Z have shown using empirical data and a better application of S-B that the average temperature of the surface of the Moon is ~90K cooler than previously thought. This is a mortal blow to Joel’s scientific beliefs, and he is desperate to get N&Z buried on any pretext.
Willis Eschenbach: “So I’m unclear why you think Velasco disagrees with me. If I understand it, which is always an open question, it seem they agree that the final distribution is isothermal. What am I missing?”
Let me address this more completely than I did above, where I said the Velasco et al. passage you quoted is ambiguous. As I said above, I resolved the ambiguity in favor of a non-zero lapse rate for finite numbers of molecules because that is what I read Velasco et al.’s Equation 8 to say.
Before I parse that quoted passage, though, I’ll briefly review what preceded it. Their Equation 5 gave state density as a function of velocity and altitude, Equation 6 gave it as a function of altitude only, and Equation 7 gave it as a function of velocity only. Since Equation 5’s left side was not the product of Equation 6’s and Equation 7’s left sides, Velasco et al. concluded in the first bullet point after Equation 7 that velocity and altitude are not statistically independent. They then presented Equation 8 to show the dependence of mean kinetic energy on altitude. This is why I resolved the ambiguity the way I did.
Now to the passage in question, against which we are to assess my interpretation of Velasco et al., which is that in an isolated system the lapse rate approaches zero as the number of molecules approaches infinity–but is non-zero for finite numbers of molecules. As you say, the Coombes & Laue paper that Velasco et al. were critiquing came to the conclusion that you and Robert Brown have, namely, that the equilibrium configuration would be isothermal, independently of the number of molecules. Here is how they characterized Coombes & Laue:
“The problem proposed and analysed by these authors is the following:
If a vertical column of an adiabatically enclosed ideal gas is in thermal equilibrium, is the temperature the same throughout the column or is there a temperature gradient along the direction of the gravitational field?
According to Coombes and Laue, there are two conflicting answers to the above question:
(1) The temperature is the same throughout because the system is in equilibrium.
(2) The temperature decreases with the height because of the following two reasons.
(a) Energy conservation implies that every molecule loses kinetic energy as it travels upward, so that the average kinetic energy of all molecules decreases with height.
(b) Temperature is proportional to the average molecular kinetic energy.
Coombes and Laue concluded that answer (1) is the correct one and answer (2) is wrong. They reached this conclusion after finding that statement (2a) is wrong, i.e., the average kinetic energy of all molecules does not decrease with the height even though the kinetic energy of each individual molecule does decrease with height.”
And here is the conclusion they drew:
“In conclusion, in our opinion a full explanation about why answer (2) to the paradox formulated by Coombes and Laue is wrong must discern between the cases of a finite system and an infinite system. In the former case, statement (2) is wrong because the assumption in statement (2b) is wrong. In the latter case, statement (2) is wrong because the conclusion in statement (2a) is wrong (as it has been established by Coombes and Laue).”
Until I had more carefully considered the equations that preceded it, I interpreted this passages as you did: I thought it meant that the finite and the infinite system are both isothermal.
But, after considering the preceding equations, I realize that when they say “statement (2)” they mean to include not just the lapse-rate conclusion but also the reasoning behind it; in the finite case, statement (2) is wrong not because its conclusion is wrong but because its reasoning is wrong. Note that for the finite case they don’t say that statement (2a), namely, that “the average kinetic energy of all molecules decreases with height,” is wrong. To do so would be inconsistent with their Equation 8. They say that only for the infinite case.
Willis Eschenbach;
As an example of the arbitrary nature of the N&Z choice of values for surface pressure in their paper, they say the pressure of the earth is 98,888.20 pascals. I particularly liked the fact that it is allegedly accurate to the nearest hundredth of a pascal.
The oddity is that standard sea level pressure for the earth is generally taken to be 101,325 pascals (no tenths or decimals) … so their number is off by a couple of percent.>>>
Until I really thought through N&Z in detail, I accepted 255K as the blackbody temperature of earth, and now realize I was wrong. That number is too high. I accepted that the average temperature of earth surface was 288K, and now realize I was wrong. That number is too low. I accepted that there has been a warming trend in the average temperature for the last 150 years or so, and now realize that some portion of that warming trend is due to the temperature of the earth becoming more uniform rather than from a net increase in energy.
So is the number of decimal points they’ve use a fair criticism? It is. Is the fact that the generaly accepted value is 101,325 rather than the 98,888 they calculate falsify their calculation? It does not.
Your cheer leader on this issue, Joel Shore, has already admitted that 288K is too low, though he maintains that is is by only a couple of degrees. The same logic applied to the calculation of 255K however, yields a value about 100K lower, a matter that Joel Shore refuses to engage in regard to. Bottom line however is that for two long accepted numbers that N&Z have refuted, Joel Shore has defacto stipulated to the innacuracy of both.
Did N&Z get the mean pressure calculation correct? Here is the important point on this, and why they only have two variables in their equation, not four. It doesn’t matter. If their method for deriving mean surface pressure is innacurate, then by all means substitute a better one. But at day’s end their work rests primarily upon correcting the misaplication of SB LAw to calculate effective blackbody temperature of earth, misaplication of averaging measured surface temperature to arrive at the blackbody radiance of earth surface, and the misaplication of trended average surface temperature data to conclude that there has been a long term energy net increase in energy retained on earth.
If they’ve erred in their calculation of mean surface pressure, then by all means, point out the error and suggest a fix. But don’t throw the baby out with the bath water.
The only problem with Perpetuum mobile is that nobody wants to buy it. I know how it should looks like : simple, cheap, small, very powerfull, very usefull. I also know how to build it for use in ships, for use in cars, for use for homes, etc … I believe there are several types of this engine, but it is not enough just that it works, it is also important how powerfull and usefull it could be. 100 kw at weight 100kg would make this engine usefull and comparable with Diesel and Otto engine. OK, 10kw at weight 100kg would be also usefull for cars, because it could produce the electricity 24 hours per day.
Davidmhoffer, I am happy to oblige, and you are entirely correct that “baby cherishing” and “bathwater discarding” both are necessary to good science and to rational skepticism.
(1) Nikolov & Zeller erred in neglecting radiative transport in the atmosphere.
(2) The symptom of the Nikolov & Zeller error is that (as is generically true of “gravito-thermal” formalisms) their model exhibits one of the following two flaws (depending upon details):
(a) the model either predicts an isothermal atmosphere
(which at odds with observation), or else
(b) the model violates the second law of thermodynamics
(3) The fix for the Nikolov & Zeller error is to incorporate radiation absorption and emission.
(4) Working through the details of this change, the standard GHE mechanisms are recovered.
Elevator Summary: The “baby to be cherished” is the practice of working through the details. The “bathwater to be discarded” is gravito-thermal formalisms that neglect radiative heat transport in the atmosphere: these theories are just plain wrong.
WHOA! GUYS!
You guys are so intent on arguing about the “end state” of Jelbring’s imaginary world you are missing the point.
The contention the atmosphere would be isothermal if it were isolated from any external heat source or sink is evidence that the earth’s lower atmosphere is warmer than it should be. (period)
That so precisely because of the gravity physics acting on expanding gases and a resistance to that response that causes world’s with solar input to display a lapse rate.
The disappearance of that lapse rate in Jelbring’s stygian world is irrelevant because it can only happen if you turn off the sun and if it doesn’t happen nothing is different except the precise mechanism of how gravity does it.
Thus the Perptuum Mobile argument is irrelevant to Jelbring’s theory, its only picking around the edges of the Jelbring paper.
davidmhoffer says:
Well, we don’t know what it means: It could be something as innocuous as trying to correct for the fact that not all of the “ground” is at sea level. On the other hand, another possibility is that they “tuned” the data in order to improve their fit. It is not a big issue, but it is a bit of a curiosity and I agree with Willis that there are too many sig figs there…which admittedly is pretty small on their list of sins.
That is not exactly true…You seem to switch between wanting the average T to be computed as the fourth root of the average of T^4 or as just a direct average according to how it suits your purpose. As far as I know, 288K is correct for the average of T. I have said that the fourth root of the average of T^4 is probably AT MOST 2K higher. Furthermore, since we are interested in the average of epsilon*sigma*T^4 to compute the average power and the effects of the non-uniform temperature distribution and of epsilon not being exactly 1 go in opposite directions, it is likely that the combined effect is even smaller.
That is even more untrue. I have engaged in discussing this in considerable detail, including why I believe your “100 K lower” claim is pure fantasy for any reasonable definition of and Earth without greenhouse gases but otherwise similar.
N&Z have not refuted anything. We never said that 33K was perfect, i.e., that it was 33.0000 K. And, we have always pointed out that the fundamental issue is the difference between the amount of power the Earth absorbs (~240 W/m^2) and the amount that its surface emits (~390 W/m^2) and that for a blackbody emitter absorbing 240 W/m^2 from the sun, the MAXIMUM average temperature that it can have without greenhouse gases is 255 K. It could be less if the temperature distribution is uneven.
tallbloke says:
Pure silliness. N&Z wave their hands around quite a bit. And, when they do operate calculators, they do so with silly, embarrassing errors like putting convection into a radiative model in a way that drives the troposphere to an isothermal state.
Furthermore, those of us who are refuting N&Z have done plenty of calculations themselves. I have not only replicated their fitting procedure but have gone on to investigate how well that procedure would fit altered data.
It is not smearing opponents. It is trying to make you guys understand how incredibly ignorant and silly you are making the “skeptic” community look in the eyes of the scientific community. Hey, but if that’s your goal, I’m okay with it!
This is not a mortal blow to any belief of mine. When people started arguing about the average temperature of the moon in Ira’s thread, I pretty much couldn’t care less and noted that this argument was really just a distraction from the real issues.
It is completely understood that Holder’s Inequality only sets a maximum limit on the average temperature that a blackbody can have given the average amount of power it emits. And, one consequence of this is that the “average temperature” one measures for the surface of an airless body like the moon is going to depend strongly on the exact definition of “surface” that one uses, which is why you see so many different numbers flying around. (This is a fact that N&Z have not come to grips with because they don’t understand how to correctly apply Conservation of Energy, as they made clear in part 1 of their reply. They think that “Conservation of Energy” says that a planet’s average temperature can’t change if its temperature distribution becomes more or less uniform, because they have failed to account for the fact that the planet is not an isolated system but is actually receiving energy from the sun. In fact, what Conservation of Energy correctly applied says is that any temperature distribution compatible with the condition that the planet is radiating back out into space as much power as it receives from the sun will be a steady-state condition.)