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.
I’ve always loved the ingenuity of those who tried and in some cases succeeded”
http://en.wikipedia.org/wiki/Beverly_Clock
A six-degree Celsius temperature variation over the course of each day creates enough pressure to raise a one-pound weight by one inch (energy extracted = .11 joules), which drives the clock mechanism.
Just ignore the next line in the description that says “It is not therefore an example of perpetual motion.”. Okay it is “naturally assisted” perpetual motion but still a darned impressive piece of work providing real output.
There were earlier clocks as well that used this principle.
Willis Eschenbach: “Where did I assume that there was a heat engine free of gravity?”
I believe you did so without realizing it. But perhaps a better way to express my meaning would have been to say that you have begged the question by assuming a heat engine could be designed that could perform work operating between the differences in altitude and temperature that Velasco et al.’s lapse rate specifies.
My contention, which I at least for the moment believe Velasco and his colleagues have established through a statistical-mechanics-based proof, is that the maximum-entropy configuration of the system you describe exhibits a small but non-zero temperature lapse rate. If that is true, then isn’t it true that a heat engine operating between the same differences in altitude and temperature would have to reduce entropy to operate? If not, then perhaps you could reveal the heat-engine design you have in mind. Otherwise, you’ve just allowed invocation of the term “heat engine” to short-circuit further analysis.
I have to confess that two weeks ago I was arguing over at tallbloke’s place for the same position you’re taking now: http://tallbloke.wordpress.com/2012/01/01/hans-jelbring-the-greenhouse-effect-as-a-function-of-atmospheric-mass/#comment-12926. Currently I think I was wrong then and that you’re wrong now. Maybe by tomorrow you and Dr. Brown will have convinced me otherwise.
Bart,
Your solution of the heat equation in spherical coordinates ( ∂T/∂t = αΔT ) is wrong. As you point out above, α is not a constant with r. α is the thermal diffusivity = thermal conductivity, k (which is a constant), divided by the product of the density, ρ, and the heat capacity at constant pressure, Cp = k/(ρCp). But density decreases exponentially with altitude so the diffusivity increases exponentially with altitude. That means the heat equation must be derived again with this condition and solved. According to the Wikipedia page on the heat equation
Then you say:
You can’t have it both ways. You have a logical contradiction. You say the temperature must always decrease with altitude but then you say the temperature increases at altitude basically without limit. You also can’t wave your hands and say the surface temperature also increases without limit because it’s warmed by the atmosphere. It can’t be by your condition that the temperature gradient is always negative (positive lapse rate). So what you’re actually saying is that the surface temperature increases without limit. But that can only happen if the emissivity of the surface is zero, or at least very small. But of course, it isn’t. In Willis’ example, it’s defined as equal to 1. You can also assert all you want about the SB equation not applying, but you have given no evidence or citation that it doesn’t. Even if the emissivity does vary with wavelength and angle, one can still integrate the Planck equation, B(λ,T) and get the total emission. The SB equation will still be a very good approximation for most real materials.
Oh, and molecules at high altitude are not in orbit even if they are moving at the same radial velocity as the surface below them. The correct reference frame for determining the RMS velocity is a rotating spherical coordinate system with the rotation rate equal to the rotation rate of the planet. A molecule that was actually in orbit would indeed have very high kinetic energy relative to the molecules around it. If that were not the case, then satellites in low orbit would not be subject to atmospheric drag.
Bryan says:
January 20, 2012 at 10:24 am
Since I obviously don’t have an unshakeable belief in my correctness (I publicly admitted I was wrong), and since I obviously listened to the ideas of Robert Brown, who actually understands physics, I fear your reading skills appear to be in desperate need of improvement …
w.
PS—This week, I learned something. I expanded my understanding of physics. You can disparage that all you want, by calling it “seeing the light”, but to me, learning is invaluable gold, and your childish sneers can’t tarnish it. You ought to try it yourself, Bryan, you might like it.
CanSpeccy says:
January 20, 2012 at 10:27 am
Quote my words, you are off in fantasy. I gave a “elevator speech” laying out the Jelbring hypothesis, which demonstrates that I understand it even if you don’t.
In addition I have never argued that it must be incorrect if no one understands it.
QUOTE MY WORDS that you disagree with, CanSpeccy, I haven’t a clue what your are talking about.
w.
jorgekafkazar says:
January 20, 2012 at 12:02 pm
John Marshall says: “I also ask my Jupiter question again. Why does this gas giant radiate more heat than it receives from the sun. your argument above makes this impossible.
My astrophysics instructor said he believed there were decaying fissionables at the core.
Was he waving his arms in a wiggle matching sort of way when he said it? 😉
davidmhoffer says:
January 20, 2012 at 10:49 am
You can believe that if it helps you to sleep. Me, I’m still waiting for someone to give a clear explanation of N&Z. Your claim, that it cannot be explained simply because its all too complex, just tells me that you don’t understand it.
But heck, let’s play it your way. You say you can do it if we break it up into pieces. OK, give me the elevator speech for the first piece of the lot, we’ll start with that.
w.
Willis says: “Thanks, Jeremy. You are a hundred percent correct, gravity can’t do ongoing work to change the temperature.”
Gravity does not do work it causes work to be done.
Q= U + W (first law)
W=FD
F=ma
a=g (g is gravity)
W=mgD
W=PdV
This is stated simply on purpose.
It is the gas that is doing the work against the force of gravity else why would a heated column of air stop rising. What the magnitude or if it is? Or is it offset somewhere else is a different story.
Bart says:
January 19, 2012 at 11:06 pm
Look at the earlier thread. I’ve got it nailed. There is no doubt about it.
Such hubris, actually you’ve got it wrong, but refuse to acknowledge it.
Your explanation contains a basic thermodynamic error as shown below (again).
F) the transferred heat accumulates in the atmosphere until:
1) highly energetic emissions are stimulated, which balances the energy fluxes all around in the same way GHGs would in the standard “greenhouse” theory
OR
2) the heat accumulates until the atmosphere achieves escape velocity and vanishes.
This is where you introduce the fundamental error in your analysis.
What it should say is that ‘the heat accumulates in the atmosphere until the layer of gas nearest the surface reaches the surface temperature at which point heat transfer ceases due to ΔT=0.’ There can be no more heat transfer to the atmosphere unless it cools down and ΔT again exceeds 0. This is the fundamental flaw in all the ‘hotter and hotter’ arguments (it’s independent of the profile with altitude).
Hans Jelbring says:
January 20, 2012 at 12:15 pm
Hans, like you I “don´t believe that an elevator speech is the way to perform scientific work.” So we are in agreement on that.
What it is useful for, as I have said before, is three things:
1. It helps me to clarify my own thoughts. When I only have a few sentences I am forced to be clear.
2. It helps me to explain ideas to other people.
3. It helps me to determine if someone else understands something, under the principle that if you can’t explain it clearly, you don’t understand it clearly.
You have claimed in the past that no “elevator speech” for your theory could be any shorter than your original paper. And indeed your paper is concise … but a much simpler explanation could be given.
I have given my simple explanation, my elevator speech for your hypothesis, in my head post. If you think any of the statements is wrong, please let me know a) which one is wrong, and b) what’s wrong with it. If you think a logical step is missing, please provide it. Blanket statements and denunciations will not serve in this case, please avoid them.
My best regards, Hans,
w.
@Hans Willis is NOT indicating the heat engine will REMOVE energy from the system! He is indicating that the temperature difference used to run the heat engine can do work on the fluid in the system, and infinitely do so per the theory. Hence the theory fails.
Bart,
I’ve calculated the thermal diffusivity, α, of air as a function of altitude at a temperature of 255 K.
km α(m²/s)
0 1.65E-05
10 6.30E-05
20 2.39E-04
50 1.28E-02
100 8.91
For reference, the thermal diffusivity of pure silver is 1.66E-04m²/s. You can see why the IPCC allows the stratosphere to equilibrate before calculating forcing. The equilibration time is going to be short.
If I’m really bored sometime, I’ll try to calculate numerically the temperature profiles for a gravitationally bound vertical column of atmosphere 100 km high with an initial temperature of 2.7 K for a monatomic, non-condensable ideal gas with a heat flux into the surface of 240 W/m² and a surface emissivity of 1.
Werner Brozek says:
January 19, 2012 at 7:30 pm
That’s the problem – outer space has no temperature. Temperature has meaning for substances (stuff), not for a vacuum. The only way to transfer heat to space is via radiation, and the only way for the atmosphere to loose heat to space is to have greenhouse gases that radiate energy.
Hans Jelbring says:
January 20, 2012 at 11:03 am
And therein lies the problem, that you’re talking about perpetual motion and you don’t know it. Hans, you are indeed proposing perpetual motion. You are saying that gravity separates the warm and cold molecules.
If that were true, we could use the temperature difference to perform work forever in your thought experiment world which is sealed off so no energy comes in or out. How is that possible?
Either you need to:
a) show that there is no problem with a sealed system performing continuous work with no energy inputs or exchange with the outside world, or
b) show that for unknown reasons, we could not use the temperature difference to perform work.
I see no reason that we could not extract work from your claimed temperature difference, we’ve been doing that for hundreds of years. So if gravity creates a temperature difference, the default assumption has to be that we can extract work from that temperature difference.
But if so, you could get unceasing work out of gravity forever … and while that would be a nice trick, no one has ever done it, there is no physical theory saying it is possible, and the laws of thermodynamics say it won’t work.
That’s why we call it a “perpetual motion machine”. If you think not, then you will have to do either a) or b) above. I see no way to do either.
In fact, your thought experiment is an excellent one to show that gravity can’t possibly affect the temperature of an atmosphere such as you postulate. If it could, you could use the gravity-created temperature difference to light Stygia forever, and you’d be a hero for solving the energy crisis, we could just run the world off of gravity …
Thanks,
w.
Willis Eschenbach says (in response to davidmhoffer):
Oh…This sounds like fun! I volunteer to give the elevator speech for Section 2.1)B:
“In Section 2.1)B, N&Z demonstrate that when you add convection to a simple radiative model of the greenhouse effect in such a way that it drives the atmosphere to an isothermal temperature distribution with height, then you no longer have a greenhouse effect. Unfortunately, however, in the real atmosphere, convection only drives the atmospheric distribution as far as the (appropriate) adiabatic lapse rate and the greenhouse effect does not disappear. That the temperature at the ‘effective radiating level’ must be colder than the temperature at the surface in order to have a greenhouse effect was already well-known.”
O H Dahlsveen says:
January 20, 2012 at 12:16 pm
Let me quote, if I may, Timothy Casey B.Sc. (Hons): Consulting Geologist who has put the papers of some of them online: “According to Weart (2003, Flannery (2005) and Archer (2009) the “Greenhouse Effect” originates with Fourier, ——.” – And further on: “Arrhenius claimed:
Fourier maintained that the atmosphere acts like the glass of a hothouse, because it lets through the light rays of the sun but retains the dark rays from the ground.”
Nothing could be more wrong – or further from the truth – Put “Fourier (1824) as translated by Burgess (1837)” into your “Computer search engine” or http://geologist-1011.net and see what comes up.
Class. I’ve reposted the Fourier translation, thanks muchly.
“It is equally probable, that in respect to most of the planets, the temperature of the poles is little above that of the surrounding space, with respect to the temperature which each of these bodies owes to the sun, it is not known; because it may depend on the pressure of an atmosphere and the condition of the surface.”
Geez, folks here move around more than ideal gas molecules > 0K. Including me.
Willis says 1/20 10:49am: “Me, I’m still waiting for someone to give a clear explanation of N&Z.”
Robert Brown says 1/20 9:34am:
*” Fact 1: One can run a heat engine between any two reservoirs of energy maintained at different temperatures. Proof: Every heat engine in the world, all of thermodynamic theory, massive engineering…
Fact 2: Heat engines cannot run indefinitely. In a closed system they cannot just take random energy in a complex environment and continuously turn it into work….
* Assertion Gravity sorts air in an adiabatically isolated environment out into hot air at the bottom and cold air at the top. This arrangement is thermodynamically stable and will spontaneously occur and be sustained.
* Argument If the assertion were true, then due to Fact 1, a heat engine placed in the container and run between the top and the bottom would run forever. As fast as it made the air at the top warmer, the heat would somehow “fall” back to the bottom, re-creating the thermal gradient that we know can drive all sorts of heat engines. This violates Fact 2.”
Trick says “No, this heat engine won’t run forever”. My view: the N&Z assertion IS true since it can be shown to comply with natural laws. Can Willis’ find a fail? Here’s my view:
As Robert Brown writes, the air container in question is an isolated closed system so by Robert’s Fact 2, that heat engine cannot run indefinitely & thus it will run to control volume (cv) equilibrium and stop. The heat can’t “fall” once in equilibrium. There is no way to perpetually “maintain” the non-equilibrium unless the heat reservoirs are infinite & they are not. Eventually, in the same control volume, every real hot & cold irreversible heat engine equilibrates the two non-infinite hot & cold “fuel” reservoirs and stops making work – up until the reservoirs are “maintained” i.e. replenished across the cv. Like my refrig. with the electricity off. Gotta’ plug it in.
In the N&Z thought experiment case at hand viz. a tall adiabatic (occurring without gain or loss of heat across cv) control volume of GHG-free air i.e. gas in the presence of gravity will reach equilibrium and the heat engine will stop. No way can it be made to run except by being an outlaw. This occurs in the non-outlaw earth & near earth planets.
There are at least three important laws applicable to understand the tall air column cv of height h in the presence of gravity, there may be more, but each of these must ideally operate at same time & are sufficient to arrive at equilibrium in the cv of interest & some conclusions:
1st law: conduction always operates from high T to low T objects made of normal matter & they touch, to equilibrium.
2nd law: energy is always conserved & usually written PE + KE = constant (here P*V = KE, ngh = PE).
3rd: ideal gas law: PV = nRT (where in the cv of interest we hold V, n, and of course R constant)
So here’s what the 3 natural laws together mean will happen at equilibrium in the cv: the inexplicable gravity field will drive the tall column of gas to stratify itself with higher pressure at the bottom (2nd law: P*V + 0 = const. at h=0) due to the “weight” of the gas above (ngh). This is sustainable in adiabatic cv.
At column top, there must be lower pressure written by 2nd law also: P*V + ngh = same const. P*V is thus lower and with V constant, it is pressure P that has to be lower. No way around it, fight the laws all you want (I know y’all will try).
That means if you put a thermometer at h>0, it will show temp. T at h>0 . Put the same thermometer at bottom (h=0) read: T + delta T. The delta T from increased KE which has to be larger since V is constant to get (P*V + 0) = same const. = (P (at h>0) * V + ngh). Try that with P0 and Ph subscripts for practice. You can do it Willis.
The temperature (KE) of the atmosphere reduces as h (really ngh PE) increases above 0 for earth & nearby planets. N&Z stands. AND with all three laws operating from top to bottom, we’ve achieved closed system equilibrium so no heat engine can operate Robert: Fact 2 n’est ce pas? Even with T at top and T+delta T at bottom, there is equilibrium with all 3 laws. Go figure.
PS: Somewhere in there is an elevator speech to understand N&Z, I have one already posted but will leave it up to the reader to check their N&Z understanding.
Note: the density anywhere in the air column control volume is given by ideal gas law rearranged or density = n/V = P/RT so at any h in the cv, density can be computed from measuring P and T at that h, same time.
Got that? Move on….ha. Never happen, let entropy calmly increase. I dislike THAT entropy law: more reading.
Lets be clear a closed system with an atmospheric temperature gradiant present could exist indefinitely without breaching thermodynamic laws.
However, that is only possible if absolutely no work is being done at all. If work is being done, and I cannot imagine a system, with a temperature gradiant, that could prevent work being done, then entropy must increase.
If work is being done then in the long run you are creating energy somewhere or you are preventing the entropy of the system from increasing. That is impossible and surely obvious to any reasonably intelligent person.
However, in an open system we have the question, can gravity affect the temperature of Earth on a continual basis. Well we know gravity can certainy affect temperatures in a system at least once.
Take a difuse cloud of particles and wait for gravity to compress them and you will certainly see a localised increase in temperature of the system. Not only that the gravitional effect is the ultimate cause of something like the Sun continuing to increase its temperature for many billions of years. So you would need to define the statement ‘once’. If ‘once’ is taken as the period between the life and death of the Universe then that would be continuously for ever.
We know that Jupiter is radiating more energy than it receives and this is ultimately due to the gravitational effect. This process has been going on and will continue to go on, for billions of years.
Is this just ‘once’ or continuous? It depends on your definition of once.
In addition is any of this gravity induced temperature difference helped along by the addition of energy from the Sun moving particles to a higher potential energy within the system making more energy available to the gravitational effect, which we know for sure increases the temperature of the planet. It must do, the exchange of energy must be producing work in the atmosphere.
So the question is, given that the Earth also receives energy continuously from the Sun, does this mean that there is a continuous temperature increase in the Earth’s system caused by the effect of gravity.
Why wouldn’t it? It is just expanding the period of ‘once’, which we all agree gravity can iat least increase the temperature of a system by.
Alan Millar
Hans Jelbring says: January 20, 2012 at 11:03 am
In the case of my model atmosphere there is a temperature difference that can be used for energy extraction. That can only be done by moving energy outside the closed insulated atmosphere. In such a case energy will be removed from the inclosed atmospherea and its average temperature would sink. However such a machine is not allowed since the atmosphere was inclosed and no energy at all was allowed to enter or leave the system.
======================
The average temperature may fall but the thermoelectric effect relies on temperature difference NOT absolute temperature.
Therefore, providing your hypothesis that the adiabatic lapse rate is fixed (10K/km), then your theory predicts that the temperature difference between top of column and bottom of column will be maintained. Therefore it is possible to extract the same power from the column for ever (or at least until the lower electrode reaches absolute zero!
Louis Hissink says:
January 20, 2012 at 4:46 am
Thanks, Louis. Very little is known about the effect of electricity on the climate, despite its obvious involvement (lightning, charge separation in clouds, auroras, the ionosphere, sprites and jets, cloud nucleation, the list goes on).
For this topic, however, we’re away from electricity. I do have a keen interest in the question, and I think it is an important one we’re just starting to investigate but this thread is about the Jelbring hypothesis, a very different question.
Thanks,
w.
MarkW says:
January 20, 2012 at 5:11 am
Let me stop you there and say that a) space has no temperature and therefore b) the top of the atmosphere cannot be “the temperature of space itself”. Since your exposition clearly depends on those errors, you’ll have to start again.
Sorry,
w.
steveta_uk says:
January 20, 2012 at 5:13 am
Since gravity has no effect on temperature, why would the shape of the container have any effect at all? The shape of the container, whether a cone or a cylinder or a pentagram, doesn’t have some magic ability to mystically give gravity the power affect temperature. Well, maybe the pentagram …
I’d say you have a problem in your assumptions, steve.
w.
Willis,
This explains why no one can give a clear explanation of quantum mechanics. According to Feynmann, nobody understands quantum mechanics.
capt. dallas says:
January 20, 2012 at 5:20 am
I’ve not usually seen that assumption made. In general, conduction of both sensible and latent heat is not “assumed negligible” unless it is in fact negligible for the particular phenomenon under study.
w.
Joel Shore;
Dave, we all know that you have become completely obsessed with this particular issue…but you have failed to refute both my and Willis’s rough quantifications of its magnitude and hence you are continuing to “make a mountain out of a molehill” on this subject.>>>
Get off of it Joel. I keep pointing out that the upper bound is not the important one to understand, it is the lower bound, and you keep coming back with noise about the upper bound. I’ve even provided sample calculations showing what a realistic estimate of the EFFECTIVE black body temperature of earth should be based on an “average” of 240 w/m2 which you have studiously avoided.
If you calculate a realistic surface temperature for earth based on actual variance of insolation, you arrive at a value of about 140K. That is the EFFECTIVE black body temperature of earth. 253K can only happen if insolation is 100% uniform and with half the earth being 0 w/m2 at all times, that notion is totaly ludicrous.
140K is far more realistic. If I accept for the moment that the earth average is anywhere near 288K, that leaves one looking for an explanation of a temperature increase of nearly 150K, not the 33K we keep on seeing quoted.
As I have asked you previously, stop modeling the error in the 288K number and start modeling the effective black body temperature of earth based on insolation varying from 0 to 1000 w/m2 on a daily day/night basis and on a tropics to poles basis. Show me what a realistic EFFECTIVE black body calc for 240 w/m2 “average” should be. Why are you afraid of coming to grips with this number? How can we possibly have a discussion of the physics required to raise surface temperatures by some amount due to the GHE when we start the discussion with a GHE number that it totaly, completely, and ridiculously, WRONG?