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.
Joel Shore says:
January 22, 2012 at 10:46 am
“However, for an atmosphere where the temperature decreases with increasing height (which is what the atmosphere will tend to when populated by greenhouse gases…and which convection can only partially cancel), the amount absorbed will be less than the amount emitted back out into space.”
It does not matter. Back-radiation allows the surface temperature to rise, which begets more back-radiation. This is classic positive feedback. Stability ensues when the overarching negative T^4 feedback balances the positive feedback.
“This means that the net effect will be to allow the average surface temperature to exceed any possible average temperature that would produce radiative balance in the absence of an IR-absorbing atmosphere.”
This statement is in no way in conflict with my Law. In the steady state, there is no difference between what I am saying, and what the greenhouse hypothesis says.
But, the greenhouse hypothesis is unstable, because reducing the back-radiation reduces the temperature, which reduces the back-radiation, and so on. There is nothing to prevent reversion to the ground state.
Stephen Wilde says:
January 22, 2012 at 10:46 am
“The atmosphere of any planet will restructure itself regardless of composition to produce the ATE determined by mass and solar input.”
I don’t think that assertion has adequate support at this time. But, my logic above is compelling. If we could establish a common cause, I would advise we bridge the moat before we assault the castle walls.
A Stirling engine, with the hot side a sea level, and the cold side at altitude is the Perpetuum Mobile being discussed. Clearly such a device could be constructed today. The question is then, what is the mechanism that makes this possible?
We all agree that solar energy warms the surface air, which expands and rises. The reason it rises is because the atmosphere has mass and because of gravity. If there was no gravity, there would be no “up” direction for the air to rise.
As the air rises, it cools because of gravity, as kinetic energy is transformed into potential energy. There are of course other mechanisms of cooling, but the specific mechanism by which (dry) rising air cools must be due to conversion of kinetic energy to potential energy. This is inherent in the formula for lapse rate, which relies on the gravitational constant.
Now, as the air cools it contracts and becomes more dense. It will descent as a result. The reason it descents is because of its mass and gravity. If there was no gravity, there would be no “down” direction for the air to descent.
Thus, all that is required for our Stirling engine to operate as a Perpetuum Mobile is an atmosphere with mass, solar energy, and Gravity and one other ingredient: TURBULENCE.
The model described above will not work in a work without turbulence. The air would simply rise until it reached a steady state equilibrium and there would sit. Convection would come to an end. What is required to set the Perpetuum Mobile in motion is a disturbing force. On earth we have this in abundance, due to rotation, latitude, topography, etc.
Something that does not exists in the cylinder of air model.
Joules Verne said @ur momisugly January 22, 2012 at 8:38 am
If we accept that the scientific community consists of just those who accept the laws of science as true, then sceptics are certainly not excluded from the scientific community. Sceptics who refuse to accept the validity of the laws of science are excluding themselves from the scientific community. I find it’s best to avoid attributing malice to someone’s statements, when a charitable interpretation of the statements can be made.
[snip – already? That’s a separate paper and separate post – confine your discussion to this one – Anthony]
Stephen Wilde says:
No…It is not irrelevant. It is what determines the temperature of the planet’s surface, not some magical “ATE” that violates the laws of physics.
Strawman argument. The ideal gas law does not imply your result. Not even close.
I must catch a plane for a conference, and will be out of pocket for the next several days. Despite Joel’s misunderstanding of feedback dynamics, my logic is ineluctable. Temperatures will rise until radiative emissions stop them from rising. More IR gases will reduce the level they are allowed to rise.
If, when I am able to check back, you guys still haven’t gotten it, and this thread has gone stale, I will have to post it again in another thread until serious people begin to take my challenge seriously. DeWitt? Tim? Where are you guys?
davidmhoffer says: January 22, 2012 at 11:24 am
“You mean other than attributing 33K to the GHE is totally and completely wrong?”
People sometimes say that Earth with the same atmosphere free of GHG would be 33K cooler. What you and N&Z claim is that Earth with no atmosphere at all would be some different temperature. This is a completely different proposition and, in my view, of very little interest.
REPLY: Nick and I find ourselves in rare agreement – Anthony
davidmhoffer says on January 22. 2012 at 8:30 am.
“Further, at night when insolation is zero, it doesn’t cool off to absolute zero because it doesn’t have TIME to cool that much. The “average” daily temperature can easily be maintained at well above the non existant imaginary 255K without a single ——-”
=========
I like your answer and have no “gripes” but would like to add,- if I may:
People who build “Climate Models” by putting their imaginary “Model Planet” in a situation that exists nowhere in this Solar System or anywhere else, as far as I know, i.e. surrounded by “multiple little suns” – or for any other reason are giving their planet 24 hour sunshine, say by averaging “The Solar Constant” to cover the complete sphere 24/7 -, do not have any chance of getting the correct answers. The two main reasons for me saying this are:
1) Earths “Solar Irradiadiation” is halved – or all attempts to find all the values necessary for correct calculations – are abandoned.
2) There is no night in their models. Therefore the efforts made, by earlier scientists, to establish the “Earth’s Surface Cooling Rate” at various latitudes are lost. –
As you say, the Earth turns and for every second that passes – the left, or eastern, part of its surface presents a “new”, small part of itself that is far warmer than zero Kelvin (0 K) to the Sun’s rays.
thepompousgit says:
January 22, 2012 at 12:02 pm
If we accept that the scientific community consists of just those who accept the laws of science
Theory and hypothesis are not scientific law. Even the laws are not absolute. They exist only so long as there is not contradictory information.
Those that believe the laws of science are written in stone are not practicing science, they are worshiping science.
Fourier said in 1824:
“The presence of the atmosphere and bodies of water, has the general effect to render the distribution of heat more uniform. In the ocean and in the lakes, the coldest particles, or rather those whose density is the greatest, are continually tending downwards, and the motion of heat depending on this cause is much more rapid than that which takes place in solid masses in consequence of their connecting power. The mathematical examination of this effect would require exact and numerous observations. These would enable us to understand how this internal motion prevents the internal heat of the globe from becoming sensible in deep waters.”
It looks to me like:
Attributing 33K to the GHE is a bit like creating enough fuel for all “Perpetuum Mobile Machines”
“Applying SB Law to the hourly increments we arrive at equilibrium temperatures in degrees K of:
0, 0, 0, 0, 0, 0, 205, 227, 280, 327, 345, 350, 350, 345, 327, 280, 227, 205, 0, 0, 0, 0, 0, 0
Averaging both these series OVER TIME we arrive at:
“Average” insolation = 242 w/m2
“Average” SB Law equilibrium temperature = 144K
….
RESPONSE
Why of course! Did you think the heat capacity of the moon was zero?”
So what is the average heat capacity of earth per square meter?
And once you add an atmosphere and ocean this heat capacity increases enormously.
Instead of: 0, 0, 0, 0, 0, 0, 205, 227, 280, 327, 345, 350, 350, 345, 327, 280, 227, 205, 0, 0, 0, 0, 0, 0 one gets something like 285 K repeated 24 times.
And all this is talking about a average spot on earth, and I would guess that is somewhere around sun light and air temperature of 38 degree latitude.
I excited about averaging, but once you start down road, one continue and average everything.
A post not posted:
“So average amount sunlight energy on earth is said to be 240 watts per square meter, and average temperature of earth is said to be 15 C. Using this data, where is the average place on earth?
So need place that averages 15 C, nite and day, summer and winter. And it gets 240 watts times 24 hrs. Which is 5760 watts per square meter in 24 hrs.
I haven’t looked. Any guesses?
So, we look at solar map. Google: solar map:
So basically southwestern states in US- southern Spain, middle east. southern part Australia, Northern countries in South America, much of India.
And I live in this region. I live somewhat close to LA. LA downtown over last century yearly average temperature have been as high as near 69 F and near 62 F as lowest:
http://www.climatestations.com/images/stories/los-angeles/lacvann2.gif
Or 69 F is 20 C and 62 F is 17 C. So it’s a bit too warm for average.
Sacramento: 60.8 F [16 C]
San Francisco: 57.1 [13.9 C]
Norfolk – Virginia: 59.6 °F [15 C]
The average temperature in Melbourne, Australia is 14.8 °C (59 °F).
Anyway average of 15 C is near or lower than 40 degree latitude.”
Nick Stokes says:
January 22, 2012 at 12:12 pm
This is a completely different proposition and, in my view, of very little interest.
I disagree. What we have in our discussion of climate is a single data point on an unknown function. That data point is planet earth. The more data points we can add, the more likely we are to arrive at the correct description of climate. By necessity this involves resolving the effects of no atmosphere versus atmosphere, as not all world have atmospheres.
ferd berple says:
January 22, 2012 at 12:04 pm
[snip – already? That’s a separate paper and separate post – confine your discussion to this one – Anthony]
I’m sorry Anthony but what I have I missed? I made reference to the “Jelbring hypothesis” which was the subject discuss in this post. Here is the sentence in the post:
“I was reading the Jelbring hypothesis this afternoon, which claims that greenhouse gases (GHGs) “
davidmhoffer said @ur momisugly January 22, 2012 at 10:26 am
re Stefan and Boltzmann
I find myself saddened that there are some in this debate who will believe this farrago of nonsense.
We’re not leaving them out. Do you understand what an inequality is? It tells you that something can’t be bigger than something else. The temperature of a blackbody emitter receiving and average of 240 W/m^2 cannot be greater than 255 K. It can be less, depending on the temperature distribution. Is that such a hard concept to understand?>>>>
Sigh. No, that’s not what it means. It means the AVERAGE cannot be higher. The actual temperatures can vary substantially both higher and lower. The average of those temperatures cannot be higher than 255K.
As seen from space, the outbound LW radiance cannot average more than 255K. BUT, the outbound LW radiance does not and cannot originate wholy from earth surface, or from any single altitude. Assuming the existance of GHG’s which, including water vapour, ozone, and so on we have plenty of, a small amount of radiance must originate at earth surface and an increasingly large amount of radiance must originate from increasing altitudes. The “average” of these must equal 240 w/m2 in order to be in equilibrium with the “average” 240 w/m2 being absorbed. In other words, some of the photons originate from a surface temperature higher than 240 w/m2 and some from a layer lower than 240 w/m2.
A quick glance at AMSU shows this to be the case. At an elevation of 14,000 feet, the temperature is about 253K. At altitudes lower than that, the temperature is higher. At altitudes higher than that the temperature decreases until about 60,000 feet and then rises again to about 253K at 135,000 feet. Since each and every layer MUST radiate, and SOME portion of the radiance from each layer MUST exit the atmosphere to space, and since the amount radiated MUST equal 240 w/m2 in order to achieve equilibrium, the fact that MOST of the air column is well BELOW 255K, and that upward bound LW has the highest possibility of escaping the earth’s atmosphere from the HIGH altitudes (because there is less in the road to potentially intercept and absorb them) the only possible conclusion is that the earth surface MUST be warmer than the average in order to balance the much colder than 255K temps in the upper atmosphere.
Add in heat capacity and you have all you need to account for the disparity. Does that mean the effects of GHG’s are zero? No. But it also means you CANNOT take 255 subtracted from 288 and attribute it to GHG’s alone.
Ferd berple said @ur momisugly January 22, 2012 at 12:17 pm
Please read what I wrote Ferd; do not put words in my mouth. I said nothing about theory and hypothesis. Nor did I say that the laws of science are absolute. I said earlier in this thread: “Please note that I am not saying that they will remain as Immutable Laws for Ever and Ever Amen. Paradigm shifts do occur. But every paradigm shift I have studied was enabled by people who clearly understood the paradigm they were overturning.”
Nick Stokes says:
January 22, 2012 at 12:12 pm
davidmhoffer says: January 22, 2012 at 11:24 am
“You mean other than attributing 33K to the GHE is totally and completely wrong?”
People sometimes say that Earth with the same atmosphere free of GHG would be 33K cooler. What you and N&Z claim is that Earth with no atmosphere at all would be some different temperature. This is a completely different proposition and, in my view, of very little interest.
REPLY: Nick and I find ourselves in rare agreement – Anthony
***********************
Then help me out guys. If we don’t know what the temperature of the earth is with no atmosphere, and we don’t adjust the temperature profile that results for heat capacity and latency (time constant), then on what basis do we quantify atmopsheric effects?
Willis Eschenbach says on January 22, 2012 at 11:01 am:
“O H Dahlsveen says:
January 22, 2012 at 9:17 am
… By the way Tallbloke has done us all a big favour by posting “Fourier 1824 as translated by Burgess 1837″ on his blog, so go read it and perhaps learn – a lot.
I’d love to … but I’m banned from the talkshop for my evil ways. Is it posted anywhere else?
w.”
=====
YesWillis,. You can either cut and either copy, cut and paste Fourier (1824) as translated by Burgess (1837) into your search engine or click on: http://geologist-1011.mobi.
Willis – My compliments.
It’s never easy to debunk a popular, yet physically incorrect argument – JoNova had much the same experience over the greenhouse effect and the 2nd law of thermodynamics. But it’s vital – if folks want to be part of the discussion, their arguments must make sense.
Again, my compliments.
davidmhoffer says: January 22, 2012 at 1:03 pm
“on what basis do we quantify atmopsheric effects?”
We don’t need to quantify the effect of atmosphere removal for anything to do with climate. We have an atmosphere, and it isn’t going to go away. But the GHG fraction has changed, and may change further. That’s what the 33K refers to, not this silly arithmetic about moonscapes.
davidmhoffer says:
Yes…You can (modulo the point that you need to replace “GHGs” with “greenhouse effect” since technically clouds are not a GHG since they are not a gas but they are part of the greenhouse effect). Because in the absence of any greenhouse effect, the effective radiating layer is at the surface and the highest blackbody surface temperature that can support the emission of an amount of power equal to 24W/m^2 times the earth’s surface area is a temperature of 255 K.
So, in the absence of the greenhouse effect, the Earth’s surface temperature has to be at least ~33 K less.
Stephen Rasey says at 10:58am:
“Trick, a coffee cup on a table is experiencing the force of gravity, but it is not moving in the table’s frame of reference, therefore it is not accelerating.”
Stephen – The cup IS accelerating at g wrt earth surface/table in their rest frame or cup would have no weight. In this table frame of reference, the coffee cup has mass m & inexplicable gravity generated weight force = mg down on the table at rest wrt surface of earth.
Equivalently in the cup rest reference frame, the table would be seen to be accelerating at a (=g) and the cup has no way of knowing whether (F=weight=mg=ma) is from table accelerating or from an inexplicable gravity field.
Wait for my maybe imperfect language to be corrected below…but that’s generally ok I think.
In your isothermal arguments you are conflating temperture and energy. Shame on you. In the absence of gravity the column would be isothermal. However gravity induces a pressure gradient and this introduces a temperature gradient along with it. Total energy in the column however does not change and neither does the total energy in any horizontal layer. Total energy is a mix of gravitational potential energy and kinetic energy. As you move further up the column total kinetic energy declines and gravitational potential energy increases commensurately. “Heat” is energy of motion, measured by thermometers (“sensible”) but it isn’t the only kind of energy. The books balance just fine with a thermal gradient produced by a gravitational field. Gravity does not produce or reduce total energy, it doesn’t change the distribution of energy, it merely changes the form the energy takes on at different altitudes.
Dearest J.V.
I’m doing no such thing. I’m showing quite clearly that in the presence of gravity a non-isothermal column of air is not in thermal equilibrium. Temperature is (kinetic) energy per molecule, not total energy in the gas or total energy per molecules. Surely my example regarding jars of air made that clear. You can move a jar up or down all you like. You can fill it with as many molecules as you like (as long as there are enough for thermal equilibrium to be a valid concept, so putting a single molecule in the jar won’t work on the low side, and putting so many into the jar that they form a solid or liquid won’t work). You can give it any pressure that you like. At the end of the day, after you’ve waited for the molecules in the jar to come into thermal equilibrium, the temperature of the air in the jar is a direct measure of whether or not it would be in thermal equilibrium with any other system, anywhere, in or out of a gravitational field, whether the second system is a solid, liquid or gas.
Having the “books balance” is a matter of the first law. There are many, many possible ways the energy in the box can distribute with the first law books balanced. The way that it will distribute, in equilibrium, is a matter of the second law. The second law requires that the equilibrium distribution in any undisturbed/isolated environment, including one in a gravitational field, be isothermal because heat will flow from hotter to colder if it can, otherwise.
Temperature does not depend on potential energy, it depends on degrees of freedom. That’s why a jar full of air at 300K riding in the space shuttle will have precisely the same velocity/kinetic energy distribution as a jar full of air at 300K sitting on the surface of the earth. It does not depend on pressure. A jar full of air at 2 atmospheres and at 300K has the same velocity/KE distribution as a jar at 1 atmosphere. It does not depend on the number of molecules (although you can get into trouble for very low numbers of molecules because your jar can get to where it only has one or a very few molecules in it, in which case “distribution” of velocities and “temperature” become shaky concepts). A jar with N molecules at pressure P and temperature T has the same average kinetic energy per molecule as a jar with 2N molecules at pressure P/2 and temperature T, whether or not one of them is floating in intergalactic space and the other is sitting (well insulated) in a balloon floating at rest in the atmosphere of Jupiter.
Until you and all of the many other people who seem to want to insist that the laws of physics, specifically the laws of thermodynamics in the context of gases, are somehow suspended learn these simple ideas out of any book on thermodynamics, you will continue to contribute — ahem — “hot air” to what should otherwise be a very cool discussion.
Let me state it clearly and categorically. Under no circumstances can any gas, ideal or not, including a gas sitting over the same gas, liquified, in a container, whether or not the gas and/or liquid are floating freely in space or sitting at rest on the surface of a planet, sit there for a very long time and end up with a separation of temperature in equilibrium. If that could ever happen, anywhere, we could build perpetual motion machines of the second kind, because heat in such a system spontaneously flows from cold to hot in order to form it from a temperature neutral initial state. Gravity can transiently do work to heat a gas as it collapses and produce a non-uniform temperature distribution, but conduction and convection will quickly thermalize it to a single temperature.
Seriously, J.V. — you seem well-read. Surely you have read and understand the arguments associated with Maxwell’s Demon, enough to realize that gravity isn’t one.
How about you, or anybody, actually try to address the perpetual motion problem? Explain how one can run a heat engine between any two reservoirs that are at different temperature unless they happen to be the top and bottom of an “equilibrium” column with a stable, gravitationally produced lapse rate, because if they could do it then they would run forever.
rgb
Nick Stokes says:
January 22, 2012 at 1:24 pm
davidmhoffer says: January 22, 2012 at 1:03 pm
“on what basis do we quantify atmopsheric effects?”
We don’t need to quantify the effect of atmosphere removal for anything to do with climate. We have an atmosphere, and it isn’t going to go away. But the GHG fraction has changed, and may change further. That’s what the 33K refers to, not this silly arithmetic about moonscapes.>>>
If one does not know what the atmospheric effects are, then by default one also does not know what the GHG effects are as they are simply a component of atmospheric effects. Further, I find it interesting that people are quite content to calculate 33K based on the theoretical blackbody temperature of earth as derived from the “average” insolation, but when I point out that the method used to arrive at that number is flawed, the come back is, well, you’re talking theoretical numbers not practical numbers.