Perpetuum Mobile

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.

Image Source

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.

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ShrNfr
January 19, 2012 4:03 pm

However, we do have a real heat source in the earth’s core with the fission of heavy nuclei. Not perhaps a lot, but some. I never have gotten any really good estimates of how large the effect is, and I am not enough of a geologist to derive it. Anyone around have an idea??

gerard
January 19, 2012 4:09 pm

I have a partner who has been taken in by the Thrive Movement and especially the Free energy -torus machine I have tried to explain about nergy to no avail. The Thrive promoters are linking their philosphy to climate change and saving the planet by promoting their device as a saviour.

tallbloke
January 19, 2012 4:18 pm

I think Hans uses a definition which is ‘per unit area’
There is more room at the top of the atmosphere for more thinly spread molecules. More area per isobar as altitude increases. Needs thinking about.
I’ll sleep on it.

Josh C
January 19, 2012 4:25 pm

ShrNfr:
http://en.wikipedia.org/wiki/Geothermal_gradient
Per Wikipedia “Heat flows constantly from its sources within the Earth to the surface. Total heat loss from the earth is 44.2 TW (4.42 × 1013 watts).[12] Mean heat flow is 65 mW/m2 over continental crust and 101 mW/m2 over oceanic crust.[12] This is approximately 1/10 watt/square meter on average, (about 1/10,000 of solar irradiation,)”

tallbloke
January 19, 2012 4:29 pm

“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.”
Except that more of the total energy of the molecules at the top is locked up in gravitational potential as opposed to being available as kinetic energy capable of generating heat in collisions.

Bryan
January 19, 2012 4:30 pm

The isothermal/adiabatic distribution for an isolated ideal gas in a gravitational field has long been debated.
For the isothermal distribution we have Maxwell, Boltzmann and Clausius.
For the adiabatic distribution we have Loschmidt, Laplace and Lagrange.
The smart money must be with the isothermal advocates but I would not regard this as a debate of which was settled and of historical interest only.
Clausius clincher argument of the perpetual motion machine being possible for the adiabatic distribution turns out to be very hard to prove with real components given 9.8K/km scale.
Perhaps Willis will suggest a real experiment with real materials to test the alternative conjectures.
Say with a thermoelectric device to make use of the temperature difference.
A computer simulation program would not be any kind of proof
I think he will find with real materials that this is beyond him
Perhaps this is why there has never been an experiment to settle the matter!
If the adiabatic conjecture turned out to be correct I’m sure there would be an explanation that did not conflict with the second law.
Here for instance is a member of the physics department of the University of California making a very up to date case for the adiabatic distribution.
http://arxiv.org/PS_cache/arxiv/pdf/0812/0812.4990v3.pdf

Mark T
January 19, 2012 4:34 pm

Some Qs:
1. can the same result be found using gas laws, i.e., as P drops, so drops n thus leaving T unchanged? Seems reasonable.
2. do P and n necessarily change 1:1? I do not know this answer.
3. in light of 1., what if the total volume of the cylinder is not fixed?
4. in light of 2., what if they do not change 1:1?
Both 3. and 4. seem like complications beyond my reach.
Mark

tallbloke
January 19, 2012 4:34 pm

Final thought for the night. Here’s the reply I gave Robert Brown on my site Earlier today:
Robert Brown says:
Second, my comment about egregious violation of the laws of thermodynamics were specific to Jelbring, who (IIRC, I’m not looking at his article again as I type this) explicitly asserted a column of fluid with no energy inputs, and then claimed that in equilibrium it would exhibit a thermal gradient. No, it wouldn’t.

Hi Robert,
I think the laws of thermodynamics talk about energy, rather than temperature or heat, but there are several formulations of them, so maybe we’d better discover who is using which definitions. We’d better do this, because in the application of classical mechanics to energy distribution in the model atmosphere, as defined by Hans Jelbring, there will indeed be a thermal gradient, as confirmed by Graeff’s empirical experimental data (Which should be replicated by an accredited laboratory).
“if A and B are placed in thermal contact, they will be in mutual thermal equilibrium, specifically no net heat will flow from A to B or B to A.” That’s the zeroth law.
Assuming your A and B have at least some dimension, then a thermal gradient across them would mean that the top surface of A will be at the same temperature as the bottom surface of B where they contact. Therefore no heat will flow. Even so, the average temperature of the whole of body A will be higher than that of B. QED.
http://www.emc.maricopa.edu/faculty/farabee/biobk/biobookener1.html
Laws of Thermodynamics
Energy exists in many forms, such as heat, light, chemical energy, and electrical energy. Energy is the ability to bring about change or to do work. Thermodynamics is the study of energy.
First Law of Thermodynamics: Energy can be changed from one form to another, but it cannot be created or destroyed. The total amount of energy and matter in the Universe remains constant, merely changing from one form to another. The First Law of Thermodynamics (Conservation) states that energy is always conserved, it cannot be created or destroyed. In essence, energy can be converted from one form into another. Click here for another page (developed by Dr. John Pratte, Clayton State Univ., GA) covering thermodynamics.
The Second Law of Thermodynamics states that “in all energy exchanges, if no energy enters or leaves the system, the potential energy of the state will always be less than that of the initial state.” This is also commonly referred to as entropy. A watchspring-driven watch will run until the potential energy in the spring is converted, and not again until energy is reapplied to the spring to rewind it.
———————-
I’m not seeing the words ‘heat’ or ‘temperature’ in these definitions, so please could you clarify. Thanks.
I’m not looking at his article again as I type this
Maybe you should. This is one of Jelbring’s chief complaints. People answer what they think he said, instead of answering what he actually said.

Peter Spear
January 19, 2012 4:37 pm

I think there is still a bit of a fudge factor in that elevator speech.
“Since the top of the atmosphere cannot be below a certain temperature…”
Why? It can’t be below absolute zero but that isn’t relevant here.

January 19, 2012 4:38 pm

Willis Eschenbach wrote:

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.

Yes, it was a long discussion and my, how time flies when you’re having fun. It’s even more fun when you finally “get it”, whatever the “it” is that’s been bugging you.
And thanks again for your help around that time and continuing pedagogy. Yer blood’s worth bottlin’ Willis.

January 19, 2012 4:39 pm

I think I need to hear an elevator speech for why “same total energy per unit volume is a physical necessity. That is not obvious at all.
Here is another elevator speech for why in the constant insolation example you get an Isothermal atmosphere.
You have a fixed amount of energy per unit (Eg) area received by the ground. This is a experiment in spherical symmetry. Things like temperature, pressure, potential energy only vary by r (radius). So at the ground, at equilibrium, you have some temperature Tg = T(r=ground) that we will constrain by the SB law of a black-body ground. The catch is that in order to radiate the ground with Eg, you must have a uniform shell at r=(very large) also radiating Eg uniformly over its entire area. When you dissipate the energy per area by 1/r^2, you also increase the area of the shell radiating the ground by r^2. But if the shell is radiating at Eg, as a black body, then the temperature of the shell is Tg, the same temperature as the ground. So T(r) = Tg at r=ground and Tg at r=(very large). But (very large) is arbitrary, so it can be any value between ground and infinity. Therefore, T(r) = Tg at all r. Isothermal regardless of pressure and gravitational potential energy.
So I can get to Isothermal with the completely artificial initial conditions of uniform insolation. If and only If. Does that tell us anything useful about the real world? I’m skeptical. We need day and night.

January 19, 2012 4:48 pm

> 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.
My thermodynamics is a bit rusty, but I am fairly sure that warm air always rises to the top.

Ian H
January 19, 2012 4:49 pm

It is called the “adiabatic” lapse rate for a reason. It arises from adiabatic processes. What you are describing is the exact opposite of adiabatic. Your atmosphere is static and you allow it to reach a static thermal equilibrium over a very long period of time. Under those conditions you will indeed see equal temperatures everywhere. Hey – it isn’t at all surprising that you can get rid of the adiabatic lapse rate if your model eliminates all possibility of adiabatic processes.
But add in some adiabatic action – a nice little bit of vigorous vertical mixing – and the temperature gradient reappears. The elevator speech goes thus: “When air moves in a vertical airflow from the top to the bottom it is compressed and thus heats. When air moves in a vertical airflow from the bottom to the top it is decompressed and thus cools. In an atmosphere with a lot of vertical mixing you therefore will see a temperature gradient.”
Our atmosphere has such a temperature gradient.

richard verney
January 19, 2012 4:53 pm

I am skeptical of both the gravitaional model and the GHG model.
With respect to the former, i think that there are a number of factors overlooked, the extent to which they may be material is moot.
First, gravity is not a constant force acting on the atmosphere in the sense that the atmosphere is not subject to only the force resulting from the mass of the Earth. The atmosphere is constantly being flexed by the Sun and the Moon (and even to a small extent by the Gas Giants). The diurnal bulge/atmospheric bulge is the consequence of this and is well known and this means that work is constantly being inputted into the atmosphere and as one knows a by product of work is heat. One can see the effect (an extreme example admittedly) of gravitaional pull on Io which is the most geologically active body in the solar system and this is due to the gravitational pull imposed by Jupiter and the other Galean moons. Thus there is a top down force (gravity from the Sun, Moon etc) in addition to the bottom up force of the gravity from the Earth all working on the atmosphere.
Second, and this is a factor of the first point, the atmosphere is constantly being displaced at the bottom with the ebb and flow of the tides. Again, although this is obviously weak, this too results in work being exerted on the atmosphere, the by product of which is heat,
The result of these two factors is that the atmosphere is being squeezed much like the walls of a car tyre and any motorsport fan will know that this flexing generates heat in the tyre. It is very effective at heating up the air in a tyre or at any rate maintaining the heat generated by inflating the tyre to the desired pressure.
Third, the Earth itself is a heat source and imports heat into the atmosphere. The Earth is geologically active such that the ground is well above absolute zero. Indeed, even if the sun was to stop shinning, unlike the moon, the temperature of the ground would take a long time to cool to levels seen on the dark side of the Moon. Further, we know little of the deep ocean and there is every likelihood that the amount of thermal energy being inputted into the oceans is considerably under-assessed.
Fourth, the sun warms the atmosphere irrespective of GHGs simply because of aerosol particulate matter in the atmosphere which then warms surrounding gases by conduction/thermalisation
;
May be all of this does not add up to all that much. However, the atompsphere was obviously born warm (being the left over from what was in effect a condensing fireball and the out pourings of volcanoes etc) and one only needs it to add up to the amount of energy that the system is net losing to space to maintain an equalibrium balance.
I think that there may be more to the gravitational theory than you presently give it credit. .

January 19, 2012 4:54 pm

I must modify my isothermal elevator speech with a slight complication. I said that to have Eg insolation at the ground, the black body shell at r=(very large) must also be at Eg. That would only be true if the index of refraction of the ideal gas is 1.000 at all pressures (r). I don’t think it is reasonable to assume index of refraction for a compressing ideal gas does not increase with pressure. Assuming that Index of refraction (Ir(r=ground) is higher near the ground than at high altitude Ir(r=large), then there is a focusing of energy. Therefore, the energy radiated per unit area by the shell must be Es < Eg. therefore T(r=very large) < Tg. But we still have an arbibrary "very large", so I'm talking myself into a slight decrease in T(r), as r increased from "ground" to "very large". Likewise, Es(r) also must = Eg at r=ground, but decrease as r increases as the Index of refraction decreases as r increases.

Jeremy
January 19, 2012 4:59 pm

Many people added comments, presumably physicists and engineers, indicating they had a huge problem with the Nikolov & Zeller theory. I think the issue is dead. There is no such thing as gravity creating higher temperatures.
Deep in the earth, radioactive decay (fission) of higher elements converts mass into energy. In extreme cases, larger bodies like our Sun, the gravitational pressures and heat can result in fusion, which creates even more energy by converting even more mass. The reality is that the center of our planet is well insulated from the near -273 C of space and it therefore remains hot as it is unable to dissipate the heat generated from radioactive decay quick enough to cool down. It has little to do with gravity and everything to do with fission heat and insulating properties of hundreds of miles of rock. What ultimately happens is what we call “steady state” (not the same as equilibrium).
It is the same for the atmosphere – it has energy sources from above (Sun) and from below (Earth black body & some reflected Sun) and ultimately our atmosphere has also reached a quasi-steady state which only fluctuates in response to the changes in energy gained and energy lost. Water being a huge stabilizer of our atmospheric temperature by virtue that it can store energy as it converts from water to a vapor and vice-versa. Anyone can see that after the sun’s radiative energy, water is the single biggest factor in the highly stable behavior of our atmosphere and finally orbital parameters and albedo play a small role to.
This atmospheric gravity thing is complete and utter codswallop.

JeffT
January 19, 2012 5:00 pm

Here’s a shorter elevator speech:
If there is a temperature gradient between two parts of a system, net heat flows from the warmer part to the cooler part. If there is net heat flow within the system, it is not in equilibrium.

January 19, 2012 5:10 pm

Give us time Willis.
I’ve now read and understood N&Z, and their first reply at TT to commenters from WUWT and TT. I now think their work is a paradigm-shifting cracker, but I also realize that paradigm-shifters, while ultimately incredibly simple, need to do a lot of background detail work to answer all significant details AND eliminate all possible scientific stupidities of one’s own AND cope with the psychological challenge of answering classy experts without letting one’s scientific immaturity, feyness or hippiedom lose one the necessary credibility, AND provide an FAQ-type approach to those who’ve found something to doubt and given up on the spot. Like I was sure your elevator speech last time was flawed but my answer, though still IMHO denting your thesis, didn’t really deal with it properly. And I just haven’t yet read Jellbring at all. I might find I agree with you, re Jellbring, for all I know.
Give us time, and we will repay our debts, I mean explain the new paradigm in acceptable ways and with sufficient evidence from data in the public domain. There really is a lot of stunning high quality evidence now available.

richard verney
January 19, 2012 5:21 pm

The problem is that GHGs and back radiation does not explain the vertical temperature of the atmosphere. The inescapable conclusion of this is that the GHG model is not capable of explaining our atmosphere and that there is more at ‘play’ than the GHG model would suggest.
The vertiacal temperature profile of Earth’s atmosphere is not fully explained by the gravitational model but there does appear to be, for the main part some, causal connection. Ditto, other celestral bodies that we know of.
Presently, we do not know enough, or understand enough to fully evaluate either model. When you neither know or understand enough thought experiments invariably lead to flawed conclusions. Testing and the accumulation of observational data is required to take the matter forward/

David
January 19, 2012 5:21 pm

Your elevator speech:
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.

The air moving up and down exchanges potential energy (PE) for kinetic energy (KE). The air moving down loses PE but gains KE, and vice versa for the air moving up. A higher KE means a higher temperature, a lower KE means a lower temperature. So the air moving down increases in temperature (KE), while the air moving up decreases in temperature (KE). This will maintain the adiabatic lapse rate, warmer air at the bottom of the column and cooler air at the top.
Your second point is wrong, there is no equalisation of temperature. Therefore, your conclusion in the third point of your elevator speech is also wrong.

ShrNfr
January 19, 2012 5:27 pm

@Josh C Thanks.

Siliggy
January 19, 2012 5:33 pm

To test any theory i like to look at the extremes and see if they work. So with this theory in mind, what temperature would the planet be left at if the sun were to switch off?
Should i now blame air pressure for my sunburn?

January 19, 2012 5:38 pm

More briefly, one might refute the gravitational theory of atmospheric warming by reference to the empirical fact that at the top of the Earth’s atmosphere, outgoing radiant flux is closely similar to incoming radiant flux, whereas, if gravity contributed significantly to warming at the surface, Earth would be luminous, i.e., have a positive net outgoing radiant flux.
The only time gravity causes a net increase in the thermal energy content of the atmosphere is during the process of atmosphere formation, e.g., when an airless planet passes through a gas cloud. Then, gravitational compression of the gas will cause heating, the greatest effect being at the surface. However, the heat added to the atmosphere during gravitational compression will warm the surface, the added energy being then radiated to space until equilibrium is reached.

Josh C
January 19, 2012 5:39 pm

If we wanted gravity derived concepts for heat, we should look at the temperature profiles of planets like Jupiter to see if there is a corresponding gravity induced effect. A quick look at the temperature profile here:
http://en.wikipedia.org/wiki/File:Structure_of_Jovian_atmosphere.png
If the elevator goes down far enough, there is a similar curve found in most planets with a solid cloud cover.

Joe Born
January 19, 2012 5:42 pm

Thanks to papers brought to our attention by Paul Dennis at tallbloke’s blog, namely:
Coombes, Ch. A. and Laue, H., 1985, Am. J. Phys, v53, 272-273
Velasco, S., Roman, F.L. and White, J.A., 1995, Eur. J. Phys. v17, 43-44
I have become convinced that the isothermal hypothesis, although correct as an approximation, is theoretically true only in the limit. The former paper purports to demonstrate the strictly isothermal result, but, if my reading (with which it is not clear that Paul Dennis agrees) of the latter, Velasco et al. paper is correct, its Equation 8, a result of statistical mechanics, dictates that average kinetic energy decreases with height even at equilibrium.
A layman’s-eye view of what’s going on in a paper by Román et al., on which Velasco et al. rely, is found at tallbloke’s here: http://tallbloke.wordpress.com/2012/01/04/the-loschmidt-gravito-thermal-effect-old-controversy-new-relevance/#comment-13608

January 19, 2012 5:45 pm

richard verney says on January 19, 2012 at 5:21 pm
The problem is that GHGs and back radiation …

Understand that ‘back radiation‘ is as if innumerable miniature dipole antennas tuned to specific wavelengths (as per the CO2 and H2O resonant frequencies) were present in the atmosphere and they ‘catch’ (the forward or out-to-space-bound EM energy) and re-radiate (in ALL directions including back-to-earth so-called ‘back radiation) that same EM energy AT the specific frequencies/wavelengths where they are resonant (and this includes spectral ‘line broadening’ due to molecular collisions at higher pressures e.g. at low altitudes) …
It is as simple as that.
(You do understand, too, that temperature is a measure of molecular vibration, and that gas molecules have different characteristics when ‘vibrating’ than do solids?)
.

Bill Illis
January 19, 2012 5:50 pm

What about the gas giant planets? Jupiter at 99% hydrogen and helium has had about 4.6 billion years to become isothermic. Yet the lowest gas/liquified gas/metallic hydrogen temperatures are 35,700K and the top of the atmosphere is only 165K.

January 19, 2012 5:51 pm

There are lots of perpetual motion machines. But only one really works.

Zac
January 19, 2012 5:52 pm

Well, he does have a point. IMHO gravity has never been fully explained.

markus
January 19, 2012 5:54 pm

“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”.
Can somebody please conceive this fact; Energy cabn be also employed, not just conserved.
Add kinetic energy to matter and the E does not equal mc/2.

January 19, 2012 5:57 pm

Dr. Brown says that your “column of gas” will have the same temperature at the top as at the bottom, due to equal numbers of molecules with identical kinetic energy moving each way between adjacent thin “slices”. So those adjacent “slices” have equal overall kinetic energy and MB distribution, and therefore equal temperature. In that case they must also have equal numbers of molecules, and so the two slices must have equal pressure. If two adjacent thin slices have the same pressure, then the whole column has the same pressure. Extend the column or cylinder to TOA and you have a mechanism to lose the top layer to space fairly rapidly, and by logical extension, the whole atmosphere.. Some disconnect with reality here?

Zac
January 19, 2012 6:01 pm

We know that gravity exists but not one acedemic has managed to explain with any confidence why our boots are attracted to the Earth’s core.

markus
January 19, 2012 6:04 pm

“”The explain the incredibly simple N&Z theory that you say you understand””.
The kinetic energy of mass is the mechanism that enhances its employment of energy.
But it is explained Willis, so fully by N&K, it turned my lights on, and what a brilliant sight it is to see.

Walter
January 19, 2012 6:10 pm

All sounds like my first year university Physics lectures.
Perhaps a few more Physicists need to read and understand and comment.
Where’s Richard Feynman when we really need him?

GeoLurking
January 19, 2012 6:13 pm

@Josh C and ShrNfr
Ref Earth’s Heat
Don’t forget that we still quite a bit left from the accretion of the planet.

January 19, 2012 6:13 pm

Willis Eschenbach wrote:
“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.”
No it is not, equipartition states that temperature is proportional to the internal energy per molecule. Energy is an extensive property, temperature intensive.

markus
January 19, 2012 6:15 pm

“Zac says:
January 19, 2012 at 6:01 pm
We know that gravity exists but not one acedemic has managed to explain with any confidence why our boots are attracted to the Earth’s core”.
They can now. Wrong way up we are.
Its not that your boots are attracted to the earths core, it’s that your boots are attracted less to the earths core, because you have more kinetic (employed) energy. As is matter with more kinetic energy above you, like gas.
Quite simple really.

bean
January 19, 2012 6:16 pm

WRT crustal heat flux: surface. http://www.solid-earth.net/1/5/2010/se-1-5-2010.pdf

Bill Illis
January 19, 2012 6:33 pm

100 kg of gas 100 kms from Earth will have 98,000,000 less joules of energy than 100 kg of gas at the surface.
Gravitation potential energy actually turns into real thermal energy for a mass that is falling through a gravity field or objects with mass that are closer/farther from the centre of the gravity field.
GPE = Mass * Gravity * Height
Without this (albeit very unnatural effect to us but nevertheless real effect in the real universe) there would be no stars or galaxies anywhere and there would no elements beyond hydrogen, helium and tiny amount of Lithium and there would no us. The universe is made up of many different types of energy beyond photonic EM radiation. There is the strong force, the weak force, gravity and dark energy in addition to the electro-magnetic force.
If we are going to just accept every “settled scientific fact” about radiation theory, then we might as well all be running climate models. If they don’t work, then there is a reason. One is, they do not consider everything that is actually happening (in the quantum world, in the real universe).

ferd berple
January 19, 2012 6:34 pm

Willis Eschenbach says:
January 19, 2012 at 5:54 pm
Lucy, thank you for your comment, but time is what you don’t have.
That is the same argument used by the cap and trade shills to try and force people to agree without due taking time for due diligence. Buy now before it is too late.
Temperatures have leveled. Sea levels have stabilized. CO2 has not. These events contradict GHG theory predictions, which in science is a strong indication the GHG theory is wrong.
It is as though Einstein predicted that gravity would bend light, and when light was measured it was found not to bend. So, then Einstein proposed a new aerosol particle to explain why gravity did not bend light as predicted, but would bend light in the future.
There is plenty of time to review the science and find out why the GHG predictions failed.

January 19, 2012 6:40 pm

Willis Eschenbach says:
January 19, 2012 at 4:58 pm
“…then how can the gravity possibly separate a low-energy, isothermal atmosphere into a higher energy state of cold at the top and warm at the bottom?
How do you know that the “cold at the top and warm at the bottom” state has a higher energy?

January 19, 2012 6:43 pm

Isothermal is just that isothermal, no change in temperature with altitude. The energy contained per unit volume would be greater at altitude than at the surface if fewer molecules occupied that volume. So here is an interesting thought experiment.
To be isothermal, the atmosphere would require perfect insulation. The number of collisions of molecules per unit volume at the surface would be the same as the number of collisions per unit volume at the top of the atmosphere. There would be no lapse rate. The density of the atmosphere would be greater, but there would still be a top of the atmosphere. How high would that be?
Now, if gravity increased, the height of the TOA would decrease. If the atmosphere was perfectly insulated, the temperature of the volume would increase due to compression. There is still no lapse rate, the atmosphere is still isothermal. The number of collisions per unit volume increase.
Now let’s let energy flow from the surface out of the TOA. Unless the atmosphere is perfectly conductive or perfectly transparent to radiant flow, energy will be lost to the atmosphere. With the additional energy, the atmosphere expands, creating a lapse rate, temperature decreases with altitude. Since energy must be conserved, the total energy of the atmosphere must remain the same if the average energy of the atmosphere is to be maintained, unless we add energy. Now the “potential temperature” of the parcel of air at altitude would equal the true temperature of the parcel of air at the surface.
Now that we have a lapse rate and the total energy of the atmosphere fixed since we have not added energy. If the surface layer of the atmosphere warms by 33C then the TOA decreases by 33C. There is a 66C difference in temperature between the surface and the TOA, which is the tropopause. Add sunlight and we have the stratosphere and a new TOA.
Manabe knows that and his estimate for CO2 forcing is half of Hansen’s. Trenberth doesn’t know that, or at least won’t admit that, so his cartoons are meaningless.
CO2 has an impact, just not as much as estimated by people that confuse the tropopause with the surface.

January 19, 2012 6:44 pm

richard
“The problem is that GHGs and back radiation does not explain the vertical temperature of the atmosphere. ”
The vertical temperature differential is a requirement for the GHG effect. You’ve not understood why GHGs cause the surface to cool less rapidily than it would otherwise.
Simply. If the upper altitudes were not colder, then GHGs wouldnt have the effect they do.
More GHGs means the earth radiates from a higher elevation.
If that higher elevation is cooler, then the surface must “warm” or cool less rapidily.
Lapse rate is a requirement for the GHG effect to take place.

Robt319
January 19, 2012 6:44 pm

Hi,
I have some questions and some observations but as I am not as smart as some please excuse my mistakes.
Due to the spherical nature of our planet, any column of air will not be parallel sided but will be trumpet shaped and the volume will not be linear. Does this effect your equilibrium of energy?
Your statement that a column of air will stratify in a gravity field is observed on earth and I believe that this temperature gradient is in part due to the effect of gravity. Does not the ideal gas law have some application here? However, as we know, the atmosphere is very complicated and probably cannot be described so simply.
The heat engine Dr Brown describes in his proof by contradiction sounds to me like the description of a thunder storm and I personally have observed many of those. If we could harness the power of thunder storms and hurricanes we could indeed power our cities but of course our atmosphere also has other sources of energy, namely the sun. Does Dr Brown disprove the theory or add weight to it?
I am not trying to suggest that anything is right or wrong but the idea that the lower atmosphere is warmed by gravitational pressure from the air above it makes sense to me.

January 19, 2012 6:54 pm

ShrNfr says:
January 19, 2012 at 4:03 pm
There are actually at least 3 intrinsic heat sources for the earth:
1) fission of radionuclides
2) primordial heat from earth’s formation, and the impact that created the moon, or other impacts
3) flexion friction from gravity interactions, especially from the moon
Chemical oxidation heat is mostly externally provided and driven (photosynthetic oxidation of carbon, oxygen being provided by conversion of nitrogen by cosmic and solar radiation, etc.)

Hoser
January 19, 2012 6:57 pm

Gas molecules don’t travel in straight lines very far. They collide. Energy in these molecules is spread in a distribution described by temperature, across various degrees of freedom (1/2 kT).
Thermal conduction in the Earth seems to be very slow. There are temperature gradients below ground. Caves near the surface seem to have a temperature roughly equal to the average yearly temperature. Temperatures under ground increase with greater depth. Could the heat of radioactive decay make much difference at the surface? Perhaps it’s the old chicken and egg dilemma.
It seems a significant contribution to the Earth having an elevated temperature compared to a black body is the delay in reradiating absorbed light from the sun. The surface warms and some of that energy works its way deep into the ground, or into water below the surface. There is heat capacity, heat conduction, and fluid mixing in the oceans all moving absorbed energy to and from the surface where it might be radiated back to space. The Earth is a heat sink with poor thermal conduction characteristics. If the Earth absorbs light more efficiently than it radiates, then the surface temperature must rise before equilibrium is reached. That higher temperature is thermal energy that can be transported deeper into the Earth. It will take time to penetrate, and it will take time to rise back up to the surface after the sun sets.
If some of the daily energy is retained and not radiated at night, then the Earth’s temperature rises. A glacier has similar properties. Eventually all of the snow that falls on a mountain melts, but if some of the snow never melts during the summer, a glacier will form. The length depends on various parameters like snowfall, but eventually all of the snow melts. The glacier length stabilizes when the rate of snowfall balances the rate of melting. If some of the heat absorbed during the day is not reradiated, then the surface the next day will start out warmer. The average surface temperature will rise until the total amount of energy radiated over 24 hours equals the total amount absorbed during the day.
The atmosphere can pick up thermal energy by conduction and move it to cooler places. The atmosphere also has its own heat capacity. However, there is no way in hell that our atmosphere retained excess heat due to some hypothetical compression event over 4 billion years ago.

Joe Born
January 19, 2012 6:57 pm

If you reduce the number of molecules to a fairly small number, you can see that Willis’s argument, beguiling as it is, is wrong. Consider a single-molecule system, for example. Does anyone doubt that the molecule’s translational kinetic energy is greater when it is lower in the gravitational field than when it is higher? Does that reverse relationship disappear when a second molecule is added?
As the number of molecules gets large, the system approaches isothermic. But a (very small) lapse rate persists.

jae
January 19, 2012 7:05 pm

DAMMIT, WILLIS:
PLEASE ADDRESS THE EMPIRICAL EVIDENCE, WHICH WILL ULTIMATELY RESOLVE THIS ARGUMENT! WHY DO YOU REFUSE TO DO THIS?
[Moderator’s suggestion: If you didn’t YELL at him maybe more would be accomplished? Maybe? -REP]

David
January 19, 2012 7:07 pm

Willis, do you have a rebuttal or reply to my post http://wattsupwiththat.com/2012/01/19/perpetuum-mobile/#comment-870067?

January 19, 2012 7:09 pm

I think that you had it right to begin with – the molecules move faster down low. That means temperature is higher down low. The fact that energy density is constant is a red herring.

Dougmanxx
January 19, 2012 7:10 pm

I am a semanticist at heart. I read with interest these posts and wonder about two little words: “at equilibrium”. I suspect these theories are thinking about something that doesn’t actually exist in the “Real World”, like so many thought experiments I see from so many very learned and intelligent people.This begs me to ask several questions:
1) Is the atmosphere of the Earth “at equilibrium”?
2)If the atmosphere of the Earth is not “at equilibrium”, does this discussion have any meaning, other than as a diverting thought experiment?
3)If the atmosphere of the Earth is not “at equilibrium”, how will it behave?
Like much climatic, I suspect we are undone by our “Human” view of things.

u.k.(us)
January 19, 2012 7:19 pm

IMHO,
When, Dr. Robert Brown speaks, people should shut up and listen.

David
January 19, 2012 7:20 pm

A gentle reminder of the core issue raised by Willis: It seems to me that many posts are injecting unwanted complexities. While it is true that the Earth includes a large body of water, rotates in a 24 hour period, has a core that produces a (small) amount of energy, and so on and so forth, the question to be resolved is the behaviour of a column of “air” – actually any gas – in a gravity field, particularly its change in temperature (if any) with altitude.
To resolve this requires the question to be formulated as simply as possible. So to understand how gravity affects temperature distribution we ignore – for the time being – anything extraneous. No sun, no rotation of the Earth, no surface or sub-surface effects. Simply a column of gas in a gravity field. Nothing more.
I appreciate the effort many have put into their posts, and many are very interesting. But first let us understand how this works in the simplest manner possible.

Ed_B
January 19, 2012 7:22 pm

David says:
January 19, 2012 at 5:21 pm
“The air moving up and down exchanges potential energy (PE) for kinetic energy (KE). The air moving down loses PE but gains KE, and vice versa for the air moving up. A higher KE means a higher temperature, a lower KE means a lower temperature. So the air moving down increases in temperature (KE), while the air moving up decreases in temperature (KE). This will maintain the adiabatic lapse rate, warmer air at the bottom of the column and cooler air at the top.”
I agree with this. Respectfully, Willis is wrong.

Rob Dawg
January 19, 2012 7:22 pm

Gravity fields are not acceleration fields. In uniform acceleration fields the temperatures are indeed uniform. For a column of material In a gravity field to be of uniform temperature the column would need to be walled radially from the gravity point source.

markus
January 19, 2012 7:22 pm

Dear Mr Willis Eschenbach;
As you have [SNIP: Markus, sorry, but this sort of stuff contributes nothing to the discussion. You can make this sort of comment AFTER a cogent debunking. Please. -REP]

Werner Brozek
January 19, 2012 7:30 pm

If we had a single pane of glass and the temperature outside was 10 degrees and it was 20 degrees inside, then the temperature within the pane would vary linearly from 10 to 20 degrees across the width of the pane. Right? Now let us pretend we had a 10 kilometre long solid copper tube in the form of a vertical pole that was totally insulated except that the bottom 10 metres was in asphalt at 30 degrees C and the top 10 metres and was exposed to air at -50 degrees C. Then you would automatically have a temperature gradient of 8 degrees C per kilometre. How is this fundamentally different from what really happens with air? If the sun heats the surface and outer space is cold, you automatically get a temperature gradient without resorting to work done by increasing pressures.

January 19, 2012 7:34 pm

I take your kilometer’s tall cylinder of atmosphere in thermal equilibrium and flip it over, like flipping an hour glass. It involved no input of work as its height did not change, so the column’s energy remains constant. But now the gas at temp T that was at the top has been wildly compressed, making it much, much hotter, while the gas at temp T that was at the bottom has been expanded, making it much, much colder. If you let it get anywhere close to thermal equilibrium I’m going to flip it over again, and since I’m not putting in any work, I can do this all day, continuously forcing your air column back to the dry adiabatic lapse rate as I sip a margarita.
I love doing jobs that don’t involve an input of work and constantly overturn an idealized thermal equilibrium, because it’s just that easy.

KevinK
January 19, 2012 7:42 pm

Willis, thanks, that is a beautiful picture of a perpetual motion machine.
When I was a lad with a crude workshop I did play for a while with the PM notion. My version was powering an air turbine with the exhaust from a compressed gas source. Of course the the turbine was going to compress even MORE gas and the turbine would produce lots of free energy.
Then I went to engineering school…..
One thing I learned in school was that if something works there will be tens or hundreds of people using it. For example the IC engine, the airplane, the integrated circuit, and (not for much longer sadly, see the recent news about Kodak) photographic emulsions on flexible roll film.
So I ask myself, if the Greenhouse Gas Effect is REAL (still in question it seems after these many decades) WHY is it that NOBODY has figured out how to apply it to any practical problem and solve, or at least ameliorate said problem ?????
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 (although there is still some debate; does the effect “suck” the plane upwards, or does it “push” the plane upwards, this one seems like tomato .vs. thamato to me). The Peltier effect has been used for decades to cool electronic devices and has lately been applied to drink coolers.
It sure seems that once a physical effect is observed and characterized some sharp engineers find a way to apply it to solve a problem.
So why is it that after decades no sharp engineer has figured out how to apply the Greenhouse Effect to solve any problem, like maybe using the effect to create “net energy gains” in the insulation surrounding a building, that would sure reduce energy usage ???
I see a few possibilities;
1) Engineers are dumber than climate scientists, seems unlikely, some are probably dumber, but I bet at least a few are smarter.
2) There are a dearth of practical problems to be solved, seems unlikely, there always seems to be lots of problems to be solved, like how do we feed everybody and keep them warm. Or how do we allow folks to have fun on a floating cruise ship without letting an incompetent skipper rip a hole in the side by driving it over rocks and “catching” one in the hull, OK we have some more work to do there….
3) Maybe the Greenhouse Effect does not exist, or it exists, but does not provide any “net energy gains” or produce a “higher equilibrium temperature” as claimed ?
Personally, I’m betting on choice #3 and giving odds of several Million to One.
I have not yet evaluated any of the “gravity caused” theories others have suggested and you are discussing, and they may in fact have some merit. But I am convinced that the ”Greenhouse Effect” hypothesis is a modern version of the Perpetual Motion Machine. BTW you are not supposed to be granted a patent on PM machines, and I see nobody trying to patent the “Greenhouse Effect” or applications of if, surely somebody would have tried to lock up all the potential business opportunities if the “effect” really existed as promised ???
Cheers, Kevin.

Jean Parisot
January 19, 2012 7:43 pm

Somewhat off topic, has anyone built up an error budget for the AGW hypothesis? Not just how skill(less) the models are, but from a mearsurement perspective.
Our understanding of the historic record has error bars that dwarf the analysis. Our recent data has significant error. The spatial error is enormous.
What is all of this hysteria actually saying? We think a 2° rise is too fast, but the historic record can’t be resolved to that fine a point; and that 2° rise is based on models that don’t replicate the record fed with data widely dispersed, inconsistent measurements of fluctuating weather.

Jeremy
January 19, 2012 7:52 pm

Gravity has NO AFFECT ON TEMPERATURE.
How many times must it be said.
You people are reading science fiction.
You have to do WORK to create a change in temperature – this is basic thermodynamics!!!!
If an object falls in a gravitational field then potential energy will be converted to kinetic energy which will create heat. However a stable column of air in equilibrium does not create any energy or heat.
This is so so so basic that I am afraid I may have to give up this website altogether in disgust.

crosspatch
January 19, 2012 7:52 pm

Imagine you have a tube of air 1km long. Now instead of being a tube, you basically turn it onto a cone. Lets say the bottom of the tube represents 1/10,000 of the surface of the Earth, and the top represents 1/10,000 of the “surface” of an imaginary sphere at 1km altitude. This is why I said I would model the atmosphere as a series of concentric spheres representing conditions at the altitude of each sphere. Now, temperature and heat. At molecule at the ground might be 100F and a molecule at 40km might be 100F but there are far fewer of them at 40km. So if you stick your thermometer out the window of the bazillionth floor at 40km altitude, far fewer molecules will strike your thermometer and transfer heat to it. So your thermometer will cool until it reaches an equilibrium where the heat it is radiating is equal to the heat it is receiving. So the temperature of the molecules can be the same (100F) but there is less heat per given amount of space because there are fewer molecules.

Luther Wu
January 19, 2012 7:58 pm

Equilibrium of the atmosphere doesn’t exist. As can be seen in this thread, just trying to understand the climate in even the simplest terms is a daunting task.
Topologists long ago proved that the wind will always blow somewhere…
right after they mistook their donuts for their coffee cups.

January 19, 2012 7:58 pm

@ David says:
January 19, 2012 at 7:20 pm

From what I’m understanding, I agree.
However, I can’t help but wondering what would happen, keeping the extraneous items out as you said – “no sun, no rotation of the Earth, no surface or sub-surface effects. Simply a column of gas in a gravity field. Nothing more” out, except in a situation where the gravity isn’t constant. Wouldn’t, in that case, we have a continuously moving gas due to the changing gravity? Would we then see heat, energy, or work being “created” by the fluctuating gravity?
Just wondering.

AusieDan
January 19, 2012 8:06 pm

Willis,
You keep asking for an elevator speach supporting the N&Z analysis.
Here is my attempt.
(1) any worthwhile theory should describe reality or it is worthless and should be discarded.
(2) When you make due allowance for differences in their distances from the sun, the temperature of Mercury, relative to Venus, is too low to be explained by the greenhouse theory.
(3) However this is very closely explained by their different atmospheric pressures at the surface.
(4) That is also true for other bodies in the solar system.
(5) That in turn suggests that the various laws on physics mentioned in this thread, while themselves highly likely to be true, do not interact in the manner that has been outlined by people critical of the two unpublished N&Z (20110, 2012) papers.
I really do not think that this arguement will be settled using theoretical “thought” experiments. These remind me in so many ways of the best work of the IPCC.

AusieDan
January 19, 2012 8:14 pm

We need a theory to explain why the surface temperature of the various solar bodies can be derived as a function of distance from the sun (solar radiance) plus near surface atmospheric pressure.
N&Z have provided their theory.
The task of critics is now to come up with better, more economical (Occham’s Razor) theories.
As Lucy Skywalker has said – this is a game changer.
the game HAS changed.
We must now all respond to the new paradigm.

richard verney
January 19, 2012 8:23 pm

Jeremy says:
January 19, 2012 at 7:52 pm
///////////////////
Jeremy
Just three quick questions.
1. How much work is involved in the creation of the diurnal/atmospheric bulge?
2. How much work is involved in the moving of the tides?
3. Are not the same processes that are involved in moving the tides also at work on the atmosphere but not so readily apparent to an Earth boud observer since he cannot see the ebb and flow of the atmosphere as it is sublected to the gravitaional forces of the celestrial bodies?
The gravitational forces being exerted on the atmosphere are not constant. The atmosphere is never in equalibrium.
Perhaps you will answer my questions before departing this web site.

Stephen Wilde
January 19, 2012 8:27 pm

In the absence of an external energy source the column would indeed become isothermal.
Temperature at both top and bottom would be the same despite the higher energy content per unit volume at the bottom.
Mass is simply a form of energy so a denser mass per unit volume contains more energy but it does not follow that it has a higher temperature than a less dense unit of volumre.
Temperature is simply a measure of kinetic or vibrational energy and molecules can have the same averaged kinetic energy in both a dense and a less dense unit of volume.
Gravity just primes the system by placing greater density of molecules at the bottom of the column. It does not provide any heat or kinetic energy in itself.
If an external energy source is then switched on then the kinetic response to that energy input is density dependent and so the temperature gradient with density then appears.
More molecules per unit volume will convert a larger proportion of the incoming radiative energy into kinetic form and it is kinetic energy that is refected in a higher temperature.
Furthermore higher density involves more collisional activity due to closer packing of the molecules so that kinetic energy stays in kinetic form for longer whilst it is bounced to and fro between molecules before eventually being released in the form of outgoing longwave.
The more incoming radiation that is converted to kinetic energy per unit volume AND the longer it stays in kinetic form the higher the temperature will become.
The adiabatic temperature gradient is therefore a consequence of gravity induced pressure PLUS uneven energy distribution (more molecules per unit volume) PLUS incoming radiation.
ALL the components must be in place at the same time to produce the temperature gradient.
THEN the entire structure of the planetary atmosphere is effectively forced to adjust itself to provide the most efficient mix of energy transfer mechanisms both radiative and non radiative so as to maintain that adiabatic temperature gradient.
Radiative processes only perform a mopping up function. In so far as non radiative processes fail to return the system to that adiabatic lapse rate then radiative processes step in to make up the difference.
The S – B equations do not deal with the non radiative processes.
The final oucome in terms of atmospheric structure can become highly complex and that is where composition becomes relevant and why no planet with an atmosphere matches the S – B equations.

Quark
January 19, 2012 8:35 pm

Imagine a glass tube 100 miles tall reaching from the surface of the earth to outer space. Insert the base of the tube in concrete and then fill it with Coca-Cola or some other carbonated beverage. Now add peanuts at the top and watch what happens. At first the peanuts sink but as the fall, they gather bubbles which slows their descent until …..
LOL.
Sorry. But Jeremy is right. This discussion is almost totally nuts.

richard verney
January 19, 2012 8:37 pm

KevinK says:
January 19, 2012 at 7:42 pm
////////////////////
Kevin
I have made this point to Willis on a number of occassions and it has always been met with deadly silence.
Why are we seeking to exploit solar energy by way of PV cells when this has obvious drawbacks such as sunlight is not received at night or when cloudy. Trenberth suggests that on average solar power is just 184 w per sq m. Why are we not exploiting backradiation or at any rate researching its use when it is claimed to be in the order of 333 w per sq m come rain or shine 24/7? If this was truly a souce of energy capable of doing sensible work, we would be exploiting it since it would cure over night the world’s energy needs. Something is amiss here and it is probably that physists employed by energy companies or at the cutting edge of research do not consider it a source of sensible work.

KevinK
January 19, 2012 8:56 pm

Richard, yes I also get silence from Willis regarding any of my comments. I think that this is his loss…
I still think that if the “greenhouse effect” had any merit a whole bunch of engineers would have JUMPED on it a long time ago. BTW I am an engineer and I always JUMP on any “effect” that helps me solve a problem.
Cheers, Kevin.

January 19, 2012 8:57 pm

Willis,
I was in the same boat as you, thinking that the equilibrium temperature profile of an insulated column of air would be warmer at the bottom than the top. Like you, I changed my mind.
I discusses the topic with a few bright physicists. We bandied back and forth several ideas. There are a few convincing (but wrong) arguments that a lapse rate is the expected result. Eventually we concluded that the equilibrium profile must indeed to isothermal, because the arguments for that were more convincing (and right).
The simplest and most convincing argument ended up being your same perpetual motion approach. You could run an insulated copper bar from bottom to top. This bar does not have the lapse rate effect. (Or use another gas that would have a different lapse rate because it has a different heat capacity). The copper should have the same temperature at top and bottom. If the gas had a different temperature, would could use this temperature difference to continually run the sort of heat engine you suggested.
And that is how theoretical science is supposed to work. You come up with a couple different ideas about the some new situation. You apply fundamental, laboratory-tested principles and discuss it with others. When several different people who understand the science agree, then you have your conclusion.
PS A “back of the envelope” calculation suggests the “time constant” for this process would be weeks. Reaching something close to uniform temperature could takes months. But in the real world, there would be other processes to remix the air long before that.
PPS. This whole gedanken experiment was, of course, predicated on perfect insulation and a constant temperature at the bottom. The same “back of the envelope” calculation suggests that heat flows involved in conduction are less and 1 mW/m^2. Even a tiny amount of GHG at the top of the atmosphere would radiate a 1,000 times more energy, meaning that conduction would never actually achieve a uniform profile.

gbaikie
January 19, 2012 9:09 pm

“• 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.”
Strange as seems I would say it’s it’s true. We are assuming the gas that we talking about can’t freeze or liquify.
Nitrogen in near vacuum pressure can be close to absolute zero. And Helium:
“All known liquids, except liquid helium, freeze when the temperature is lowered enough. Liquid helium remains liquid at atmospheric pressure even at absolute zero, and can be solidified only under pressure.”
Liquid helium: Boiling point at 1 atm: 4.2 K 3.2 K
http://en.wikipedia.org/wiki/Liquid_helium
So certainly true if you are talking about a helium atmosphere.
Of course to have gravity you need mass- something which is giving 1/10th of gee will have internal heat.
Question is would work with artificial gravity.
I think there some thought experiment which says under certain you can’t tell the differences between acceleration and gravity, perhaps this would be a way to tell the difference, and maybe not.
• This is the cause of what we erroneously refer to as the “greenhouse effect””
Hmm, don’t think this explains everything in regards to the “greenhouse effect”.
If include the sun’s energy, the heat capacity of atmosphere, water vapor, clouds, ocean temperature, and land temperature, then yeah, most of the greenhouse effect.
And I don’t think it explain stratosphere and higher.

mondo
January 19, 2012 9:12 pm

A question about the diameter of the column of air extending upwards 1km. If the column were small diameter (say 5m across at ground level – expanding as it rises) would we not get different conditions/events than if it were, say, 1 km diameter? At some point, won’t we see convective effects happening? With hot air rising as it would in a hot air balloon? As Willis has so convincingly explained with his thunderstorm arguments (or did I miss something somewhere?).
And, further demonstrating my lack of knowledge, if warmer air rises due to convective effects, how come we notice that air temperatures are (generally) warmer at lower altitudes? Is that to do with the relatively greater air density at surface than at altitude.
Clearly I must do more reading to keep up.

January 19, 2012 9:12 pm

the universe is a perpetual motion system, expanding and contracting simultaneously in patterned ways, ad infinitum.
the universe is matter and space. temperature is associated with matter. it seems that a critical amount of matter determins black hole versus supernova outcomes for astronomical bodies.
what is the trigger for a big bang ? an accumulation of matter.
given that time is a measure, we could describe the life cycle of big bang as how many years ?
my point is that entropy is the normal condition.
more specific phenomena are contextual. our entropy is affected by local conditions, but in the end physical constructions return to matter and space.
my miniscule understanding of the topic under question favours the idea of gravity increasing temperature. where are the hottest places in our environments ? the centres of our astronomical bodies ?
ergo gravity wins up to the point of bigbang initiation, which may well be another gravitational effect.
of course I’m brain-sailing, surmising, and thinking aloud.

January 19, 2012 9:20 pm

I have a follow-up thought experiment to my previous comment.
If flipping the air column upside down doesn’t require an input of work and returns the column to the dry adiabatic lapse rate, then the dry adiabatic lapse rate must be the column’s thermal equilibrium because a system cannot be shifted from thermal equilibrium without an input of work.
If the adiabatic lapse rate is the thermal equilibrium then it should be impossible to devise a heat engine driven by a column of air whose temperature varies with the adiabatic lapse rate. If the isothermal condition is the thermal equilibrium then the same should apply, because a system in thermal equilibrium can’t drive a heat engine.
If I take a tall column of isothermal air in a gravitational field and exchange a pair of parcels from top to bottom, the descending parsel warms up and the ascending parcel cools down, with no change in energy and no net work. Yet in their new positions both these parcels have a large delta T relative to the surrounding air, and that delta T can drive a heat engine such as a Stirling cycle.
If I try moving parcels within a column whose temperature follows the adiabatic lapse rate, each parcel always stays at the same temperature as the surrounding air, so I cannot drive a heat engine. From that I conclude that an isothermal column of air in a gravitational field is not in thermal equilibrium, and a column of air at the adiabatic lapse rate is.
So if the column of air is isothermal, I can drive lots of little heat engines until it reaches the adiabatic lapse rate, after which I can extract no more energy from the system.
On caveat is that if the system is at the adiabatic lapse rate then the bottom air is warmer, and thus less dense, raising the center of mass of the entire column in slightly increasing its potential energy, so perhaps flipping the column does involve an input of work. Perhaps a more detailed analysis would take this into account and provide a slightly shifted equilibrium point.

gbaikie
January 19, 2012 9:33 pm

“Temperature at both top and bottom would be the same despite the higher energy content per unit volume at the bottom.”
The “higher energy content” seems to mean it’s hotter.
It seems the gas molecules would all have same average velocity- with exception that faster molecules would tend to be higher and slow molecules would be lower. This tendency- depends upon the amount of gravity- 10 gees would more of tendency than 1 gee. But this means more fast molecules could found and average speed isn’t different, the gravity sort them more. If follow a molecule it tends to stay lower, and spend less time higher.
Or the gas molecules are always varying velocities, the velocity is random, but is averaged by the zillion of molecules. If heads is faster, molecules with 10 heads in a row are tend to be higher, those with 10 tails in row tend to be lower.
In gravity field the average molecule speed will lower in the higher density.
Put 1 cubic meter of 1 atm gas, into another 1 cubic meter of 1 atm gas- doubles pressure to 2 atm, and is hotter, when cools to “room temperature” the 2 atm gas will have more density and less velocity.
“Energy content” to me suggests density and/or higher velocity of gas molecules- *either one or both” are higher temperature.

January 19, 2012 9:33 pm

Willis says:

You have not allowed for the fact that the atmosphere in the cylinder is mostly at the bottom. As a result, you have to move much more air up than down when you flip it. So it does involve a large input of work, despite the fact that its height did not change.

But I get all that work back when it passes the tipping point and the air rushes back to the bottom, just like flipping over a half-full bottle. The kinetic and potential energy in the final state is the same as in the initial state (except, in the case of a gas, for that thermally induced change in the center of mass I mentioned above), so there is no net input of work. You could drive the bottle flip with a spring and make a cute perpetual motion machine whose only flaw would be internal friction.

TimC
January 19, 2012 9:37 pm

David says “To resolve this requires the question to be formulated as simply as possible. So to understand how gravity affects temperature distribution we [should] ignore – for the time being – anything extraneous. No sun, no rotation of the Earth, no surface or sub-surface effects. Simply a column of gas in a gravity field. Nothing more.”
But this then considers only the local effect of gravity on the planet itself – not the effect of the gravitational fields of other bodies. The second law (and gravity) applies universally – you must take into account that no known planet simply wanders about the universe as an orphan; all known planets (and moons) are under the control of some greater external gravitational force (unless perhaps caught in a supernova explosion – but that would be a special case!). This implies rotation (Keplerian orbits, axial rotation by conservation of momentum or gravitational/ tidal coupling), therefore nights and days, atmospheric mixing, heating, and radiation by the atmosphere itself.
Part of the problem with Jelbring is the assumptions applying to the model planet. Interestingly the same applied to Willis’s orphan planet with the non-GHG atmosphere (in his original Some Gravity “trap” thread) – perhaps in the hypothetical world we will find some form of paradox applying until it is accepted that all known planets rotate.

bones
January 19, 2012 9:49 pm

The actual atmosphere temperature distribution cannot be modeled in terms of random molecular motions alone. The atmosphere is heated at the base by the absorption of UV and visible light. It warms to the point of hydrodynamic instability in the day and there is bulk flow energy transport from the warm base to higher elevations. Even without water vapor, CO2, methane or other greenhouse gases, ozone would absorb some of the outgoing IR. Without attributing either validity or falsity to any of the theories of atmosphere heat transport in discussion here, this is a complicated problem that is not going to be settled by simple arguments. Do the diurnal fluid mechanics problem along with atmospheric circulation and pole-equator insolation differences and then try to explain it in simple terms if you can.

dp
January 19, 2012 9:58 pm

Willis – at some point I got lost and it was at the molecular replacement part. A highly energized molecule takes up more space than a lesser energized molecule. For there to be a one-to-one replacement of a displaced (convected) molecule, the molecule replacing it has to consume the same volume. Meaning it has to be at the same energy level. What compels molecules at the same energy level to swap chairs? Describe what happens to a lesser energized molecule when it drops into the hole left by a more energized molecule. And I know you know.
Then we will need to talk about gradients where all gradient elements are very close to every other gradient element. This gets to a very earthly feature known as long runout earth slides such as that which buried Pompeii. But first things first. Please give me the elevator speech description of why molecules of identical energy levels would swap chairs. I will snip your posts if you go off topic.

johnpb
January 19, 2012 10:01 pm

Willis, It is hard to argue with your thought experiment due to your requirement of equalibrium which excludes convection. Once convection is allowed then adiabatic temperature differences will result.

James of the West
January 19, 2012 10:10 pm

Temperature vs Energy of a gas.
What is the temperature of a gas? It is proportional to the *average* kinetic energy of the gas molelules whose temperature you are trying to measure but then we must always define which molecules are and are not included for the temperature measurement. We can do this by defining a region in space – a volume with x,y and z dimensions. The gas molecules in our region of interest don’t all have to have the same kinetic energy – as long as the average kinetic energy of the molecules in a given region of gas is the same it has the same temperature.
The total Energy (kinetic plus potential energy) can be very different in a cubic meter of gas at sea level to the same volume of a gas at the same temperature at altitude. The density (and mass) of gas in a given unit of volume also changes with altitude. It is simplistic to think of one molecule of gas as it turns potential energy into kinetic as it falls, when you consider a given volume of gas as it falls the number of gas molecules per unit volume increases this means that the potential energy of 1 unit of volume of a gas does not decrease simply as a function of altitude but also of density (mass per unit voume).
At altitude the number of gas molecules per unit volume is less than at the planets surface so that means the total kinetic energy (sum of the kinetic energy for each gas molecule) is declining with altitude even if the gases have the same temperature (average kinetic energy of the molecules). Again the Potential energy of the unit of volume of gas at altitude is higher per molecule but there are less molecules per unit volume so the sum total of the potential energy for a unit of volume of the atmosphere is also a function not only of gravity but also of the number of molecules in a unit of volume.
My hat goes off to those who delve into this further! Good luck to all of the smart people thinking about these matters.

jorgekafkazar
January 19, 2012 10:14 pm

Willis-san: Here’s your logic, above, with the symbolic logic thereof:
“If an energetically isolated system is in its lowest energy state, it cannot perform work”
If EIS = LES THEN -W
“If the isolated atmosphere in Jelbring’s thought experiment is warm at the bottom and cold at the top, I can stick a thermocouple into it and use the temperature differential to generate electricity to perform work.”
If EIS = HBCT THEN W
“Therefore, the isothermal state…is the lower of the two energy states, since I cannot use it to do work.”
-W THEREFORE EIS = LES
Do you see what you’ve done, Willis?
If Roger is a goose, I can’t ride him like a bicycle.
If Roger is a Schwinn, I can ride him like a bicycle.
I can’t ride Roger like a bicycle, therefore he is a goose.

January 19, 2012 10:18 pm

We seem to be in the same boat Willis.
* We both thought that the lapse rate might be the equilibrium condition in this thought experiment.
* We both discussed it with other smart, informed people and decided the equilibrium condition is isothermal.
* We both realized a perpetual motion machine was the simplest argument against the permanent lapse rate situation.
That is how science should be done. I hate to admit I was wrong about physics, but there is no other conclusion possible here about the answer to this question. In our defense, there are arguments that sound very convincing that the temperature should drop as it go up. You REALLY have to know thermodynamics to avoid getting sucked in by those alluring arguments.
PS. The thought experiment is a very specific situation, not likely to be seen in the real world. Thermal conduction through the atmosphere is less than 1 mW/m^2 if the lapse rate is the maximum stable amount of 10 K/km. This number is SO much smaller that other energies involved (convection, incoming solar, GHG radiation, evaporation) that such an isothermal condition would never be realized in real life.

January 19, 2012 10:20 pm

For those of you that believe empiricism trumps thought experiment, consider the following, attributed to Galileo, though it was also recorded ~1,000 years before Galileo by John Philoponus and also Oresme (IIRC) more than a century before.
Galileo asked us to consider what would happen if two iron balls were tied together as one by an iron rod. The smaller and lighter ball, according to Aristotelian physics, would slow down the ascent of the larger, heavier ball. Yet the combined weight, being greater than either ball alone, meant that they would fall faster when tied together, as well as slower. Since a contradiction was (and remains) not allowed, the answer to the problem was that objects necessarily fall at the same rate, regardless of their weight. Galileo had successfully demonstrated that Aristotle had been wrong about falling weights.
While Galileo is widely (and incorrectly) believed to have performed the experiment of dropping two cannonballs of differing weight from the tower at Pisa, this cannot be the case. In his record of the experiment, Galileo refers to the height from which a wooden and iron cannonball were dropped: 300 feet. This would make his assistant the tallest man in the world — ever!
In the event, Galileo recorded that the wooden cannonball initially fell faster than the iron cannonball, and that the iron cannonball overtook the wooden cannonball, beating it to the ground by a measurable margin.
Think about what we are doing when we attempt to reconcile the empirical result withe the deductive result.

Thomas L
January 19, 2012 10:22 pm

Willis:
The problem is that the atmosphere Jelbring described cannot exist, and thus no meaningful statements can be made about it.
Suppose we have an atmosphere with a near surface temperature of 288K, and translucent in infrared frequencies. Then it must radiate to space at about the black body rate. Thus it will cool to the temperature of space, about 3K. In order to keep the atmosphere at a temperature above 3K, energy must be added. Indeed, to keep the atmosphere at 3K, energy must be added, via the cosmic background radiation. Once energy is added, whether at the top or the bottom of the atmosphere, the conditions for an isothermal atmosphere no longer apply.
It’s like dividing by zero. Once we let that slip in, whether by Jelbring or Eschenbach or Mann & Jones, we can get to any conclusion we want by following one chain of logic while ignoring another.

January 19, 2012 10:24 pm

okay Willis, I take your point re gravity not affecting temperature. however I would argue that gravity is associated with temperature – I assume that temperature is highest in the core of astronomical bodies, as written.
yes temperature dissipates by convection and radiation.
but what is kinetic energy other than mainly a gravitational effect, a pull or a push ?
whilst this topic is ‘restricted’ to movements of air and temperature in a tube, and the subject of a planetary body minus an atmosphere, the real life said body of air operates in relation to a wider context – wind, height, temperature of surrounding air.
equilibrium is a temporary phenomenae. perhaps slowest rate of change is a near definition.
I have to go out. I’ll return to this later.

gbaikie
January 19, 2012 10:26 pm

“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.”
[-Sounds wrong.-]
“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.”
So, it’s the “average molecule” which has same energy [velocity] and in less density the amount energy per cubic meter is less [and is therefore is colder- doesn’t warm as much something like thermometer].
But no molecule stays at same velocity. Or make it simple, maybe, molecules don’t go [normally] in any vector for more nanosecond.
In convection one can have a group “averaged molecules” going in one direction or vector or have something one calls velocity- but none of these actual molecules is actually going in one direction- it’s more like sound wave. it’s possible for a gas molecule travel say a meter or more in one direction, but chances are low of this happening. With zillion and zillion them, one probably goes mile fairly commonly:)
Example of the theory as I understand it.
Have two flat areas of real estate. Have them at different elevation. On at sea level and one at 10 km in elevation. And they are on same planet. They will have different density of air 1 meter above their surfaces.
On the land at 10 km in elevation should receive more sunlight. But let’s say the both receive same amount of sunlight. These areas of real estate are hundreds of square km and flat.
The one at higher elevation will not warm the air to as high a temperature as the land at sea level. The higher elevation land will increase the gas molecules speed to same velocity as the sea level land, but there is low density, so it’s cooler.
And even with more sunlight in higher elevation it would make the gas molecules travel faster, but it still would be cooler air temperature.
If this is true, than lower elevation has a “greenhouse effect”.
And the land at higher elevation should have it’s dirt at higher temperature [if has more sunlight]- and less greenhouse effect in this sense.

Poriwoggu
January 19, 2012 10:30 pm

Gravitational heating comes from contraction of a gas. Potential energy is converted to kinetic energy.
The sun when it originally formed would have had enough kinetic energy to shine for about 18,000,000 years. However – after about 18,000,000 years it would be cold and dead without nuclear fusion.
The atmosphere of earth may have contracted at some point but that energy dissipated several billion years ago.
The gravito-thermallers are kind of right – it may have happened, once. But that train has left the station and doesn’t impact current atmospheric conditions. The potential energy was converted and radiated away a long time ago.

Mike Wryley
January 19, 2012 10:31 pm

Willis,
I am beginning to think that there may be another effect at work to raise the temp due to gravity, but not for the reasons suggested. Because of the small angle subtended by the earth vis a vis the sun, the energy comes in a collimated beam. Essentially, most of the photons, whatever their energy, have a pretty good shot at the surface of the earth. However, once the surface or the gas
near (first couple miles let’s say) the surface reradiate this energy, it goes off it all directions. Due to density differences in the atmosphere caused by gravity, I would expect some of this energy to be reflected back at lower angles of incidence to the horizon due to refractive effects in the atmosphere, similar to the mirror like effect seen on a hot highway at low look angles. The compressed gas of the atmosphere creates a diode effect for inbound radiant energy. No clouds required.

Thomas L
January 19, 2012 10:33 pm

George Turner says:
January 19, 2012 at 7:34 pm
Nice try. Before you rotate the cylinder, the air at the top of the cylinder has lower pressure than the air at the bottom of the cylinder, and therefore the density at the top is less than the density at the bottom. So when you turn the cylinder over, you are doing work, as moving the bottom up takes more energy in a gravity field than you get from moving the top down. And the air in what was the top (now the bottom) gets compressed and heated, while the air in what was the bottom (now the top) expands and cools. But you knew this.

Theo Goodwin
January 19, 2012 10:34 pm

Bryan says:
January 19, 2012 at 4:30 pm
Perhaps Willis will suggest a real experiment with real materials to test the alternative conjectures.
Say with a thermoelectric device to make use of the temperature difference.
A computer simulation program would not be any kind of proof
I think he will find with real materials that this is beyond him
Perhaps this is why there has never been an experiment to settle the matter!
Yes, the distance from textbook to rigorously formulated physical hypotheses is huge. In fact, it is so large that it contains all the science, except for checking the predictions. To the Warmists it is a vast desert that they dare not enter.

January 19, 2012 10:34 pm

JeffT says: Jan 19, 5:00 pm If there is a temperature gradient between two parts of a system, net heat flows from the warmer part to the cooler part.
/headslap! Thank you, Jeff, it is that simple. Total energy, chemical Potential energy, mechanical potential energy do nothing to prevent temperature equilibrium.
Take a pressure cylinder. Fill it with iron springs and Freon. Put in the piston. Place it is a bath or air, water, or any other fluid. Press the piston to its max. The contents of the cylinder heats, the iron springs compress, the Freon compresses then liquefies releasing more heat. Wait a bit. The Cylinder system contains a lot of potential energy, but it and its bath will come to the same temperature in time.
Release the piston and the temperature of the cylinder will drop and then be warmed by the bath back to a lower temperature. This example does not employ gravitational potential energy, but I’m convinced. Total energy is irrelevant.
So on a uniformly heated, dead planet at equilibrium, the atmosphere will have a zero lapse rate, isothermal atmosphere. But bring on a day and night cycle, then differential heating will force a lapse rate to become established by adiabatic processes regardless of the atmospheric composition. All we need to know is the specific heat of the atmosphere and the surface gravity: Cp/g. http://wiki.answers.com/Q/What_is_the_dry_adiabatic_lapse_rate_on_Venus.

anna v
January 19, 2012 10:36 pm

Could one do the experiment using water as the fluid?
A long insulated tube (thermos like?) with temperature sensors along and a small tube inside for air to get out. Pour water at fixed temperature. Measure along tube. It would not have to be very long with good temperature sensors, a tower would do.

Downdraft
January 19, 2012 10:46 pm

1. The elevator soliloquy:
The mass of the atmosphere, solar insolation, and the temperature of the upper atmosphere determine the temperature at the surface of a planet of sufficiently thick atmosphere. The exact makeup of the gasses of the atmosphere is not important, as it can be assumed that essentially all outgoing long wave radiation is absorbed and re-radiated in the lower atmosphere, finally being radiated to space from the upper atmosphere. Surface temperature is simply a function of the temperature of the effective black body temperature of the upper atmosphere required to radiate heat equal to the net insolation of the total planet, the mass of the atmosphere, and the gravity of the planet.
Climate change and excursions from average can be attributed mainly to changes in the mass of the atmosphere, albedo, and insolation, and are largely independent of minor changes in LW absorption in the atmosphere.
2. I must disagree with Dr. Brown. In a tall column of gas acted on by gravity, and at equilibrium, in a perfectly insulated container, the top of the column will be colder than the bottom of the column. All gas will be at an equal energy state (by mass, not volume), and since gas at the top has more potential energy, it must be at a lower thermal energy state in order to have the same entropy value. In other words, the adiabatic lapse rate still applies. This is essentially the situation that occurs in the atmosphere, on a very large scale.

January 19, 2012 10:46 pm

Stephen Rasey says: 4:54 pm: Assuming that Index of refraction (Ir(r=ground) is higher near the ground than at high altitude Ir(r=large), then there is a focusing of energy.
Nope! Effects cancel out. Index of refraction might make it possible for someone on the surface of a planet to see more than 180 degrees of the outer shell. But each point on the outer shell is illuminating an equally larger area of the planet, thus diluting its contribution at any one point. Therefore, there is no net focusing, no net increase in energy, and an isothermal atmosphere even with index of refraction that increases with pressure.

Thomas L
January 19, 2012 10:53 pm

Willis Eschenbach says:
January 19, 2012 at 10:32 pm
You have a planet not near a star and heat the atmosphere to 288K. You construct an insulating sphere to hold the heat in. If the atmosphere is isothermal, the TOA is at 288K. This will heat the insulation to 288K. The insulation will then radiate to space at 288K. Of course the radiation rate could be very slow, but we are talking about equilibrium here. If we make the foam slightly radioactive, then we get near equilibrium, but only until enough half-lives have passed.
If there is a material that is 100% reflective at microwave through visible frequencies, that would keep the atmosphere either isothermal or iso-energetic. Iso-energetic implies a lapse rate related to the gravity gradient. My memory of thermodynamics is not enough to tell me which way the energy gets partitioned, but I think it’s iso-energetic.
Or we could surround the planet with insulation in the form of turtles. Then it’s turtles, all the way up.

jorgekafkazar
January 19, 2012 10:58 pm

Thus spake Willis (re thermonuclear heating): “I ran the numbers in the past. I don’t have them in front of me, but it is very small, less than a tenth of a watt per square metre from memory. There are a variety of geothermal regions, and hot vents under the sea, and hot springs and pools on land. But you have to consider—for every hot springs you know of, there are thousands of square miles of land with no hot springs, where if you go to sleep in the morning, you wake up very cold. So yes, you are right, there is a heat source down under. But it is very small, even if we have greatly underestimated it.
Right, Willis. I did the calculation a couple of years ago, and the conducted core heat is minuscule. If we look at mass transfer of hot material (hot springs, volcanoes, etc.), the numbers may be more significant. It is estimated that there are on the order of three million undersea volcanic vents. Most of these are small, but we don’t really have a handle on their total heat load, nor do we know exactly where it goes or how fast. (These seeps also emit CO2, but that’s another story,)

Bart
January 19, 2012 11:06 pm

“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.”

There is no equilibrium of a column of air in the gravitational field of a spherical planet unless there is a heat sink drawing energy away from the atmosphere. The heat equation does not allow a spherically distributed atmosphere to attain thermal equilibrium.
Without radiating gasses to draw the heat energy away, the atmosphere of a planet is like an ideal electrical capacitor hooked up to a constant voltage source, or an ideal inductor hooked up to a constant voltage source. It has nowhere to dissipate the energy, so the energy just keeps accumulating.
Eventually, the capacitor pops, or the inductor melts. In the real world, stray conductance or resistance, respectively, if they are large enough, prevent destruction. In the same way, a planet with insufficient radiation boils away its atmosphere, or achieves an equilibrium when sufficient radiation takes place from unaccounted emitting particles.
I have fleshed this all out in the previous thread starting about here.
So-called greenhouse gasses do not heat the surface – they prevent it from overheating. They are like a resistance put in parallel with that capacitor, or in series with the inductor.
In steady state, there is no difference between my description and the standard greenhouse hypothesis. On Earth, IR emitting gasses arrest the runaway heat accumulation that would otherwise exist. Backradiation equilibrates with the net overage in steady state Stefan-Boltzmann emissions from the planet’s surface.
So, there is no discriminator in the steady state, which is why people have been led astray for so long. They have been using Stefan-Boltzmann in ways it was not intended to be used – Stefan-Boltzmann only holds in conditions of equilibrium or, at least, quasi-equilibrium. The atmosphere of a planet without significant emissions is never in equilibrium, or even quasi-equilibrium.
The solution of the heat equation in spherical coordinates tips the balance in determining the real process going on. Without atmospheric emissions, there is always a temperature gradient leading into the atmosphere, and the atmosphere therefore continually accumulates energy. There is no adiabatic lapse rate possible without a heat sink in the atmosphere above. But, there is a lapse rate.
Look at the earlier thread. I’ve got it nailed. There is no doubt about it.

Bart
January 19, 2012 11:07 pm

Erratum:
Without radiating gasses to draw the heat energy away, the atmosphere of a planet is like an ideal electrical capacitor hooked up to a constant current source…

January 19, 2012 11:15 pm

“On average, that exchange equalizes temperature, moving slightly warmer air up and slightly cooler air down.”
Willis, I’m not sure whether that summarizes what Dr Brown said, but it’s wrong, and for a fundamental reason.
When the lapse rate is below the dry adiabat (toward isothermal) it is referred to as convectively stable. Above the adiabat, it is unstable. At the adiabat, it is neutrally stable.
At the adiabat, rising air cools by expansion, at exactly the rate at which the nearby air is becoming cooler (by lapse rate). And falling air warms. There is no buoyancy issue created. Moving air retains the same density as the environment. And no heat is transferred.
But in the stable regime, falling air warms faster than the change in ambient. It becomes less dense, so there is a force opposing its rise. That is why the air is stable. This motion both takes kinetic energy from the air and moves heat downwards (contra your statement). It is a heat pump which works to maintain the lapse rate.
Rising air does the same. It cools faster, and so rises against a buoyancy force. It takes KE from the air and moves “coolness upwards”, ie heat down. It pumps heat just as falling air does.
That is why air in motion tends to the adiabat lapse rate. A heat pump requires energy. Where from?
The atmosphere is famously a heat engine, driven by temperature differences, most notably from equator to pole, but also innumerable local differences, eg land/sea. This provides the kinetic energy that maintains the lapse rate, and it is hard to imagine any planetary atmosphere where the energy would not be available.
The effectiveness of the heat pump tapers as the adiabat lapse rate is approached. Beyond, in the unstable region, everything is reversed. The pump becomes an engine, with heat moving upward creating KE. This of course quickly diminishes the temperature gradient.
I blogged about this here.
It’s true that with no motion at all, conduction will render the air isothermal.

January 19, 2012 11:19 pm

“a force opposing its rise”
I meant, opposing its fall.

Bart
January 19, 2012 11:28 pm

A few posts from the other thread to help the discussion:
Solution of the Heat Equation in Spherical Coordinates
Bart says:
January 18, 2012 at 12:11 pm
In an atmosphere with no convection (the thought experiment world), the PDE governing the temperature is
dT/dt = alpha*del^2(T)
where alpha is the conductivity parameter and “d” is actually a partial differential operator and del^2 is the Laplacian. To solve this equation, we set T = T1(t)*T2(r), where T1 is wholly a function of t, and T2 is wholly a function of r. This leads to
(dT1/dt)/T1 = alpha*del^2(T2)/T2
where the “d’s” are now total differential operators. Since the left side is wholly a function of time, and the right wholly a function of r, they must both equal a constant, call it lambda.
Then, the solution of dT1/dt = lambda*T1 is elementary, T1 = T1(0)*exp(lambda*t). The solution of
del^2(T2) = (lambda/alpha)*T2
is a modified and adjusted zeroth order Bessel function of the second kind, which is qualitatively similar to a constant divided by radius.
Thus… the full solution is
T = T(0,0)*exp(lambda*t)*F(r)
There is always a gradient downhill in the radial direction. Thus, there is always heat flow into the higher altitudes. This heat flow will continue until it stops, either by high energy radiation if the atmosphere allows, or boiling away of the atmosphere.
Solution is a little more complicated than that, but same general morphology
Bart says:
January 18, 2012 at 1:56 pm
The alpha parameter is actually called “thermal diffusivity”, and it is inversely proportional to density. So, as the altitude increases, alpha will grow larger. So, even the Bessel function solution is not precise, and will only hold approximately in the lower atmosphere and before significant thermal expansion has taken place. A precise global solution would have to take all of these factors into account.
But, there is no chance of steady state because the steady state solution is T = B/r for a constant B, and since there is a gradient, there cannot be a steady state, and that creates a contradiction. So, the conclusion remains: there is always a thermal gradient pushing heat continuously into the atmosphere, and it will not stop until either there is some kind of radiative release, or the atmosphere flees.
Why the solution cannot be a constant, part I
Bart says:
January 19, 2012 at 1:52 pm
…Starting from some temperature at the base, in any finite time, the temperature is going to be less out farther than it is nearer, and it is going to go to zero at infinity. So, there must be a gradient over any finite time.
What is the form of that gradient? Well, through separation of variables, the temperature function is the product of a time varying part, and a spatial varying part. The spatial varying part is a function of spatial coordinates only, so it does not change with time. Therefore, since for any finite time, the spatial solution is of the form A + f(r), where A is a constant and f(r) is a monotonically decreasing function of r, and A must be zero at that time, then it must always be zero, and f(r) must go to zero as r approaches infinity.
QED.
Why the solution cannot be a constant, part II
Bart says:
January 19, 2012 at 8:14 pm
…So, if the “mode shape” of this thing is a constant independent of radius, that means the entire spherical shell has to heat uniformly. It starts at zero everywhere. It is at 1K everywhere at the same time. It is at 100K everywhere at the same time. This is physically impossible based solely on the fact that the rate of heat conductance is finite.

F. Ross
January 19, 2012 11:31 pm

Willis,
If I understand what you are asking in this post, here is my elevator speech. If I have misunderstod, my apologies.
Imagine a 10km perfectlyl insulated column of gas.
Outside the tube connect one end of a suitably sensitive, perfectly insulated thermocouple to the top and bottom of the tube.
1. If a continual current flow is detected from the thermocouple, then the temperatures at the top and bottom of the column are different and one has a perpetual motion machine. *
* Series-parallel enough of these structures and our energy problems are solved – until gravity runs out, anyway.
2. If, after a suitable period of time no current flow is detected then the top and bottom of the column are at the same temperature.
I’m betting on #2.

Kasuha
January 19, 2012 11:43 pm

I disagree with idea that the temperature on each layer is the same or that the energy per volume is the same, both are IMO wrong.
Let’s imagine an ideal gas container in gravitational field. In our gas particles don’t interact at all. As long as the gas is in equilibrium, each of its particles has the same total energy at every moment (but the important point is that total energy is sum of kinetic and potential energy). These particles travel on parabollic trajectory, bouncing off the bottom. This gives us overview of the energy distribution over the container volume – at the very top, the speed of particles is zero and the temperature is zero as well. At the very bottom the particle temperature is proportional to square of the height of the trajectory. The equilibrium condition is held too because on each horizontal layer boundary you get exactly the same number of particles traveling up and down at exactly the same speed.
This model I believe gives us very good idea about temperature, pressure and energy distribution over the container even for normal gases with interacting particles.
Another important thing is, your thermal perpetuum mobile cannot work in this temperature gradient as the medium you use in it follows the same rules the gas does. To raise your medium to the height where you intend to let it cool down you use more energy than you gain by letting it cool down there.
_______________
Now, I may be completely wrong somewhere in the above (transition from ideal non-interacting gas to normal interacting one feels to be the weakest point) so my main points are:
– potential energy is completely omitted in the article arguments
– the argument with thermal perpetuum mobile is invalid because the medium must follow the same rules the atmosphere does. If gravity created temperature gradient, it cannot be used by thermal engine.

Legatus
January 19, 2012 11:47 pm

One needs to ask, why is our air at different temperatures on earth at different altitudes? For one thing, we do not have an impervious membrane around us, and we have this thing called the sun shining at us. Result, the ground and especially water is heated or energized, and conducts heat to the lower air by direct contact, evaporation, etc. Result, the air at the bottom is warmer than air higher up. However, if you go very high, you reach ozone, which can and does absorb UV radiation, making it hot (and heating the non ozone around it) and causing it to expand way out into space. This will have some effect heating from the top down, although since this air is very thin the total amount of energy it can add to air lower down isn’t much. There is also some heating caused by the various GHG’s (especially water vapor) being heated by radiation and heating the air around them. Conclusion, there are reasons why our air is at different temperatures at different altitudes and it has nothing to do with any gravito thermal effect.
Second, if earth were as described, with an energy impervious barrier around it (and it had no fissionables), it would be at absolute zero. Even if gravito thermal worked, any air that contacted the earth would contact a very cold surface. The much more dense earth would quickly absorb all the heat from the air, which would freeze out rapidly, goodby gravito thermal effect.
However, let us assume, for arguments sake, that the surface of the earth and the air start out at the same temperatures as our surface and air. If gravito thermal works, and the people make huge heat engines, they will have to produce a lot of energy to make up for the fact that the cold ground will absorb and keep on absorbing the energy. They could, I suppose, surround the entire earth with an insulating material to slow this heat loss. If they did, they could be comfortable assuming the heat engines can create enough heat and light for them and to make up for the slight loss to ground. An impervious insulator below them would result in the energy and heat from their engine building up rapidly in the space between the insulator above and below them, which would continue until it melted the engines and stopped their operation. A not quite perfect insulator below them could keep them comfortable until the ground below the insulator had warmed up all the way through, at which point the people would find it slowly getting warmer, continuing until once again it gets warm enough that the heat engines melt and no more heat is, apparently, being produced from nothing.
Third, let us assume that the earth, as ours does, has fissionables in it’s core, and that is why the surface is warm. However, since there is a barrier to energy above them, this heat will slowly build up, since it cannot escape, until all the fissionables are used up. If it has a lot of them, as our earth seems to, it will get very hot before that happens, and once all the fissionables are gone, it will stay at that hot uniform temperature forever. However, lets us say, for arguments sake, that the last fissionables are used up just as it reaches a nice comfortable temperature (one where air does not freeze out). Now let us say that the people there, somehow, in the dark, invent heat engines to take advantage of this gravito thermal effect to make light and power. This will slowly add heat to the earth (the solid planet will absorb most of it) and very slowly heat things up. Eventually, it will get too hot, all the people will die, the engines will stop, and it will stay at this new, somehow elevated temperature forever. If you could somehow create indestructible heat engines that never melted and didn’t need tending, the heat would slowly build up forever, eventually the inside of the membrane would be hotter than any sun (which, I suppose, since it melted the earth, would stop the gravito thermal effect). As we can see, even under ideal starting conditions, if we assume that this membrane surrounds the earth, and we assume ideal starting temperatures for gravito thermal to work, it always results in energy being created from nothing, and the space inside the membrane getting hotter and hotter.
I think all this shows that under any circumstance we start with, even absolutely ideal (and impossible) starting conditions, gravito thermal results in an impossible outcome, with energy inside the membrane building up from nowhere. It should also be noted that the whole thought experiment is ridiculous anyway, such and energy impervious barrier cannot exist in our universe with it’s laws anyway. Thus we see that the only way gravito thermal can work is in a universe that is entirely imaginary, and has different natural laws that ours does. In other words, the authors of this idea are living in a world all their own, literally. They would realize that if they thought through all the implications of all this, as I have above.

wayne Job
January 20, 2012 12:06 am

Let us forget gases for a moment and consider golf ball size particles made from lead, as our atmosphere, closely packed near the surface and twenty miles above loosely packed.
The potential energy of the balls at twenty miles up is huge. Consider these as cold molecules falling under gravity and impacting other molecules. Other molecules heated by conduction from the Earth by the sun are rising to meet them, and meet them they do head on. Thus slowing the transfer of Sol’s heat, graciously given to the world back into space. This is the major part of the misnamed green house effect. The rest of the green house nonsense can be explained by compression of the atmosphere close to the surface, where the molecules are elbowing for room.
The modulation to all this is water in it’s various phases, that gives us a livable planet, chaotic as it is.

joshua Corning
January 20, 2012 12:08 am

For such machines to work, they’d have to create energy, and energy cannot be either created or destroyed, only transformed.
So the earth can’t orbit around the sun because that would break the laws of thermodynamics?
I hate to break it to you Willis but you have gone off the deep end.
The reason that gasses in an atmosphere are of higher temperature then if they were floating around in a vacuum are the same reasons why the earth can continue to orbit the sun without constantly being pushed.
i will restate my thought experiment again.
Imagine gas floating around in a cloud in the vacuum of space. it is spread out and the interactions between the atoms in the cloud are sparse…now imagine that cloud being pulled down a gravity well of a planet. the gas gains no energy yet it is now under pressure….now the atoms are all close together and colliding and doing what atoms do when they are forced to be in close proximity to one another. Again the atoms energy has not changed. yet their temperature is higher.
see how that works?
And it can be proven. Take the temperature of any old room….now compress air from that room into a container…now measure the temperature of the compressed air in that container…..guess what the air inside the container is hotter then the air in the room.
now i know what you are going to say “you used energy to compress that air” you are correct i did…but when atoms are compressed by gravity as in an atmosphere then no energy is used to compress it.
anyway i just thought of how this can balance thermodynamics….think of school teacher holding a ball in the air then he drops it. the teacher then says the ball while he held it had potential energy and when he released it it had kinetic energy. Think of the gas floating around in space as potential energy and when they are pulled down a gravity well of a planet as kinetic energy….you see they had that potential energy from when the universe was created and now that they are compressed by the planet’s gravity they have kinetic energy.
I really cannot explain it simpler then this…..if you cannot grasp it i have to suspect it is from willful ignorance.

joshua Corning
January 20, 2012 12:22 am

“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.”
Note that the atoms at the top have the highest energy and the lower ones the lowest.
The reason the temperatures are reversed is simply because at the top of the column you have less atoms hitting the side of your thermometer then you do at the bottom.
I think part of the problem is that although you understand that hot air moves to cold air i think you either are forgetting or don’t understand why atoms do that.

Editor
January 20, 2012 12:30 am

Willis replied to Ferds comment;
‘Temperatures have leveled. Sea levels have stabilized. CO2 has not. These events contradict GHG theory predictions, which in science is a strong indication the GHG theory is wrong.’
By remarking;
‘Thanks, ferd. I come to a very different conclusion from the same facts. I say that the greenhouse effect has done the heavy lifting of bringing us to our warm current temperature….’
Temperatures have been slightly higher than today and sea levels also higher on several ocassions during the last 5000 years. Self evidently that wasn’t due to raised co2 levels (according to the stated records)
What did the ‘heavy lifting on those occasions? Natural variability? if so couldn’t that be the cause again today?
tonyb

January 20, 2012 12:30 am

Willis Eschenbach says: January 19, 2012 at 11:52 pm
“I don’t see why you say Dr. Brown is wrong.”

In the quote that I cited, it explicitly says that motion of the air equalizes temperature. And it doesn’t, for the reasons that I gave.
But I was more concerned to say what it does do. It provides the heat pump which counters conduction and radiative transfer down the gradient.
And still air is impossible. You need a heat source to prevent liquefaction (from radiative loss), and that in practice will create temperature differences and motion, which in turn pushes toward the adiabatic lapse rate.

alex
January 20, 2012 12:31 am

What the guys makea big tohuwabohu out of a very simple problem?
What is all this poetic story about?
Willi, it’s trivial as a nutshell.
1. There is a big difference between a tall air “container” and an atmosphere: the atmosphere is MIXING (troposphere = mixing sphere), your “tall container” is not.
2. If there is mxing, the only equilibium is very simple: ds/dz=0, where s is the entropy density. You have the thermal source at the bottom – the Earth surface heated by the Sun, and the thermal sink at the top – radiation to the space by the GHGs or clouds. In between you automatically get ds/dz=0. This is the adiabate that gives you the temperature lapse.
3. In your non-mixing “tall container”, there is no energy sink at the top. Thus, the temperature is constant. T=const. Very simple.
4. The temperature at the Earth’s surface is NOT defined by the GHG concentration, if the GHGs screen the Earth’s IR radiation completely. In this case, you must calculate the energy balance AT THE RADIATING SURFACE that is special for every wavelength: it is the altitude, where the atmosphere becomes transparent for the radiation. In this way you obtain the temperature up there.
5. Now you start your adiabate from this radiation surface at the top of the troposphere (the energy sink) and go down to the planet surface. Here you use the adiabate with its temperature lapse rate. The higher the atmospheric pressure at the bottom, the higher the temperature. Has nothing to do with “perpetuum mobile”.
6. For the reason discused above, Venus is hot as a hell due to the high atmospheric pressure (NOT GHG “concentration”), Mars with its low atmospheric pressure (although 20x more CO2 than the Earth!) is freesing and we have the comfortable climate.
Alex.
5.

January 20, 2012 12:36 am

Thomas L said:

Nice try. Before you rotate the cylinder, the air at the top of the cylinder has lower pressure than the air at the bottom of the cylinder, and therefore the density at the top is less than the density at the bottom. So when you turn the cylinder over, you are doing work, as moving the bottom up takes more energy in a gravity field than you get from moving the top down.

But that’s also true if the air was already at the adiabatic lapse rate. In that case, when I flip the cylinder, the end state will be exactly the same as the initial state, so no net work was performed. I lift the air, I lower the air. I do work lifting, then have work done to me as I set it down. I do work tilting the cylinder 90 degrees, then have work done to me as I resist the further rotation as the dense air pours to the other end to try and complete the flip. It’s the same as pendular motion.
Back to Willis’s original thought experiment (and perhaps its key point) I’m not sure you can pull work out of the adiabatic atmosphere with a thermocouple, as I’m not sure anyone has dug that deeply into heat transfer in a solid in a gravitational field. For example, the thermocouple has to conduct the energy (as heat) along its length. If we pick the best standard material for heat conduction, silver, and work at the Earth’s adiabatic lapse rate of about 2 degrees C per thousand feet, we can only conduct about 2.4 Watts per square meter of silver conductor, even horizontally. Such low levels of heat transfer over such vertical distances might require the inclusion of effects that are irrelevant in most applications. putting us below the round-off error in the equations that work acceptably well in other applications. I’m pretty sure nobody has tried to use 2 degrees C to move only 2.4 watts upward through a silver or copper slab a thousand feet tall and a square meter in cross section, which is the same as using 160,000 tons of silver, the weight of almost four Iowa class battleships, to cool a 200 Watt CPU by just 2 degrees.
We could sidestep the question by positing that solid masses are allowed to reach thermal equilibrium at the top and bottom of the atmosphere, then are insulated and moved into contact with the thermocouple. I don’t know if this would raise questions about KE and PE of the solid bodies, though, or whether moving them that distance without losses would itself be a perpetual motion machine.

Colonial
January 20, 2012 12:43 am

Joe Born (January 19, 2012 at 5:42 pm) wrote:
[If the] … Velasco et al. paper is correct, its Equation 8, a result of statistical mechanics, dictates that average kinetic energy decreases with height even at equilibrium.
I’m not an atmospheric scientist, just an electrical engineer who had a single thermodynamics class 40+ years ago, but the comment above matches my reservations. Let’s postulate a sealed container filled with a perfect gas (defined as an ideal gas which additionally is completely transparent to radiation), similar to that proposed by Willis. The container begins at ground level, where the pressure is 1,000 millibars, and extends to the altitude at which the pressure would be 500 millibars if the gas were isothermal. Let’s grab a small amount of gas at ground level and raise it (without disturbing any other molecules) to the top. When we do that, we add potential energy of position to the gas molecules that rode the elevator to the top.
Where did that energy come from? Unless there’s another source of energy that can be tapped (a violation of the assumed equilibrium conditions in our sealed container), the energy has to come from the kinetic energy of the molecules that were raised from bottom to top. If it comes from anywhere else, we’ve added extra energy to the molecules that were raised that can then be used to perform work, creating yet another perpetual motion machine!
If we take the sealed container postulated above and evacuate it until there’s only a single gas molecule left, it’s clearly true that the total energy of that lonely gas molecule is the sum of its potential energy of position and its kinetic energy. When the molecule is at ground level, it will have the highest possible kinetic energy (implying a higher temperature), and zero potential energy of position. If it travels straight upward until it reaches the top of the sealed container, it will have the highest possible potential energy of position for that system, and correspondingly lower kinetic energy (implying a lower temperature).
When the sealed container has the normal complement of perfect gas within it, the mean free path of any given gas molecule will be very short (Wikipedia says 68 nanometers for air at 1013 millibars). However, between collisions, the vertical component of each molecule’s velocity will be affected by gravity, just as in the case where only a single molecule is present. If the vertical component is upward, it will trade kinetic energy for energy of position, cooling slightly in the process. If the vertical component is downward, it will trade energy of position for kinetic energy, warming slightly in the process.
So, the heresy, spoken aloud: A perfect gas within a sealed container will exhibit a temperature gradient in a gravitational field. This is not, however, a substrate for a perpetual motion machine. The total energy (kinetic plus potential energy of position) of each molecule is the same. Any attempt to extract energy from the difference in temperature between the top and bottom will founder on the reality that entropy has already been maximized for the gas within the sealed container. There’s nothing left to get.
You’ll note that at the beginning, I specified that the sealed container had a pressure of 1,000 millibars at the bottom and 500 millibars at the top. It’s been too many years since I took physics to allow me to easily perform the calculations, but someone who performs such calculations regularly should be able to calculate the energy required to raise a molecule from the bottom to the top, subtract it from the assumed kinetic energy of a molecule at 1000 millibars, and determine the remaining kinetic energy for that molecule. This would allow calculation of the actual pressure at the top (nominally 500 millibars), and the temperature gradient that would exist in the sealed container because of gravity.

Neil
January 20, 2012 12:46 am

I have never seen so much ignorance in one blog
Does no one understand the dry adiabat for the atmosphere on Earth (DALR=9 degrees per Km)?
This is entirely controlled by gravity and by the mass of the atmosphere– nothing else.
(hence it varies for other planets)
It applys to the larger atmosphere in exactly the same way it it does in an insulated cylinder of dry air
Does no one here understand the TePhigram which plots equal lines of equal entropy against air pressure (altitude)?
Why not take 5 minutes and get out of this ignorance
Neil

Bryan
January 20, 2012 1:03 am

Tim Folkerts says
“The simplest and most convincing argument ended up being your same perpetual motion approach. You could run an insulated copper bar from bottom to top. This bar does not have the lapse rate effect. (Or use another gas that would have a different lapse rate because it has a different heat capacity). The copper should have the same temperature at top and bottom. If the gas had a different temperature, would could use this temperature difference to continually run the sort of heat engine you suggested.”
Tim go one stage further and source any real heat engine connected by real copper connections of one kilometer in length for a 9.8K temperature difference.
Factor in the resistance of the copper.
Who’s to say that one kilometer of copper will not have its own gravitational/thermal effect with its own value?
Indeed perhaps all this is in accordance with the second law
Maybe you can now see why an experiment to settle the isothermal/adiabatic distribution has never been attempted.
Its interesting that Claudius (who supported the isothermal conjecture) dropped the second law proof later on in life

jorgekafkazar
January 20, 2012 1:03 am

Willis: Sorry to have confused you. WordPress doesn’t allow the use of symbolic logic symbols here. I thought you’d immediately see the problem. In essence, you state:
1. “If [the isolated system is in its lowest energy state]{B} THEN [it cannot perform work]{not W}”
2. “If [the isolated system…is warm at the bottom and cold at the top]{D} THEN [it can perform work]{W}”
3. “[The isolated system cannot perform work]”{not W}
4. “therefore [the isothermal state…is the lower of the two energy states,]{J}”
Simplified even more, your argument boils down to:
1, if B THEN not W
2. if D THEN W
3. not W,
4. therefore J
But what you’ve proved, so far, is simply “not D.” (I can think of another state which can’t perform work.) For the argument to be valid, you must establish
1a. if not D THEN B, as well as
1b. if B THEN J, and so forth, 2., 3., 4., as you state.
Sorry for the confusion. I looked for the symbols for quite a while before giving up.

joshua Corning
January 20, 2012 1:04 am

“The Jelbring thought experiment concerns a closed system, with no energy going either in or out. I don’t recall saying the earth could not orbit the sun, you’ll have to cite that. In any case, that’s an open system.”
Atoms of high energy will be able to climb higher against gravity in the column then atoms of low energy. Energy is not going in and out but atoms still run into one another within the system right? and at any given time some atoms will whack into each other harder, simply by virtue of angle and velocity, then other atoms right?
If low energy atoms can only be at the bottom and high energy atoms can be anywhere in the column simple addition should tell you there will be more atoms at the bottom then on the top.
If there are more atoms on the bottom then the likelihood of those atoms (even though on average they are of a lower energy then the top) hitting your thermometer at the bottom then there is of them hitting the thermometer at the top. ie the temperature will be higher on the bottom then on the top.
You are confusing temperature with heat.

Robert L
January 20, 2012 1:04 am

Hi Willis,
I think the thermocouple analogy is broken. In order to extract energy from a thermocouple, it is true there has to be a temperature difference, but there has to be heat to operate the thermocouple pair. The top thermo has no ‘sink’ and as a result would simply get warm by conduction, from the lower thermocouple.
It your hypothetical isolated planet the atmosphere would become Isothermic. My reading of N&Z is that an input of energy is required to maintain the gradient. The mechanism is unclear, however ignoring KE, PE and convection is as foolish as expecting gravity to do all the work (pun intended)
Cheers
Robert

Bryan
January 20, 2012 1:07 am

Willis says
“To the contrary. Thermal equilibrium simply means that the objects have stopped exchanging energy because they are at the same temperature. This happens all the time.”
No at equilibrium they exchange equal quantities of energy

joshua Corning
January 20, 2012 1:15 am

“But you cannot get continuous work out of that. ”
yes you can. An object in motion will to stay in motion. Atoms don’t stop…they don’t have wind resistance, they don’t get tired, they just keep going and going and going, and as you stated no energy comes in and no energy goes out. So those atoms cannot transfer energy out…ever. they will bounce around in your column until the end of the universe and they will segregate out into a pressure gradient simply by virtue of the fact that at any given time some atoms will have low energy and some will have high energy…the low energy atoms stay close to the bottom while higher energy ones will be everywhere….thus you get high pressure at the bottom and low pressure near the top….a thermometer will measure this gravity induced pressure gradient as hot below and cold on top simply because more atoms will hit the thermometer on the bottom then will hit it on top.

tallbloke
January 20, 2012 1:28 am

Willis,
Firstly, thank you for the courtesy of your response. It is encouraging that we are able to set aside non-scientific issues that hang between us and conduct scientific debate rationally and reasonably.
Some preamble, and then some science.
You said to Lucy that
“time is what you don’t have. The clock is running, the elevator speech for N&Z is way overdue.”
Nobody is king of the clocks. Lucy and I are not sales people with obligations to meet targets within timeframes or elevators. Paradigms don’t change overnight. Resistance to the theory of plate tectonics continued for as long as the old guard were in tenure at their institutions. Time must be spent in evaluating new theories properly, not concertina’d into a gish gallop of instant rebuttal and ‘counterproof’.
A more relevant example than plate tectonics is the Loschmidt vs Maxwell and Boltzmann debate regarding thermal gradients matching the theoretical dry adiabatic lapse rate in equilibrium atmospheres subject to a gravitational field. It’s been going on for over a hundred years without resolution and we don’t need to force a conclusion within the next few days just because it has been thrust to the centre of the stage at the moment.
OK thanks for reading that, lets address some science.
Willis Eschenbach says:
January 19, 2012 at 6:26 pm
If an energetically isolated system is in its lowest energy state, it cannot perform work.

Agreed
If the isolated atmosphere in Jelbring’s thought experiment is warm at the bottom and cold at the top, I can stick a thermocouple into it and use the temperature differential to generate electricity to perform work.
Excellent, a proposed experiment. Let us know the result. I think you’ll find that even as a thought experiment it doesn’t work out though. Peter Berenyi emailed me that argument and I sent him my disproof. He hasn’t got back to me in the two days since. I’ll post it in a separate comment if you are interested in defining your setup.
As Tallbloke points out, the second law says an isolated system can only move towards a lower energy state. That means Jelbring’s thought experiment must inexorably move towards the isothermal condition as its equilibrium state.
No, as we’ve been saying all along, as have other people on this thread, at the lowest energy state, molecules at the top of the atmosphere have the same total energy as those at the bottom, but less of the total is available as kinetic energy which manifests as heat via collisions because more of the total energy is locked up as gravitational potential energy.
Since Jelbring claims an adiabatic state will obtain at equilibrium, his hypothesis is falsified.
If my statement above is correct, or if the equivalent macroscopic arguments provided on this thread and by Jelbrings 2003 paper are correct, then this statement is false.
Willis Eschenbach says:
January 19, 2012 at 9:21 pm
Jeremy says:
Gravity has NO AFFECT ON TEMPERATURE.
How many times must it be said.
You people are reading science fiction.
You have to do WORK to create a change in temperature – this is basic thermodynamics!!!!
If an object falls in a gravitational field then potential energy will be converted to kinetic energy which will create heat. However a stable column of air in equilibrium does not create any energy or heat.
Thanks, Jeremy. You are a hundred percent correct, gravity can’t do ongoing work to change the temperature

Jeremy and you are 100% wrong. Work is done by energy. Gravity is not a type of energy, it is a force. It cannot and does not need to “do ongoing work”. Nor is a change in temperature under discussion. Gravity, via the pressure profile it induces in an atmosphere, and considering the compressibility of the medium, causes the denser per unit area of the atmosphere near the surface to be warmer than it is at higher altitudes. g/Cp
If you are fighting basic ignorance of science, you will be deluged with ignorant people. Not much I can do but just keep putting the facts out there.
Certainly there are a host of much more sophisticated threads, and those tend to attract a more scientifically literate commenter. But when you are discussing “gravito-thermal” theories …

This is an ad hominem attack which has no place in scientific discourse.

markus
January 20, 2012 1:28 am

“joshua Corning says:
January 20, 2012 at 12:08 am
but when atoms are compressed by gravity as in an atmosphere then no energy is used to compress it”.
Probably be better to say, “then no energy is used to compress it, other than the potential energy of its mass.”
IR is (forced) employed into potential energy viz conduction of paired electrons around a molecules covalent bond, heating its chemicals, and adding kinetic energy to its energy budget
.
The adding of kinetic energy to mass causes heat, because of the collisions and transfer of the Atmospherically Thermally Enhanced kinetic energy that has been temporarily employed by the energy of mass.This heat is enhanced at higher pressures.
The energy budget of atmospheric trace chemicals should equal the square of its mass plus its employed kinetic energy.
And all the UW IR, DW IR, IR from enhanced mass, are just mixing gases in a pot up to re-radiation when kinetic energy of mass returns the employed energy to space
I have confidence in the N&K equation describing this phenomenon.
..

Michelangelo
January 20, 2012 1:28 am

Fascinating stuff in all these comments ..As a reader I especially liked the ones posted by ed_b , Ian H and I found the intriguing question why there are no PV-cells exploiting the energy supposedly radiated from the GHG:s during night by Richard Vernay very reveiling.

Bryan
January 20, 2012 1:33 am

Nick Stokes say
“When the lapse rate is below the dry adiabat (toward isothermal) it is referred to as convectively stable. Above the adiabat, it is unstable. At the adiabat, it is neutrally stable. ”
At the adiabat the parcel of air has no unbalanced force.
It can move up or down at constant speed or stay stationary.
This condition is called the neutral atmosphere and it can be surprisingly stable at night.
In dry conditions the gradient will be – 9.8K/km.
So its not correct to say that in OUR troposphere, the air will become isothermal if still.

Hoser
January 20, 2012 1:37 am

That’s an awful lot of talking people. So? What did you come up with?
Let’s try this again.
1) Sun heats surface. Some heat goes into land and sea, below the surface.
2) If an atmosphere is present, hotter areas are cooled and the heat is transported elsewhere and not radiated away as quickly.
3) After the sun goes down, the latent heat begins to radiate away. However a lot of energy remains below the surface and takes time to reach the surface.
4) If not all of the energy absorbed during the day is radiated away, then the surface will start off warmer the next day.
5) The average surface temperature continues to rise until the surface is able to radiate in 24 hours the same energy it absorbs during the day.
At least on land, the key difference between the Earth and the Moon is the atmosphere. On Earth the hot surface is cooled by air and therefore is unable to radiate as efficiently (because it was cooled). Cooler (shaded) areas are warmed by the heat transferred to the air by conduction from the warmer locations. On the Moon, shadowed areas radiate to 3K and are very cold. The Sun can heat surface rocks and these will get hotter until they are able to radiate efficiently the same amount of energy they absorb. No heat is transfered from one location to other places on the Moon. It should be no surprise the Moon’s surface cools rapidly after sunset. Although water is interesting, it seems not the driving factor given the data from planets and moons we saw a few weeks ago.

January 20, 2012 1:51 am

A recent BBC TV programme on the Earth’s core featured a claim by some scientist that the strength of the planet’s magnetic field has been falling significantly for the past 170 years. If true, might this tie in with the Svensmark hypothesis that changes in cosmic rays hitting the atmosphere affect cloud cover? Might one of WUWT’s resident brainboxes look into this and see if it has legs?

January 20, 2012 2:05 am

Same answer as I gave early in the “Matter of Gravity” post on January 14, 2012 at 2:45 am

John Marshall
January 20, 2012 2:13 am

Your argument about a heat engine using heat difference not working has been countered by the Norwegians who had a power station off coast in the Atlantic using the heat difference between water layers. It produced 60Mw, until the first severe winter storm when it sunk without trace.
The gravitic heat is better called adiabatic heat by compression which does exist and is the principle used by many machines used daily by everybody. It would happen in a planetary atmosphere because that is open to space and has free movement to all sides. there would be vertical movement due to convection and atmospheric pumping between day and night sides due to temperature difference/heat loss rates. Also your column, despite being at the same temperature, would not have the same heat content at the top compared to the bottom because gravity would introduce a density differential, A Km high enclosed column of air does NOT represent an atmospheric column by any stretch of the imagination.
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.

Birdieshooter
January 20, 2012 2:30 am

My reply to all the questions raised above on both sides is WWES…….What Would Einstein Say? I would genuinely like to know. I wonder if he would have enjoyed these blogs. Anyone channel him lately?

gbaikie
January 20, 2012 2:57 am

“George Turner says:
January 19, 2012 at 9:20 pm
I have a follow-up thought experiment to my previous comment.
If flipping the air column upside down doesn’t require an input of work and returns the column to the dry adiabatic lapse rate, then the dry adiabatic lapse rate must be the column’s thermal equilibrium because a system cannot be shifted from thermal equilibrium without an input of work.”
I am sure what would happen. It seems you going heat the top when reaches bottom- and that heat isn’t going to get back to the new top.
Let’s move to orbit, where you could spin it [forever], and you have gravity gradient- the length column will make lower part travel slower than upper part. You will have gravity- gravity gradient in “free fall”.
Of course spinning will also add artificial gravity.
As I said you will heat the lower end- and therefore cool the gas.
So how a way to cool gas.
Now, let’s insulate it somehow.
Hmm. Use water instead of gas.
So without spinning water will cover entire inside [water tension] and will end up at lower end, mostly. Start slow rotation, and water will run to to middle then new bottom.
It seems that will affect the orbit somehow:).
But question is whether cools.
It doesn’t seem to. Back to air.
A new question is how fast would air move.
It’s going to fall, so it’s going to move fairly fast.
So back to surface again [or be some orbit and have respectable amount gravity gradient-big column]
The vacuum end when rotates to ground will “suck” the heavier air
and heavier air will fall- and this is going to be violent- as in supersonic.
So, there will be good mixing of the air- because the hot air going go straight up,
or break your machine.
You going to cause the air to become more directed.
It seems is you made air more balance in it’s direction- every molecule stopped another other molecule you get colder temperature.
But seems that if you start with cold air you could get hot air- and the more vacuum the better:).
One problem is normal atmospheric air isn’t balanced in terms of weight- the bottom is a lot heavier than the top.
So work is being done by rotating it.
So question is how small can make this thing and have do something. 1 km long seems challenging. But if used colder air and have vacuum at top, it seems something smaller is possible.
If it was 5 km in length falling velocity is somewhere around 500 mph, which somewhat interesting- but smaller are going make a little bit of wind. So entire atmosphere excitement, and 5 km maybe somewhat interesting, but probably something even bigger in space environment and using gravity gradient- might actually do something useful..

David L
January 20, 2012 2:57 am

Your first thought experiment sounded like Mawells Demon in which a gas can be partitioned into a hot side and a cold side by a force (a demon) that only allows high kinetic energy molecules to move in one direction and excluded the slow ones. In this case gravity is the demon.

Bill Hunter
January 20, 2012 3:08 am

I still don’t like your “perpetuum mobile” argument and a claim it violates the law of conservation.
I am not a physicist, but instead a logician. As I understand it physics claims energy cannot be destroyed. Thus it cannot be used up just converted and lost.
Jelbrings model according to my reading encapsulates energy and does not allow any to exit the atmosphere. So while you talk about light forever, if that energy is manifested as light and its always light where does it go when it cannot go anywhere?
Logically it seems to me the only issue is whether the atmosphere would be isothermal or not.
If isothermal then Jelbring is wrong and gravity does not cause the lapse rate and if the lapse rate exists at internal equilibrium he is most likely right.
I tend to think, but could be wrong, that for molecules under less pressure with the same temperature need to contain more energy.
So the question is what equilibrium is, is it energy or is it temperature. Personally I like the basal concept that its energy and not temperature but I have not wrapped my mind, or perhaps warped it, with Caballero.

A physicist
January 20, 2012 3:11 am

There are some terrific quotes by Richard Feynman in his Nobel Lecture The Development of the Space-Time View of Quantum Electrodynamics, that bear on these issues of thermodynamics:

We are struck by the very large number of different physical viewpoints and widely different mathematical formulations that are all equivalent to one another. The method used here, of reasoning in physical terms, therefore, appears to be extremely inefficient.
It always seems odd to me that the fundamental laws of physics, when discovered, can appear in so many different forms that are not apparently identical at first, but, with a little mathematical fiddling you can show the relationship. … There is always another way to say the same thing that doesn’t look at all like the way you said it before.

What we teach our engineering students is that you don’t really understand a phenomenon until (1) you can analyze it in more than one framework (formalism), and (2) within each framework, you can present it as an picture, an equation, and a numerical computation, and (3) you are able to unite all these frameworks within an encompassing narrative, that dovetails with other folks’ time-tested narratives.
With regard to thermodynamics and transport theory (which is broadly what this WUWT topic is about), an historically recent and very broadly applicable framework regards thermodynamics and transport theory as (essentially) the study of the geometry of flow on manifolds, specifically the study of Hamiltonian dynamical flows on manifolds that are equipped with a symplectic structure.
One great virtue of the symplectic approach to thermodynamics and transport is that it naturally encompasses both classical and quantum dynamics. A pretty significant downside, though, is that it takes a full year to learn the basic ideas and notations of differential geometry, in terms of which the whole framework is given.
What the resulting geometric dynamical frameworks predicts, though, is simple. If we computationally model the atmosphere (by a brute-force numerical calculation of molecular dynamics) as a cloud of particles in a gravitational potential, such that the particles bounce off each other elastically (with each collision conserving both energy and the number of particles), and the distance between collisions is small compared to the height of the atmosphere, and we do not “stir” the atmosphere with radiation heating at the bottom (or allow any other external influence to do work on the particles), then we will find (from the brute-force numerical codes) that the kinetic temperature of the particles is constant from top-to-bottom (note: the Wikipedia page the kinetic theory of gases has a picture of this kind of simulation, which are described in-depth in the well-respected textbook by Frenkel and Smit, titled Understanding Molecular Simulation: from Algorithms to Applications).
The dynamical geometer will argue as follows:

“We don’t even have to write that brute-force numerical code! Because we know in advance what the answer will be, by the following reasoning: if we consider the atmosphere as a stack of thin layers, and we allow each layer to exchange both energy and mass with the layers above and below it, and we remember to offset each layer’s chemical potential (the thermodynamic potential associated to mass exchange with adjacent layers) by that layer’s gravitational potential, then we appreciate that any atmosphere so modeled necessarily will evolve to an isothermal equilibrium, without regard for the details of the particle interactions.”

Summary: The folks here on WUWT who conceive that the gravitational potential gradient of the earth’s atmosphere has to induce some kind of thermodynamic gradient are 100% correct—but that thermodynamic gradient is a gradient of pressure (or equivalently, of chemical potential), not of temperature.
If these ideas sound kind of complicated and subtle … well, they are! Mistakes are very easy to make, and that is why it is prudent to evolve multiple independent explanations (pictures, analysis, numerics) as a cross-check on any given calculation.

Bill Hunter
January 20, 2012 3:24 am

A final thought when you have an equilibrium you need energy to change it. Thus our Stygian friends cannot tap into the equilibrium and generate light, they need energy to throw it out of equilibrium or if that energy is manifested as light to change the lighting arrangement concentrate it, focus it, or do any work with it.

January 20, 2012 3:39 am

re perpetual motion machines, we can say that there is ‘perpetual’ motion in our universe, such as orbits, bigband expansions and the like. how many motions are we undergoing at the moment ? 5 ?
If it’s energy for work you are seeking, then the best perpetual producer of energy on our planet might be it’s magnetic field. the findings of Nikola Tesla are to be considered. wiki has a reasonable summary. I am led to believe that I can access the electrical differential between 2 points separated by height, enough for a domestic supply.
my view is that there is much to be said for domestic solutions to energy requirements, passive solutions in the main.
getting back to the flow of energy, matter, temperature and gas atmospheres, bottled and otherwise.
heat is associated with increased molecular activity, ditto for pressure and molecular activity. we have bonding processes, chemical aggregations, there’s an evolution of structure. certainly our systems are extremely dynamic (large energy packages) with a myriad of structures – guess a number.
entropy – the eventual breakdown of structure and atoms. our little atom no longer has the energy to maintain it’s structure. pop ! it stops, electrons touch protons and neutrons, probably losing their shape. the molecular structure loses it’s space, and the volume of the matter reduces by a massive amount. in our astronomy class we would marvel at how a battleship could fit into a matchbox if you removed the space between the atoms. so we can ‘witness’ the reduction of volume at the earth’s core, I don’t know the pressure or gravitational measurements at that place, nor electrical discharge. obviously the process depletes the fuel source and imploding occurs. so we are supported from below as well as from above.
I do believe in using a multivariable approach to solving problems, rather than isolating certain variables.
I think we can generally expect more of the same; cosmic rays, sun bursts, volcanic eruptions, convection currents, and the odd meteorite.
cheers !

Bomber_the_Cat
January 20, 2012 3:40 am

anna v says:
January 19, 2012 at 10:36 pm
“Could one do the experiment using water as the fluid?”
Yes, you could, but there is no need. We already have some; they are called oceans and lakes. The water at the bottom of the ocean is under great pressure. Dos this make it warmer? No, we all know that warm water rises. The hotter water is at the top. You can verify that in your bathtub. So pressure does not cause warming. QED.
So what is the difference between water and the atmosphere? We all know that warm air rises too, just like warm water rises. But in the atmosphere the cold temperatures are at the top ( up to the tropopause). So what is different? I could indicate this in one word! – but it is best left as an exercise to the reader. Some individual thought will promote a more general understanding.

January 20, 2012 3:43 am

What Bart said.

Joe Born
January 20, 2012 3:46 am

As others have observed above, Willis’s argument has a then-a-miracle-occurs step: he postulates a heat engine that is free of the gravity to which the gas column is subjected. He skipped the the step where Harry Potter removes the gravity from the heat engine’s location.
The mean single-molecule kinetic energy in a system of the type Willis describes is (3E/(5N-2))(1-mgz/E), where N is the number of molecules, E is total system energy, m is molecular mass, g is the acceleration of gravity, and z is altitude. If you put numbers to it, you see that the lapse rate is exceedingly small but non-zero.

DirkH
January 20, 2012 3:54 am

Imagine Willis’ container to be finite, and filled with air with a pressure of 1 bar, and being in his isothermal condition, with constant pressure and temperature throughout, as required by the Ideal Gas law. Now consider a second container on topo of it, with infinitesimal height, with vacuum inside. Now we remove the lid that separates these two containers. Brownian motion will make gas molecules dissipate into the vauum but the gravitational field pulls them back; and a pressure gradient develops, and with it, according to the Ideal Gas law, a temperature gradient.
And that is the stable configuration, not the isothermal one. What we end up with is the dry lapse rate, assuming that we have no radiative energy redistribution.
The notion that in equilibrium, there must be the same density of kinetic and potential energy in every partial volume must be false, because it would require infinite temperatures at the top end of the gas column.

Joe Born
January 20, 2012 3:59 am

I failed to mention that the formula I gave above applies to monatomic gases.The factor on the right is different for gases with higher degrees of freedom, but the overall expression remains dependent on altitude.

January 20, 2012 4:08 am

Another never ending debate is seems. How about escape velocity?
The atmosphere of a planet cannot be completely isothermal since the velocity i.e. energy of the uppermost molecules at some point would exceed escape velocity. Venus and Earth both have roughly the same mass so they would have the same escape velocity. If Venus is a perfect greenhouse effect, since its black body temperature is 184K (65Wm-2) or -89C, the Earth would have the same constraints, -89C, Anyone noticed the minimum temperature of the Antarctic lately?
Gravity places limits on atmospheric energy, if gravity fluctuates it would change those limits. Earth’s gravity doesn’t fluctuate enough to have a significant impact on temperature at the surface. If someone would like to show that Earth’s escape velocity changes enough to have an impact on surface temperature, I would love to see it.
Since mass is energy, Gravity and the Geomagnetic field both help retain atmospheric mass, perhaps a mass balance would be an interesting exercise?

Johan i Kanada
January 20, 2012 4:09 am

This argument should be possible to resolve in 5 min by any reputable physics professor.
So why not invite one (or several) to comment/clarify?

January 20, 2012 4:19 am

In 2010 I had a discussion about Hans Jelbrings theory with John Wallace, atmospheric scientist at the university of Washington. He wrote me:
“To understand how radiative transfer influences surface temperature, one needs to go beyond the concept of the adiabatic lapse rate and consider an atmosphere in “radiative-convective equilibrium, as discussed on p. 421-422 of the 2nd edition of our textbook. In such an idealized 2-layer atmosphere, the lower layer, which is comparable in depth to the troposphere, has a lapse rate equal to the adiabatic lapse rate . Two points emerge from this simple analysis:
(1) Were there is no greenhouse effect, the lapse rate in a planetary atmosphere would be isothermal (i.e., temperature would not change with height. In this case, the dry adiabatic lapse rate would be unchanged from its present value, but it would be completely irrelevant to the interpretation of the observed lapse rate.
(2) Greenhouse gas concentrations have no effect on the adiabatic lapse rate in the lower “convective” layer, but they determine the depth of that layer: increasing greenhouse gases increases the surface temperature of the planet not by changing the lapse rate, but by deepening the convective layer. “.
I think that’s it.

John Marshall
January 20, 2012 4:33 am

There is a difference between temperature and heat. whilst temperature is a measurement of heat we need to know the specific heat of a substance to know how much heat is present. So this imaginary Km high column could have identical temperatures top and bottom but heat content will be different due to the density difference.
I think I have said this before. Sorry for a boring repeat.

Alexander Harvey
January 20, 2012 4:36 am

Hi Willis,
I am pleased that you have retruned to this.
First, something I said on the previous thread was both hasty and in error. In terms of Potential Energy the change from isothermal and the DALR modes does not lower the centre of mass of the atmosphere as I speculated, it is not energetically prefered as I suggested, in fact it makes no difference as far as I can tell. Now on to more interesting things.
As I see it, you now expose their model as being inviolation of both the 1st and 2nd Laws. That is the way I have seen things.
Having derived the isothermal as being the prefered profile, a way is open to you to do something rather useful, in my opinion. That is to determine the GHE without appeal to the notion of “heat trapping”, which I consider to be bogus and generally unhelpful.
The naming of the GHE, is I suggest, due to our inhabitting the surface. To illustrate this and my issue with “heat trapping”, I will pose the following question in an idealised atmosphere (see below for part of the idealisation).
In terms of just the atmospheric part, does the addition of GHGs move an atmospheric system as a whole towards a warmer or cooler state, or make no difference?
My preference, or prejudice, would be to say that it tends to cool an atmosphere as a whole but also redistribute energy towards the DALR profile. The notion of a GHE being solely a POV issue. For a denizen of the upper atmosphere it might be termed the IBE (Ice Box Effect). I like to put it this way for I find that everybody hates the notion. It seems clear to me that the effect of adding GHGs when viewed from an atmospheric system perspective is to produce a strong cooling tendency that is acted against by a strong response in the form of sensible and latent fluxes.
There is a level of idealisation going on here, Notably an absence of SW absorption and the production of warming in the stratosphere of our Earth. For those who can put that to one side, I think that there is an opportunity for insight into an origin for of the surface GHE in terms of an overall cooling tendency. The complication due the real stratospheric warming and the way that may contribute to the production of the tropopause and in the determination of its height puts the question of whether the real atmosphere as a whole would actually warm, cool, or stay the same into some doubt. That is by the bye in terms of the idealisation I have assumed.
I view the GHE and the IBE as two inseparable sides to the same coin. Compared to the non-GHG isothermal case where the whole system assumes the SB equillibrium temperature, the addition of GHGs causes the surface to be warmer (GHE) but crucially the upper troposhere (on the real Earth) to be cooler (IBE). If people must have “heat trapping” I say they must also have “heat releasing” but I would rather they simply dropped that metaphor altogether. GHGs couple the atmoshpere to the radiative field and whether a cooling or a warming takes place locally, is determined by the spectra of the GHGs, their local density, the local temperature and the local strength of the radiative field at each frequency.
I don’t expect anyone to agree with this, amongst skeptics it may be viewed as a AGW trojan horse, amongst the staunch AGW dogmatists it seems to be viewed as deeply unhelpful perhaps largely due to the loss of the “heat trapping” metaphor, or simply wrong. Hopefully it is a POV that people can have fun with and might just break down some barriers to thinking about GHGEs (Greenhouse gas effects).
It is not all about warming.
Alex

January 20, 2012 4:46 am

Willis,
please get back to me via email, not here – I just don’t have the time.
Put simply, ignoring the electrical input into the earth system will lead you down many, intellectually attractive, paths.
Have a look at plasma physics and its applicability to your topics – you might be more than surprised,
Louis

LazyTeenager
January 20, 2012 4:47 am

David says
The air moving up and down exchanges potential energy (PE) for kinetic energy (KE). The air moving down loses PE but gains KE, and vice versa for the air moving up.
——-
I have not entirely digested the article but an important consideration may be that Willis is referring to an atmosphere that is in equilibrium, without external energy sources. This means that there is NO motion of the air.
David you are referring to air in motion. Which means there must be an external energy source to keep the air in motion.
So David and Willis are describing different situations.

markus
January 20, 2012 5:01 am

An inverted cone 1klm in DIA, 5klm high, 10m DIA at top, on stilts above water, so atmosphere can enter down low.
Intoduce Co2 @ 5,000ppm with a Co2 drip feed relative to the life of atmospheric Co2. Headed by a turbine.
Just like GH theory, the Co2 enriched atmosphere inside must warm more than the atmosphere coming in below, and because of thermodynamics the heat at the top will turn that turbine.

MarkW
January 20, 2012 5:11 am

I’m looking at the problem from a different direction. That of stability. Think of a column of air running from the ground to space. The temperature of this column of air at the very top is fixed. It is the temperature of space itself. As you descend through this column of air, the rate at which the air warms is determined by the lapse rate. Anytime a particular patch of air gets above the temperature determined by the lapse rate for that depth, it immediately becomes more boyant than the surrounding air and starts rising. It cools, but it still remains above the temperature of the air in it’s new surroundings. It rises until it reaches the top of the column, where it radiates it’s excess heat out into space.
This is not a perpetual motion machine, because it isn’t gravity that is causing the heating. It’s the sun. Take away the sun and quickly the whole column of air freezes. Increasing or decreasing the amount of energy coming from the sun will increase or decrease the total energy in the column of air, but the result of this is and expansion or contraction of the air, causing the column to grow or shrink. When the column expands, the average density of the air changes, which decreases the lapse rate. However the temperature at the top of the column and the bottom of the column remain the same. Decrease the energy from the sun, and the density of the air increases, and the height of the column decreases, but the temperature at the top and bottom still remain the same.
This relationship stays true until air cools to the point that it becomes a liquid.

Bill Illis
January 20, 2012 5:11 am

The basic assumption of the radiation theory is that as mass gains energy when it enters a gravity field, all that energy will eventually be radiated away to space as EM radiation. This could take some time but for a gas it wouldn’t be that long.
All the thermal energy gained from gravitational potential energy is then eventually radiated away to space as EM radiation (give or take some cosmic background radiation re-entering the system).
Therefore: Gravitational Potential Energy = EM Energy
Therefore: the gravitational energy will eventually be radiated away to space – for gasses this should be relatively fast.
Well, that now gives us the theory of everything.
Except gravitational energy is not observed to decrease/radiate away over time unless the mass declines so the basic assumption is not complete. Thermal energy radiates away, but gravity does not.
That then implies:
– when an object which has gained energy in a gravity field loses EM energy through EM radiation, it must gain that back from the gravity field; or,
– gravitational energy is only interchangeble with EM/thermal energy at a limited level. It must be so small that we cannot detect a decline in gravity. Higgs bosons do not directly turn into EM photons, or only rarely; or,
– whatever gravitational energy that is not converted into EM energy remains in the system and is what we perceive as gravity.
There are all kinds of issues with this picture that are not understood at all.

tallbloke
January 20, 2012 5:12 am

Birdieshooter says:
January 20, 2012 at 2:30 am
My reply to all the questions raised above on both sides is WWES…….What Would Einstein Say? I would genuinely like to know. I wonder if he would have enjoyed these blogs. Anyone channel him lately?

He would say:
“If Jeremy and Willis are right, there goes relativity!”

steveta_uk
January 20, 2012 5:13 am

Willis (or Dr Brown) the case for the isothermal cylinder seems to be fairly well established.
But on Earth, any given area on the surface has a conical section of atmosphere above it, and by my sums, I’d expect that if you have 15C at the surface, you’d expect to see about 13C at 15km simply due to the larger volume.
Not sure this has any implications for the overall argument or not.

January 20, 2012 5:20 am

Rob said, “(1) Were there is no greenhouse effect, the lapse rate in a planetary atmosphere would be isothermal (i.e., temperature would not change with height. In this case, the dry adiabatic lapse rate would be unchanged from its present value, but it would be completely irrelevant to the interpretation of the observed lapse rate.”
That is not entirely true. The lapse rate would attempt to approach isothermal. Even without “greenhouse effects” there is conductive heat transfer. The viscosity of the lower atmosphere would increase to improve conductive heat transfer reducing convection. Gravity would limit the amount of energy that could be contained in the atmosphere. The energy of the upper most molecules in steady state would be less than gravity imposes for the escape velocity of the planet. This is another, “all things being equal” example.
“(2) Greenhouse gas concentrations have no effect on the adiabatic lapse rate in the lower “convective” layer, but they determine the depth of that layer: increasing greenhouse gases increases the surface temperature of the planet not by changing the lapse rate, but by deepening the convective layer. “.
Another all things being equal example. “Greenhouse Gases” have differing thermal conductive properties, molecular weights and heat capacities. The “mix” in a mixed gases environment has more than just radiant effects.
Conductivity is generally assumed negligible in radiant atmospheric physics. The possibility that it is not negligible, reflects poorly on the estimates of the “radiant” portion of the ATMOSPHERIC EFFECT.

Frank
January 20, 2012 5:23 am

Willis,
I think Dr. Brown’s thought experiment makes a mistake by linking the temperature to the vertical component of the molecule speed, only, when he says: “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”.
If there is a difference in horizontal speed (i.e. wind) between the layers, the temperatures can be different while the layers do adhere to all of the conditions mentioned in the quote.
On another note, Willis, when you tell Jeremy: “You are a hundred percent correct, gravity can’t do ongoing work to change the temperature”, I hope you’re not forgetting that the Earth does negative work on the molecules going up, which in equilibrium cancels out the positive work being done on the molecules going down, the net energy effect being zero.

Joe Born
January 20, 2012 5:30 am

Bart: “Without radiating gasses to draw the heat energy away, the atmosphere of a planet is like an ideal electrical capacitor hooked up to a constant voltage source”
I know you changed this to “constant-current source,” but, actually, you had it right the first time If voltage is temperature and the earth’s surface is the voltage source. An atmosphere of the type you describe would acquire energy from its source only when its temperature is less than the surface’s. Of course, the earth’s “voltage” isn’t constant, and its outgoing radiation provides a (highly nonlinear) parallel conductance, but that doesn’t detract from the point: the capacitor won’t pop.

Richard M
January 20, 2012 5:34 am

AusieDan says:
January 19, 2012 at 8:14 pm
We need a theory to explain why the surface temperature of the various solar bodies can be derived as a function of distance from the sun (solar radiance) plus near surface atmospheric pressure.

I’ve given it several times now. It’s called the standard GHE at its maximum. That maximum effect is determined by atmospheric pressure. Nothing else is needed. This conjecture explains all the data.
Now, why is there a maximum? I’m not sure, but it could be where the “cooling effect” of GHGs exactly matches the “warming effect”. The latter one is the only one climate scientists look at. The former one is what you get when a GHG extracts energy from the atmosphere and radiates that energy to space.

Luke
January 20, 2012 5:41 am

All right, here is my attempt at the elevator speech for what I understand the Jelbrings paper to be, based on the discussions here. I’m sure someone will find something wrong with it. It’s a little bit longer than Willis’ elevator speech, but I believe that his misses some crucial pieces.
* If left undisturbed in a gravity field, a tall container of air will stratify vertically, with the coolest temperature at the top and the warmest temperature at the bottom.
* In an undisturbed environment that column of air will eventually reach energetic equilibrium, meaning that any given cube of air will contain exactly the same amount of energy, whether at the top or the bottom.
* Because an air molecule at the top of the column (gravitational body) is further away from the earth (gravitational body) than a molecule at the bottom of the column, by the universal law of gravitation less force is being exerted on the molecule at the top of the column.
* Therefore the pressure at the top of the column will be higher than the pressure at the bottom of the column.
* It also then follows, according to the ideal gas law, that P1 * V1 / T1 = P2 * V2 / T2 where 1 is the top of the column and 2 is the bottom of the column.
* Therefore, when examining two identical volumes of air, one at the top of the column and one at the bottom of the column, the one with the greater pressure (bottom of the column) must also have a greater temperature for energetic equilibrium to have been reached.
* This property of an undisturbed column of air in a gravity field, is the cause of what we erroneously refer to as the “greenhouse effect”.
Willis, such a column would never be isothermic throughout the whole column of air. Instead, it would be isothermic at any given layer of the column. In other words any given horizontal slice parallel to the earth would be isothermic, but they would not be isothermic from one layer to the next. The faulty assumption necessary to yield an isothermic column is that the strength of gravity field acting upon any given molecule in the column is uniform throughout the column. It clearly is not, both theoretically and empirically.

Luke
January 20, 2012 5:56 am

Bomber Cat:
Real oceans and lakes are not a good facsimile for this thought experiment. The reason, their primary thermal input comes from the top of the ocean (i.e. the warming rays of the sun) because the depth of water does not allow the sun’s radiation to reach the bottom of the ocean floor to be absorbed and redistributed back upwards.
If you look at how a solar pond works (when the sun can penetrate to the black bottom) you see the warmer water at the bottom and the colder water at the top. The problem in your example is the lack of transparency of the ocean and an energy source at the top.

January 20, 2012 5:56 am

Why is the N Z paper called a gravity model? I always interpreted their model as a delay model. Sun heats the surface through a largely transparent medium. The surface heats this transparent medium though particle contact. Eventually this distributes through the transparent medium.
The delay in the heated surface to lose it’s temp because of the transparent medium allows the surface to heat more than it would without the transparent medium.
I read what was posted in this article that ignores any of the above as completely missing the point.

JJThoms
January 20, 2012 6:03 am

Consider a 10km long box 1m x 1m cross section of perfect insulating material (aerogel?). Coat the outside with 100% reflective material (to stop the aeogel radiating it will not conduct)
Fill it with argon.
Lay it horizontally 5km above ground level. It will of course be perfectly balanced
Leave it for a few days.
The temperature must stabilise so that all the gas is at the same temperature – there are no external influences on the gas and it cannot radiate and cannot conduct out of the box
Rotate it 90 degrees. (it will do some of the work itself as the argon compresses in the lower end and decompresses in the higher unbalancing the system.
When vertical the argon will be heavily compressed in the lower end and therefore much hotter and very decompressed and therefore cooler in the high end. In fact it will have the profie dictated by the lapse rate.
Leave this for a few months. Those warm and cool atoms of argon will be wizzing about in the box but they will be loosing no energy. All that wizzing eventually equalizes the temperature throughout the gas – the low pressure gas will have the same temperature as the high pressure gas.
There is no energy in or out to disturb this. Maxwells deamon is not in the box to sort the hot from the cold! the gas is isothermal.
It will stay in this state forever.
Now rotate the box through 180 degrees and magically the low pressure end becomes the high pressure end and therefore the lapse rate is re-established.
HOWEVER
You have just turned a box that is heavy at the lower end. raising it 10km up in the air, working against gravity. There has been much work done.
Leave the box for a few more months and the gas will again become isothermal.
BUT
The temperature will now be hotter than before because you put all that work in rotating the box.
You can continue this rotation untill the argon is white hot of course!
BUT
it only gets hotter because you put in work
Leave the box vertical for as long as you like and no work will be done. Gravity is static it does no work. If gravity maintained the adiabatic lapse rate temperatures the it would be magically operatinhg as a maxwell deamon.
By the way look up “vortex tube” for a way of separating hot and cold air! A maxwell deamon powered by compressed air.

Luke
January 20, 2012 6:04 am

As a follow-on to the solar pond comment I just left, I do not consider it a reasonable facsimile of the experiment either. I was only pointing out that there are bodies of water that violate the example of oceans and lakes. In order for it to be a reasonable facsimile, there would have to be no light source, i.e no sun.

January 20, 2012 6:06 am

Tallbloke says: “No, as we’ve been saying all along, as have other people on this thread, at the lowest energy state, molecules at the top of the atmosphere have the same total energy as those at the bottom, but less of the total is available as kinetic energy …”
As has been stated many times in many way, science is not decided by consensus, and science is certainly not by consensus of non-experts. Of the people on this list who seem to have formal training in physics, the agreement seems quite strong that isothermal is the the equilibrium condition for the given thought experiment.
Among OTHER trained physicists I have consulted, that is ALSO the agreement for isothermal rather than a lapse rate.
For instance, they say:
“all of the following are true:
— Boltzmann distribution of kinetic energy
— Boltzmann distribution of potential energy
— Boltzmann distribution of total energy.”
This is in contrast to Tallbloke’s claim that ONLY total energy follows the Boltzmann distribution.
EACH of these separately will have the same distribution and the same temperature. I could also go into the rather involved discussion of the partial derivatives involved, like

               ∂S
       β  = --------
             ∂E | N

but I don’t think it would help much in this discussion.
[COMMENT: I fixed the formatting, Tim, using the “pre” tags (for “preformatted”). WordPress ignores leading blank spaces. —w.]

Luke
January 20, 2012 6:13 am

Oops… I reversed on point in my elevator speech…
* Therefore the pressure at the bottom of the column will be higher than the pressure at the top of the column.
The whole thing should read:
* If left undisturbed in a gravity field, a tall container of air will stratify vertically, with the coolest temperature at the top and the warmest temperature at the bottom.
* In an undisturbed environment that column of air will eventually reach energetic equilibrium, meaning that any given cube of air will contain exactly the same amount of energy, whether at the top or the bottom.
* Because an air molecule at the top of the column (gravitational body) is further away from the earth (gravitational body) than a molecule at the bottom of the column, by the universal law of gravitation less force is being exerted on the molecule at the top of the column.
* Therefore the pressure at the bottom of the column will be higher than the pressure at the top of the column.
* It also then follows, according to the ideal gas law, that P1 * V1 / T1 = P2 * V2 / T2 where 1 is the top of the column and 2 is the bottom of the column.
* Therefore, when examining two identical volumes of air, one at the top of the column and one at the bottom of the column, the one with the greater pressure (bottom of the column) must also have a greater temperature for energetic equilibrium to have been reached.
* This property of an undisturbed column of air in a gravity field, is the cause of what we erroneously refer to as the “greenhouse effect”.

Warren in Minnesota
January 20, 2012 6:14 am

There must be some Peter Principle corollary or perhaps Parkinson’s Law of Triviality corollary with this discussion.

Joules Verne
January 20, 2012 6:16 am

Luke says:
January 20, 2012 at 5:41 am
“* This property of an undisturbed column of air in a gravity field, is the cause of what we erroneously refer to as the “greenhouse effect”.”
This conclusion is not supported. The temperature at the bottom of the column would be the same with or without gravity! Gravity merely trades off temperature for gravitational potential energy with increasing column height. That’s all it does. It can’t add or substract energy from the column, it can’t change the distribution of energy in the column, but it CAN change the distribution of sensible/insensible energy and that distinction is important because potential energy won’t save any brass monkeys from disfigurement.

A physicist
January 20, 2012 6:18 am

Here is a Car-Talk Puzzler-type question that (hopefully) will illuminate why Luke and other posters are mistaken.
A WUWT Puzzler
Alice has a cannon that shoots vertically, with a random initial vertical velocity, whose root-mean-square initial value is 100 meters/second, whose mean value is zero, and which is normally distributed (a Bell-shape curve).
Puzzler Remarks:
(1) on half of the firings, Alice’s shell shoots down into the dirt
(2) the other half of the firings, Alice’s shell shoots up-in-the-air
(3) a typical maximal height is (100^2)/(2*10) = 500 meters
(4) some shells fly higher, others lower
Puzzler Question: Of all the shells that pass the “X” meter height, what is their mean square velocity, as measured at “X” meters altitude?
Asserted Puzzler Answer: No matter what the value of height “X”, the shells that pass through height “X” have a root-mean-square velocity of 100 meters/second.
So amazingly, our “Puzzler Shells” do not “cool off” as they fly to higher altitudes. Rather, there are simply fewer-and-fewer of them.
As with “Puzzler Shells”, so with gas molecules: their temperature is independent of elevation, but their density decreases.
And that is my “elevator explanation” of Willis’ problem.

JJThoms
January 20, 2012 6:19 am

John Mason says: January 20, 2012 at 5:56 am
… The faulty assumption necessary to yield an isothermic column is that the strength of gravity field acting upon any given molecule in the column is uniform throughout the column. It clearly is not, both theoretically and empirically.
============
The force of gravity changes little over a 10km distance above the earth:
http://en.wikipedia.org/wiki/File:Erdgvarp.png
Surface g=9.81
10km g=9.78
less than 0.5% change

January 20, 2012 6:20 am

Luke says: January 20, 2012 at 5:41 am
All right, here is my attempt at the elevator speech…
* If left undisturbed in a gravity field, a tall container of air will stratify vertically, with the coolest temperature at the top and the warmest temperature at the bottom.

You are starting from a wrong hypothesis. My first thought was also that this might be the equilibrium condition, but a bit of actual study of the issue made it clear this is wrong
“* This property of an undisturbed column of air in a gravity field, is the cause of what we erroneously refer to as the “greenhouse effect”.
If you start with a wrong postulate, then is is easy to come to all sorts of incorrect conclusions. For example, this property of an undisturbed column is ALSO what allows you to run a perpetual motion machine from this air column.

wayne
January 20, 2012 6:23 am

I recently made a very relevant comment to Dr. Robert Brown on one of his past threads. Maybe some here might also read and consider the topic on multiple horizontal Boltzmann distributions at each and every level upward a tall gravitationally held column under an actual DALR. See: http://wattsupwiththat.com/2012/01/12/earths-baseline-black-body-model-a-damn-hard-problem/#comment-870527

Joel Shore
January 20, 2012 6:32 am

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.

Because Jupiter is a gas giant undergoing slow gravitational collapse. I.e., the thermal energy is generated by the conversion of gravitational potential energy. See for example the discussion here http://nineplanets.org/jupiter.html :

Jupiter radiates more energy into space than it receives from the Sun. The interior of Jupiter is hot: the core is probably about 20,000 K. The heat is generated by the Kelvin-Helmholtz mechanism, the slow gravitational compression of the planet. (Jupiter does NOT produce energy by nuclear fusion as in the Sun; it is much too small and hence its interior is too cool to ignite nuclear reactions.)

This is not happening for the Earth.

Paolo M.
January 20, 2012 6:40 am

“Gravity has NO AFFECT ON TEMPERATURE.”
As far as planet Earth is concerned, the correct statement would be:
Gravity has NO EFFECT ON POTENTIAL TEMPERATURE!
In a gravity field, with a costant source of energy (the Sun), in presence of two sinks (the Poles), the vertical profile of temperature would be that of the adiabatic lapse rate.
The presence of water, other GHGs and ozone makes the thinks more complicated, but vertical mixing can’t be ignored.
Of course gravity doesn’t make the difference between two planet, one with GHGs and the other without. It just rearranges the vertical distribution of absolute temperature (thanks to density), but not that of POTENTIAL temperature that would be costant. Actualy, potential temperature in our troposphere is higher aloft due to the release of latent heat after (mainly) wet convection has occurred

OzWizard
January 20, 2012 6:43 am

Willis,
N & Z have indeed produced a game-changer here and no thought experiment is needed to understand their ‘Unified Theory of Climate’. Simply stated, their hypothesis consists of their two key equations, (7) and (8).
The existence of a dimensionless ATE ‘factor’ does not imply that “gravity causes heating of the lower atmosphere”, in defiance of the 2nd Law of Thermodynamics. I believe the relevant science is nicely encapsulated in their (non-linear) equation (8),
Ts = 25.3966 (So + 0.0001325)^0.25 NTE(Ps).
That equation enables them to calculate the surface temperature (Ts) of ‘any planet with an atmosphere’, knowing only the TOA TSI (So), the surface pressure (Ps) on the planet and the dimensionless Atmospheric Temperature Enhancement factor (NTE).
The NTE factor for any planet is derived from observations already made (see N & Z, Table 1) and a thorough reassessment of the physics of what they term ‘grey body’ temperature (Tgb) of a real, airless planetary object (our own moon) – a conceptual physical model which is used in equation (7) to derive their NTE values.
The experiments have been done, the data have been analyzed; their ‘grey body’ temperature model and their simple regression are now out there to be pondered for veracity and significance.
The fact that nobody can explain “how it works” (to your satisfaction) is not a valid reason to try to demolish their hypothesis by thought experiments (which include unproven assumptions).
Try to understand it Willis, please. All your thought experiments are irrelevant unless you can demonstrate where their math, or their data, or their ‘grey body’ model, or their regression is wrong. To do that you need to understand what they have done and, by your own admission, you do not yet understand what they have done.

tallbloke
January 20, 2012 6:45 am

Tim Folkerts says:
January 20, 2012 at 6:06 am
Of the people on this list who seem to have formal training in physics, the agreement seems quite strong that isothermal is the the equilibrium condition for the given thought experiment.

Whereas the engineers and meteorologists tend the other way. And this is interesting, because it shows who has more common sense. 🙂
Tim, it’s no good appealing to Boltzmann when he is one of the protagonists in the unresolved dispute.
Loschmidt, Lagrange, Laplace, Jelbring and me vs Willis, you, Jeremy, Boltzmann and Maxwell
Outside, now!
lol.
I’m reading up on what happened between Maxwell’s formative thinking about classical molecular mechanics (engineers and meteorologists) and his part in the development of statistical mechanics (physicists and mathematicians) to see if I can find the key to this fascinating puzzle.

quondam
January 20, 2012 6:57 am

Last year this was discussed in a Climate Etc. thread. Perhaps a conceptually simpler Perpetuum Mobile machine can be constructed from two identical vertical columns of gases of different heat capacity, e.g. helium and argon thermally connected at their bases and totally insulated otherwise. If the lapse rate is an equilibrium property, there will be a constant temperature difference at the tops of these two columns. Making identical thermocouple connections between these points at the same gravitational potential, one has an electric potential difference and can then use this to dissipate energy. Energy is being extracted from both columns, cooling both while a constant temperature difference persists at the thermocouples.
If one is mathematically inclined, it is not a difficult exercise to start with a fixed volume of an isothermal, ideal gas and show that any perturbation of its density and thermal profiles leads to reduced configurational entropy, total energy held constant.
When one sees the expression “radiative-convective equilibrium” employed, it’s a giveaway that the writer is unconditionally misinformed. There can be radiative-convective steady-states, but any steady-state requires a constant dissipation of either mass or energy for maintenance. That the troposphere might be described as a steady-state implies such an energy of dissipation and, perhaps not too surprisingly, convective stirring takes a steady input ca. 240W/m^2 to be dissipated, but that’s reverting to pre-postnormal science.

DirkH
January 20, 2012 6:57 am

DirkH says:
January 20, 2012 at 3:54 am
“And that is the stable configuration, not the isothermal one.”
Looks like I misunderstood the definition of “isothermal” – and my explanation is in no contradiction to Willis’ isothermal configuration. So it seems Willis and I agree that we will observe the lapse rate as defined by the Ideal Gas Law. Sorry for any confusion.

DR
January 20, 2012 6:58 am

After 24 years of being inundated with “greenhouse effect” theory lectures, first from James Hansen in 1988 which those of us old enough to remember was quite a display of fear mongering (very convincingly so I might add), multiple documentaries on television and never ending use of the term since then in the media and science publications, the whole damn thing has evolved into an unfalsifiable hypothesis . Anyone can use the internet to find these “high school physics” descriptions of how the GHE works.
All I would like an answer to is why the very basic tenet of the GHE, that being the tropical troposphere should be warming at a faster rate than the surface, is unsupported by observational evidence. This was culminated by the debunking of Santer 08, perhaps the most dubious peer reviewed material released for public and scientific consumption since MBH 98. To keep the pseudoscience alive, scientists promoting the failed experiment tell us the observations must be wrong, not the “theory”.
I was fully convinced in 1988 of the “greenhouse effect” and it’s deleterious effects it would have on the earth, yet here it is 24 years later and it isn’t working as advertised. If anything, it is upside down.
There is something wrong with the GHE hypothesis as it has been promoted lo these many years.. I’m not qualified to enunciate what it is in technical jargon, but I don’t need to be an atmospheric scientist or physicist to know something is wrong. Does anyone else feel like they’ve been sold a lemon? Even here on WUWT,with the arguing going back and forth, the “theory” is no better explained or proven than it was 25 years ago.
“If it disagrees with experiment, it’s wrong”.

Tamara
January 20, 2012 7:00 am

Regarding N and Z, my understanding of it is this (could be totally wrong, IANAPhysicist):
When a star is accreting, gravitational contraction converts gravitational potential energy into thermal energy. It is this thermal energy which acts as an opposing force to gravity, preventing the star from collapsing completely. As the star gains mass, its gravitational attraction increases as does its thermal energy. At some point thermal energy becomes large enough that fusion occurs and the star becomes stable. What does this have to do with N and Z? As I understand it, they claim that they can estimate atmospheric temperature from the density of the atmosphere. A volume of air that is more dense has more mass than the same volume of air that is less dense. Therefore, shouldn’t the dense volume of air have more gravitational potential energy that can be converted to thermal energy? And, can we assume that any volume of air that is being contracted by gravity will have some thermal energy above the black/gray body energy?

Jeremy
January 20, 2012 7:09 am

richard verney
The affects of the tides and other orbital parameters will indeed affect the atmosphere. Work is indeed done in the thermodynamic sense of external force acting on a closed system. In fact the Moon and Earth system will experience a loss in Kinetic energy from the “gravitational drag” of tides. These are third or fourth or even higher order effects. Like variations of the trace gas CO2, the affect of these things on “atmospheric temperatures” are extremely small and inconsequential compared to radiative forcing from our Sun.

DirkH
January 20, 2012 7:10 am

JJThoms says:
January 20, 2012 at 6:03 am
“Leave this for a few months. Those warm and cool atoms of argon will be wizzing about in the box but they will be loosing no energy. All that wizzing eventually equalizes the temperature throughout the gas – the low pressure gas will have the same temperature as the high pressure gas.”
But according to the Ideal Gas Law, this is not possible. The temperature distribution must follow the pressure distribution so that PV = NkT
where P is the absolute pressure of the gas measured in atmospheres; V is the volume (in this equation the volume is expressed in liters); N is the number of particles in the gas; k is Boltzmann’s constant relating temperature and energy; and T is the absolute temperature.
http://en.wikipedia.org/wiki/Ideal_gas_law
They very fact that there is a vertical pressure gradient results in a temperature gradient.

Stanb999
January 20, 2012 7:13 am

So in this mythical elevator….
First it has no sides. It has no top. The bottom can vary widely…. Density can be 50% different.
With temperature changes the hight as well as the width of the elevator can grow or shrink.
What is so hard to figure out? As the atmosphere has heat added it grows. This growing increases it’s surface area. This increased surface area. Increases the thermal exposure to the cold of space. It cools.
The atmosphere as well as earths temperature is self regulating.

mkelly
January 20, 2012 7:17 am

Jeremy says:
January 19, 2012 at 7:52 pm
Gravity has NO AFFECT ON TEMPERATURE.
How many times must it be said.
You have to do WORK to create a change in temperature – this is basic thermodynamics!!!!
Jeremy please use the standard equation to state your case. simply (Joel I said simply) Q= U+W.
If W=FD and F = mg then W can be done by heated air rising IF volume changes. We have been told there is a diurnal bulge. As W is a path function and W1-2 (air going up) does not have to equal W2-1 (air coming down) then W could be being done via gravity.
KE and PE in U do not change IF the center of gravity does not change.

anna v
January 20, 2012 7:24 am

Bomber_the_Cat :
January 20, 2012 at 3:40 am
In my books an ocean is not a closed system, the way this column of gas is proposed. It is not a good example.

Kelvin Vaughan
January 20, 2012 7:27 am

Cosmologists believe in perpetual motion. They believe light travels through the universe ad infinitum without using any energy!

Steve Fitzpatrick
January 20, 2012 7:33 am

Good luck in this quest to make those who do not understand begin to understand….don Quixote….. er ….. Willis.

Spector
January 20, 2012 7:34 am

For me this is a very simple issue:
1. The Earth is only receiving enough power (or energy flow) from the sun to emit an average of about 240 W/m² from the surface of the Earth. That is derived first, from the solar constant divided by four, the ratio of flat spherical surface area of the Earth to the area of the disk of solar radiation absorbed by the Earth and second, by applying an assumed 30 percent optical reflection factor. Reflected solar energy is treated as never having arrived.
2. According to the Trenberth diagram and the Stefan-Boltzmann equation, the Earth is actually warm enough to be radiating something on the order of 396 W/m² average power from the surface.
3. A transparent, non-greenhouse gas containing atmosphere cannot, by definition, prevent or stop the surface from radiating all this power to outer space. Thus, the surface would be continually losing a net average of 156 W/m² as long as it remained that warm. Fixing this would require a close relative of the perpetual motion machine–the perpetual power creation machine.
4. An average surface power radiation of 396 W/m² can only continue with an atmosphere that can absorb a net 156 W/m² from the outgoing radiated power and return it to the surface.
All technical details of exactly how that happens are irrelevant to this power balance requirement.

Steve Fitzpatrick
January 20, 2012 7:39 am

Kevin Vaughan,
No they don’t, light is red shifted if it moves opposite a gravitational field, and blue shifted if moving with the field. The frequency shift shows a change in energy due to the gravitational field. Gravity influences everything, even electromagnetic waves.

AJ Abrams
January 20, 2012 7:40 am

Willis, or anyone else.
First, the gravity theory is a non-starter. Willis is correct and people seem to keep missing some very fundamental properties here. Heat is not temperature. Heat is temperature at volume. Keep molecular temperature the same, but increase density and you have more heat. Willis is exactly correct in saying that the upper less dense molecules can have the same temp as the lower more dense molecules and it all be at equilibrium.The PE and KE will vary over height (as related to the gravity point source) so total energy (TE) of any specific given volume of gas can and will come to complete equilibrium over time as the temperature of each given molecule reaches the same temperature. It’s a volume issue. His proof is also correct. If this didn’t happen, you would and could have a perpetual motion issue to deal with. Case close, can we move on to something new please? This doesn’t prove GHG theory correct, it just says the alternative theory is incorrect and people are looking like buffoons. (Engineer by schooling)
I do have a question though. As has been said over and over, our atmosphere volume has to increase if it warms (Total heat). Why are we trying to measure average temperatures, which is meaningless and damn near impossible, instead of not just measuring the height of the atmosphere instead? You would think that an average height of the atmosphere would be much easier to do as a function of time and any trends would then be easy to spot.
AJ

AJB
January 20, 2012 7:51 am

Tim Folkerts says @ January 20, 2012 at 6:06 am
Tim, please refer to this page and specifically to the sentence that reads “Ignoring tiny corrections for gravity, the gas will be distributed uniformly in the container, so the only unknown is the velocity distribution function”.

Richard M
January 20, 2012 7:54 am

OzWizard says:
January 20, 2012 at 6:43 am
Try to understand it Willis, please. All your thought experiments are irrelevant unless you can demonstrate where their math, or their data, or their ‘grey body’ model, or their regression is wrong. To do that you need to understand what they have done and, by your own admission, you do not yet understand what they have done.

Their math, etc can be completely correct AND Willis can also be correct. All it takes is understanding that the GHE has a maximum value determined by exactly the parameters K&Z use. So, you have a GHE, just as Willis’ thought experiment requires, to warm the surface. You also have many planets that all have reached their own maximum GHE based on atmospheric mass, gravity and irradiance.

PeterGeorge
January 20, 2012 7:59 am

“For such machines to work, they’d have to create energy”
I certainly don’t believe in perpetual motion machines, but the above statement is dead wrong. For such machines to work they would have to reduce entropy, not create energy.

son of mulder
January 20, 2012 8:00 am

One of my imaginary friend lives on a spherical planet that is not rotating, has an atmosphere consisting of one type of gas and a spherically uniform gravitational field.
There was a time when the planet was uniformly lit from a light source in the surface fed by geothermal energy and some of that geothermal energy uniformly warmed the atmosphere from the surface.
Unfortunately the geothermal fuel ran out and now the planet has no light or heat since.
Before this event my imaginary friend built a tall tower of regularly spaced temperature guages.
They were fortunate that the heat source was not strong enough to cause atmospheric molecules to achieve escape velocity. They found a magic point where the atmosphere reached a maximum height at which the molecules had zero kinetic energy and the temperature read 0 deg K. But the temperature below was none zero because of the geothermal heat source and heat was lost to space through radiation from the atmosphere to maintain equilibrium.
Since the heat source died it has been found that the height at which the molecules of atmosphere have zero velocity is decreasing and the molecules of atmosphere below are cooling.
They have a theory of global cooling that predicts that unless a heat source is found, one day in the future the whole atmosphere will have a uniform temperature of 0 deg K but until then the surface will be warmer than the top of the atmosphere because it is always 0 deg K at the top.

tallbloke
January 20, 2012 8:06 am

anna v says:
January 20, 2012 at 7:24 am
Bomber_the_Cat :
January 20, 2012 at 3:40 am
In my books an ocean is not a closed system, the way this column of gas is proposed. It is not a good example.

Not only that but water is incompressible.

Coach Springer
January 20, 2012 8:07 am

From the “lay” sidelines:
I know of a perpetual motion machine: a priori scientific debate. Generates its own energy. Of course that’s debatable.

January 20, 2012 8:13 am

AJB says: January 20, 2012 at 7:51 am
“Ignoring tiny corrections for gravity, the gas will be distributed uniformly in the container, so the only unknown is the velocity distribution function”.
I agree completely. If you can ignore gravity, then gases are distributed uniformly in a container. This is a very good approximation for car engines or steam turbines, and so engineers can reasonably ignore the effect of gravity that makes the pressure at the top of a steam vessel 0.0001 atm less than the pressure at the bottom.
However, the thought experiment here specifically removes ALL OTHER EFFECTS BESIDES GRAVITY. Now we are ONLY dealing with those “tiny corrections”. And for a column 10 km high (sort of like the atmosphere), then those gravitational effects become quite important. Density and pressure are known to drop with altitude due to those effect. The question remaining is “does temperature also drop with elevation in a perfectly insulated container?” I say “no”.

tallbloke
January 20, 2012 8:20 am

Tim,
Have a think about why you say no. Then let the rest of us know. And please don’t just throw names around. Describe the physical phenomenon that leads you to the conclusion.
Thanks

wayne
January 20, 2012 8:27 am

“Otherwise heat will flow from the hotter (right-shifted MB distribution) to the colder (left-shifted MB distribution) slice until the temperatures are equal.”
Robert, your mistake seems right there in the last statement. The molecule members of the upper hotter right-shifted MB distribution cannot equalize (they are actually already in equilibrium) with the lower cooler left-shifted MB for the acceleration that changes the molecules vertical velocity. I think I am right on that, would you reconsider?
You keep want to say the molecules at various levels must be at the same mean velocity but by your own same example, they can’t in the gravity well case. Maybe the MB derivation doesn’t have a gravitation terms when applied vertically. I’ll stop and check it now.

January 20, 2012 8:39 am

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.
Hi Willis,
Permit me to make a small change to this (most of the rest of what I’ve read so far of your post is fine). The final equilibrium arrangement is one where the average kinetic energy per molecule is the same everywhere in the gas column. There are a lot more molecules in the denser gas at the bottom, so there is a lot more internal kinetic energy per unit volume down there, even though the kinetic energy per molecule does not change.
One has to be very careful about how one combines internal kinetic energy and work-based energy. The usual approach is to turn them into the enthalpy of the gas, especially when the gas is in thermal equilibrium with a non-uniform density profile. The usual formula for enthalpy of an ideal gas, E = U + PV, assumes a closed volume, thermal equilibrium, and more or less uniform pressure. Thus one can look at how the enthalpy changes as one e.g. compresses the gas or adds heat. This again becomes complicated when one takes into account variation in density and is the sort of thing that goes into estimating the DALR.
The simplest way to view this is in terms of the heat capacity. The heat capacity of the gas in any volume large enough to hold “many” molecules and be at thermal equilibrium is proportional to the number of molecules in the volume. The gradient in the density that gravity generates in the compressible fluid is accompanied by a gradient in the heat capacity, so that in equilibrium (at the same temperature) the gas at the bottom does have more energy per unit volume than the gas at the top.
The air temperature in the thermosphere can be well over 1000C — in principle hot enough to melt metals. But the atmosphere out there is very thin and the heat capacity is miniscule. The stratosphere — a layer named because of the lack of vertical transport and turbulence — gets warmer from the bottom to the top. That doesn’t necessarily mean that the energy per unit volume increases though, as the density still decreases. It just means that air molecules at the top of the stratosphere are moving, on average, faster than the molecules of air at the top of the troposphere, exactly the opposite of what one would expect from a naive “greater density equals greater temperature” model.
We now return to the regularly scheduled discussion (I haven’t finished reading your post:-).
rgb

Hans Jelbring
January 20, 2012 8:39 am

Tim Folkerts says:
January 20, 2012 at 6:06 am
Tallbloke says: “No, as we’ve been saying all along, as have other people on this thread, at the lowest energy state, molecules at the top of the atmosphere have the same total energy as those at the bottom, but less of the total is available as kinetic energy …”
–As has been stated many times in many way, science is not decided by consensus, and science is certainly not by consensus of non-experts. Of the people on this list who seem to have formal training in physics, the agreement seems quite strong that isothermal is the the equilibrium condition for the given thought experiment.
Among OTHER trained physicists I have consulted, that is ALSO the agreement for isothermal rather than a lapse rate.
For instance, they say:
“all of the following are true:
— Boltzmann distribution of kinetic energy
— Boltzmann distribution of potential energy
— Boltzmann distribution of total energy.”
This is in contrast to Tallbloke’s claim that ONLY total energy follows the Boltzmann distribution. —
Hello Tim,
I am just intrigued by your logic. You state about the Tallbloke´s statement: “science is not decided by consensus, and science is certainly not by consensus.” This is absolutely true regarding scientists that are not corrupt or ingorant.
Then you state:
“Among OTHER trained physicists I have consulted, that is ALSO the agreement for isothermal rather than a lapse rate.”
Then you use the consensus argument to “disprove” what Tallbloke claimed.
Do you recognize your fallacy? I am making the comment since you pretend to be scientific.
I can ssure you that I didn´t bother about consensus when I wrote my E&E article. If I had done it would never had been written.
Best Hans Jelbring

Steve Richards
January 20, 2012 8:41 am

Why not place a 10metre double insulated tube on a long arm centrifuge, fill tube with dry gas at surface pressure, allow temperatures to settle, the temp should be the same at both ends of the tube.
Rotate centrifuge to give 20g.
We should have multiplied the gravity effect by 20, the short length of tube 10m not 1km, would reduce the effect by 1/1000 so the temperature difference measured should be in the order of 180 millidegrees C assuming 9degrees/Km.
Any temperature difference other than zero would be worth investigating…..

January 20, 2012 8:43 am

Tallbloke says:
“Loschmidt, Lagrange, Laplace, Jelbring and me vs Willis, you, Jeremy, Boltzmann and Maxwell
Outside, now!”
Thanks for the laugh. ☺
Let me make one purely semantic argument. The adiabatic lapse rate is ~ 10 K/km. “Adiabatic” means “no energy flow”. So if you can make the approximation that there is little energy flow compared to other energies involved, then the adiabatic lapse rate would be a good estimate of the situation ion the atmosphere. Conduction of heat from one part of the column to another is by definition non-adiabatic. Therefore if conduction is the primary means of energy transport, the situation would not be expected to follow the adiabatic lapse rate.
And that lead me to one slight variation of the though experiment. Consider our perfectly insulated column. I will modify this SLIGHTLY by putting a heat reservoir at the bottom that holds at exactly 300 K (this would be similar Willis’s uniformly lit planet where the SB temperature is 300K at the surface). Now I force the air in the column to be well beyond the adiabatic lapse rate (perhaps I add temporary barriers every 100 m and cool each section by 2 K from the one below ie twice the adiabatic lapse rate). If the barriers are removed, two things will happen.
1) the column of air will be unstable to convection, and the air will start mixing like crazy.
2) there will be heat conduction P/A = k * (Delta_t).
Process 1 will continue until the lapse drops to ~ 10 K/km, at which point it will stop. Process 2 does not need to stop when Process 1 stops. In fact, Process 2 will continue as long as there is any temperature gradient.
NOTE 1: Process 1 will be MUCH quicker than Process 2. I guesstimate Process 1 would be mostly completed within a few hours. But even after convection stops, Process 2 would drive the whole column toward a uniform temperature of 300 K. I guesstimate this would take several months due to the low thermal conductivity of air and the great distances involved.
NOTE 2: If there the air is not perfectly isolated from the rest of the universe causing even a TINY heat sink at the top of the column (even a few mW/m^2), then the rate of conduction will not be enough to erase the lapse rate. GHGs (and even tiny bits of dust) in the upper stratosphere are enough to radiate thousands of mW/m^2 (ie several W/m^2), which means any real atmosphere will have a lapse rate. This tiny leak from the top is enough to maintain the lapse rate, and hence explain why the thickness of the atmosphere plays a major role in surface temperature.

Hans Jelbring
January 20, 2012 8:50 am

A physicist says:
January 20, 2012 at 6:18 am
“Here is a Car-Talk Puzzler-type question that (hopefully) will illuminate why Luke and other posters are mistaken.”
“Alice has a cannon that shoots vertically, with a random initial vertical velocity, whose root-mean-square initial value is 100 meters/second, whose mean value is zero, and which is normally distributed (a Bell-shape curve).”
Is there any relevance about your shooting of she is all the time shooting fron the same altititude?
Will she shoot with the same initial root-mean square 100M/s from any altitude?
I am not a physicist so excuse me if misunderstanding you.

A physicist
January 20, 2012 8:53 am

Yet another elevator argument for isothermal (same temperature) atmospheric equilibrium is as follows: we imagine a very tall (10 km tall) thermopile column (a device that converts temperature differences to electricity), and we insulate the body thermopile column so that only its top and bottom exchange heat with the atmosphere.
Now supposing that the upper air is colder than the lower air, our thermopile generates electric power continuously and forever, with no external source of power. Which is impossible. And so we conclude that, at equilibrium, the entire atmosphere must be at one temperature.
Of course, in the real world, such a thermopile column would generate electricity. And this electricity would constitute (ultimately) a form of solar power, deriving from sunlight acting to warm the earth, thus creating rising thermals that stir the atmosphere, creating a temperature gradient that the thermopile can exploit.
This is one more line of reasoning showing that the isothermal folks have got the thermodynamics right.

Hans Jelbring
January 20, 2012 9:03 am

Tim Folkerts says:
January 20, 2012 at 6:20 am
“You are starting from a wrong hypothesis. My first thought was also that this might be the equilibrium condition, but a bit of actual study of the issue made it clear this is wrong”
If you read my E&E, 2003 carefully you will realize that it is based on two major assumptions and these are:
1) The first law of thermodynamics and
2) Second law of thermodynamics.
The application of these laws in the thought experiments leads to a constant energy content in any two equal submasses of the inclosed insulated atmospherea after relaxation time has passed (approximately 2 weeks).
This was not declared explicitly in the text since it was a topic I wanted to debate but few scientists wanted such a debate. It took 8 eyars for the debate to flourish. Do notice that these laws apply to energy and not temperature.

Man_Tran
January 20, 2012 9:04 am

In all the posts I have scanned, with the possible exception of Joe Born, no one seems to be looking at the extreme case of the very top of the air column. Pick an arbitrary altitude where one N2 diatom is occupying one cubic meter of near vacuum (1 km^3?). What is its PE, KE, freq, temperature? Does it just pop off to space? I think that coming from that direction the argument quickly gets to ‘turtles all the way down.’

Jim G
January 20, 2012 9:06 am

” For such machines to work, they’d have to create energy, and energy cannot be either created or destroyed, only transformed.”
This is another conventional wisdom based upon the incomplete information available at this time. Where did all the matter and energy that exists today come from? I guess if you buy one of the oscillating universe theories, it has always existed. Or in the multiple universe theories it may have been “transferred” through collision with another universe or leaked into our universe. But it could have been created as well. The how or from where or Whom of the potential “big bang” is as yet not explained by science.

pochas
January 20, 2012 9:08 am

Tim Folkerts says:
January 20, 2012 at 8:43 am
“Process 2 [thermal conduction] will continue as long as there is any temperature gradient.”
Well said, Tim

January 20, 2012 9:11 am

“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.”

Except that more of the total energy of the molecules at the top is locked up in gravitational potential as opposed to being available as kinetic energy capable of generating heat in collisions.

Except that you meant to say not. Not locked up. How can I put this gently, firmly, and understandably.
How about temperature has nothing to do with gravitational potential energy.
Look, if you want to comment on thermodynamics and temperature, learn what temperature is and what it isn’t.
As far as an ideal gas — the kind considered throughout this discussion, including by Jelbring and N&Z — is concerned, temperature is a direct measure of the average kinetic energy of a molecule of the gas. Note well, I did not say average potential energy and I certainly did not say average total energy or a jar of matter would get hotter or colder every time we lift it or lower it. Here, let me chill my beer by picking it up off of the table and lifting it to my mouth. No.
Please, please, please. Buy an introductory physics textbook that has a halfway decent thermodynamics section. Pretty please with sugar on top. I beg you. Read it.
Look, you have a choice. Either you can pretend that the Laws of Thermodynamics don’t exist and reinvent them at will, making up a brand new definition of the word “temperature” and pretending that your definition will still work to describe things like equilibrium, the flow of heat and entropy, ideal gases, and so on, or you can learn the ones that we already have. Personally, I think your contributions to the discussion would be better if you did the latter, but suit yourself.
Note well, however, that you will not, and should not, be taken seriously if you assert that temperature of a monatomic ideal gas is related to anything but:
U = 3/2 NkT = 1/2 Nm v^2_avg.
or, “the total internal energy of the gas is equal to the number of degrees of freedom times kT per molecule”, for three — note well, three degrees of freedom. Gravitational potential energy is not a degree of freedom, and if it were it still wouldn’t affect equipartition of energy so kinetic energy is a different one.
rgb

Hans Jelbring
January 20, 2012 9:13 am

Paolo M. says:
January 20, 2012 at 6:40 am
I am not sure you understand what “potential temperature” actually means. It is a misnomer, at least within the science of meteorology. The meaning is actually constant total energy per mass unit. This state will be be found almost every sunny day above land from the surface up to 1000-4000 m or more. It is best devoloped about 1 hour before sunset. The observational evidence for its existence is just overwhelming.
Another way to put is that at such occations the measured dry adiabatic temperature lapse rate will be very close to -g/Cp or -9.8 K/km (no clouds allowed).

Robany
January 20, 2012 9:20 am

I’ve been trying to wrap my head around the thermodynamic arguments for the last few days. The isothermal column of air argument seems to have some problems:
1) The atmosphere has a measurable temperature gradient. An argument that suggests it should be isothermal seems to immediately be falsified by contradiction.
2) Although it’s an equilibrium system overall it is not in thermal equilibrium. We are discussing a system that has a constant energy input (insolation through a transparent atmosphere) at the bottom where the planet’s surface forces a boundary condition on the temperature of the air at sea level. If the planet/atmosphere system is not to heat up then the energy output at the top of atmosphere must match the input. Therefore there must be a flow of energy from the planet’s surface to the TOA and this can only occur if the atmosphere has a temperature gradient and thus is not in thermal equilibrium.
Or have I missed something basic?

January 20, 2012 9:20 am

Hans asks me “Do you recognize your fallacy? ”
I recognize your point. But I think it is not quite the fallacy you think it is. I am saying that even a single person who knows what they are doing has applied the principles of known science. He/she has a “proof” (actually several proofs) that the temperature profile must be uniform for the conditions given (and assuming that “textbook thermodynamics” is correct) . That proof has been checked by others to make sure there is no error. This is more akin to “spell-checking” than “consensus”. We now have a new addition to “textbook physics”. (Actually, this is very OLD textbook physics.)
To counter this proof, you need to show a specific error. Maybe there was a sign error. Maybe they took a partial derivative incorrectly. Maybe you can show that a perpetual motion machine IS possible and the 2nd law of thermodynamics IS NOT correct. But if we simply throw back and forth intuition or soundbites, this will not cut it (from either side).
PS This is precisely why “consensus” in climate science is NOT so useful. In the case of the column of air, the situation is very well-defined, so it is easy to apply basic physics and come to a clear solution. For climate science, the situation is very poorly defined. There are sources and sinks of energy all over the place; there are feedbacks; there are continuing subtle changes in orbits, the initial conditions are not well known, etc. All of these mean that you have to include MANY factors in the calculations. This means a computer to determine the predicted affect.
And now there are MANY places for problems. Basically, each person studying climate can only say “I took into account as many of the affects as I could, and here is what I found”. There are (nearly) endless “what if” questions. There are (nearly) endless lines of code to check. This means that there will be considerable uncertainly in the results.
So it is “settled science” that “CO2 radiates IR well and will warm the surface”, because short, easily verified theories (and repeatable experiments) lead inexorably to that conclusion.
It is “settled science” that the air column will be isothermal, because short, easily verified theories (and repeatable experiments) lead inexorably to that conclusion.
It is not “settled science” that “doubling the CO2 levels will cause a 3.7 K increase in temperature” because there are so many other factors and feedbacks that nailing this number down precisely is a damn difficult problem.
PPS Of course, no science is ever 100% “settled”. Relativity showed that newtonian mechanics was not quite right. But overturning “settled science” requires extraordinary evidence. So far I have seen no “extraordinary evidence” that a perpetual motion machine is actually possible and that there could be a continued temperature gradient in a perfectly insulated air column.

Hans Jelbring
January 20, 2012 9:27 am

DR says:
January 20, 2012 at 6:58 am
” Does anyone else feel like they’ve been sold a lemon? Even here on WUWT,with the arguing going back and forth, the “theory” is no better explained or proven than it was 25 years ago. ”
No, I don´t feel like that since I have been fighting IPCC and its unscientifc statements since it was created. However, Willis is good at keeping the confusion alive which favours the IPCC organization.

Bryan
January 20, 2012 9:29 am

A physicist says:
“Yet another elevator argument for isothermal (same temperature) atmospheric equilibrium is as follows: we imagine a very tall (10 km tall) thermopile column (a device that converts temperature differences to electricity), and we insulate the body thermopile column so that only its top and bottom exchange heat with the atmosphere.”
Have you factored in the resistance of the 10km copper(lets say) leads to your thermopiles?
Once you use real thermopiles and realistic conductors you will realise why this experiment will not work.

January 20, 2012 9:34 am

Final overall comment and off to work.
First, there are actually two kinds of perpetual motion machines that people propose. They are called perpetual motion machines of the first and second kind.
Perpetual motion machines of the first kind violate the first law of thermodynamics. The perform work with no (net) input of energy at all, and thereby increase the mass-energy content of the Universe as they function. They thus violate a very, very basic physical principle as well as a law of thermodynamics.
Perpetual motion machines of second kind violate the second law of thermodynamics. No energy is created or destroyed, it is just moved around so it can be reused again and again.
Both are magic, and actual mythological magic can be classified identically — magic of the first kind is responsible for creating Universes out of nothing, turning lead into gold, and so on. Mass-energy violating magic. Magic of the second kind is more subtle — rising from the dead, healing the sick, walking on water. No energy is created or destroyed, these things are all technically possible, they are just enormously improbable.
Jelbring’s hypothesis enables one to create a perpetual motion machine of the second kind to light stygia. The work done by their Carnot cycle engine and turned into light eventually turns back into heat, so the total energy of Stygia remains unchanged. It is just re-sorted by gravity acting as a Maxwell’s Demon into separated hot and cold reservoirs so that it can be used once again to drive the generator to make more light. The same energy is made available over and over again.
It is this that should make your “horseshit” detectors give a ring. You would have to have been born yesterday to think that Nature gives you any sort of free lunch like that. That hasn’t stopped optimists from seeking PMMs of type 1 or 2, or physicists from proposing theories that violate the laws of thermodynamics, imagining that they are more like “suggestions” than actual laws. But they aren’t suggestions. They are common sense.
* 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. Proof: It’s the second law of thermodynamics Kelvin statement, supported by enormous amounts of evidence and common sense. So much so that if anyone doubts it, I have a bridge that I’d like to sell them in Brooklyn, it should be worth a lot.
* 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.
* Conclusion The assertion is therefore false. It contradicts two everyday, well-known facts. Anybody who believes Jelbring’s conclusions is invited to make themselves infinitely wealthy, as they have just solved the energy crisis. Just don’t ask me to invest.

PeterGeorge
January 20, 2012 9:35 am

“Then the people living in the stygian darkness inside that impervious shell could use that temperature difference to drive a heat engine.”
Wrong. If this argument were correct we wouldn’t need to care about temperature differences. The perpetual motion machine could be driven be the pressure difference alone.
The people would create a massless container to send up and grab some of the low pressure air and bring it down to where the air is is at higher pressure. Then, they could use the pressure difference to drive an engine and do work. Right?
No, of course not. As they bring the massless container of lower pressure (and lower density) air from above it would become a lighter than air balloon. So, it would take work to force it down to the level of the high pressure air. That would negate work done by the pressure difference. No perpetual motion machine.
Couching the argument in terms of temperature doesn’t change the result.
IMhO, there is no way to answer this question about gravity and lapse rates without discussing entropy. Entropy is king. Every other result in thermodynamics – including Boltzman distributions and all the rest, derive from the principle of Equal Apriori Probabilities and the consequence that a system will, in time, inevitably migrate to the macrostate with maximum entropy.
If the isothermal macrostate has higher entropy, that’s where it will go. If a macrostate with a lapse rate has higher entropy, that is where the system will go.

Hans Jelbring
January 20, 2012 9:37 am

Spector says:
January 20, 2012 at 7:34 am
“For me this is a very simple issue:
4. An average surface power radiation of 396 W/m² can only continue with an atmosphere that can absorb a net 156 W/m² from the outgoing radiated power and return it to the surface.”
Any surface radiation power exceeding 100 W/m^2 is bull regardless if it is from equatorial, midlatitude or polar regions during days or night. Just show how this fantasy power radiation changes between day and night in polar regions as an exsample.

DeWitt Payne
January 20, 2012 9:39 am

Bart,
Your argument begs the question. Your postulate that the atmosphere must decrease in temperature with altitude assumes your conclusion. But it doesn’t have to decrease in temperature. The pressure and the density must decrease with altitude. But a transparent atmosphere is perfectly thermally insulated at the top. It can’t lose energy to space. If the surface is at constant temperature, then eventually, so will be the entire volume.
In the other thread you asked how to define the top of the atmosphere. Here’s a definition: The top of the atmosphere is the altitude which includes 99.9998% of the total mass of the atmosphere. That’s ~100km.
As pointed out above, your first crack at the capacitor example was correct. It’s a constant voltage source. Even a constant current source reverts to a constant voltage source at some voltage.

Joel Shore
January 20, 2012 9:40 am

OzWizard says:

N & Z have indeed produced a game-changer here and no thought experiment is needed to understand their ‘Unified Theory of Climate’. Simply stated, their hypothesis consists of their two key equations, (7) and (8).

All they have done is fit some data using a form with many free parameters: There are 4 free parameters in Equation (7) and that is not even including any freedom they may have exercised in choosing the fitting form, choosing how to define T_gb, or even which estimates of the average surface pressure and temperature of various bodies to use.
Hence, it is not surprising that they have fit the data. I got almost as good a fit to the data restricting myself to their particular fitting form when I change 3 of the data points (basically by changing the average temperature of the 3 planets that have a substantial radiative greenhouse effect so that their average temperature is taken to be the conventionally-determined blackbody temperature instead of the observed temperature).
And, that’s another point: Only 3 of the 8 celestial bodies they fit to have a significant radiative greenhouse effect and only for one of them, Venus, is it large enough to be the majority of their calculated surface temperature enhancement. Hence, they are not even fitting data for the greenhouse effect…They are mainly fitting to the effect that a planet can have a number of different average temperatures that are compatible with radiative balance…with airless planets having low average temperatures because of a wide temperature distribution and planets with more atmosphere having higher average temperatures.
One of the strange things about N&Z is how few people have investigated it well enough to even have the most primitive understanding of what they have done!

Frank
January 20, 2012 9:42 am

George Turner and WIllis: I’m interested in the idea of turning the tall cylinder of gas, but let’s start with a horizontal cylinder of gas, which should have the same temperature and pressure throughout its length. Let’s say the cylinder is 1 m2 in diameter, contains 10^4 kg of ideal gas (the same weight of gas as above ever m2 of the earth’s surface), and is 20 km/10 mb tall (99% of the atmosphere). Let’s imagine that there are barriers every meter that are closed during rotation and later opened, so we don’t have to worry about what happens during rotation. Alternatively. we can imagine piston barriers that will allow changes to be made reversibly or irreversibly before opening the barriers. What happens when we rotate the cylinder to vertical and open the barriers reversibly or irreversibly?
Based on what we know about our atmosphere, we can be confident that most of the gas will “fall” to the bottom of the cylinder, increasing the kinetic energy/temperature of the gas at the bottom of the cylinder and therefore it’s pressure (ideal gas law). It certainly seems to me that the cylinder MUST be cold on top and hot at the bottom after rotating. If we didn’t just violate the 2LoT by transferring heat by spontaneously creating a temperature gradient where one didn’t exist before (and I assume we didn’t), then we need to be careful about how we describe entropy in this system.
Alternatively, we could say that the gas at the high end expands under reduced pressure and the gas at the lower end is compressed under higher pressure. However, first we need to explain why the pressure on the gas has changed in these regions. We say the weight of the gas above contributed to the pressure on the gas below, but the gas in this cylinder HAD a pressure before it was rotated. Why is pressure in the vertical position defined by the weight of the gas above while pressure in the horizontal position was not? The answer is that pressure is not really created by the weight of the gas above, it arises (according to the kinetic theory of gases) from momentum transferred by collisions (to the walls of a container or whatever is measuring the pressure). We usually assume that motion in all three directions is ISOTROPIC, but in a gravitational field the speed of the molecules moving upward is slightly less that the speed of the molecules moving downward. The “weight of the gas above” appears to transferred downward by non-isotropic motion of the gas molecules in a gravitational field. (See Section 2.3 of your Caballero reference.)
In Brown’s explanation of molecules crossing a plane, he says that the molecules moving up and down :
“have to have exactly the same velocity distribution moving in either direction”
This statement appears to be incorrect. If there weren’t a velocity difference, the pressure at the top and bottom of the atmosphere would be identical. The molecules moving upward have very slightly less energy that the average for their altitude (given the local temperature) and those moving downward have slightly more energy. As they move past each other, they will create a temperature gradient.

DeWitt Payne
January 20, 2012 9:47 am

Can we lose the argument that the collision rate, i.e. pressure, has an effect on measured temperature. It doesn’t. A thermometer in contact with a gas at temperature T at low pressure will simply take longer to equilibrate than a thermometer in contact with a gas at the same temperature but higher pressure.
For a gravitationally bound atmosphere at constant temperature, the total energy content per cubic meter decreases exponentially with altitude. The density drops much faster with altitude than the gravitational potential energy increases. See graph here.

January 20, 2012 9:51 am

mkelly said, “Gravity has NO AFFECT ON TEMPERATURE.”
Everything is relative 🙂
http://redneckphysics.blogspot.com/2012/01/that-dang-cartoon-again.html

DeWitt Payne
January 20, 2012 9:59 am

Hans Jellbring,

Any surface radiation power exceeding 100 W/m^2 is bull regardless if it is from equatorial, midlatitude or polar regions during days or night. Just show how this fantasy power radiation changes between day and night in polar regions as an exsample.

Here’s a plot of upwelling IR radiation measured over 24 hours at Desert Rock, NV by a SURFRAD station there. It looks to be more than 100W/m² to me. Note that the time axis is UTC. Desert Rock is -8 hours from UTC so local noon would be 2000 on the time axis.
There are seven SURFRAD stations in the US. You can access the data here.