Guest Post by Willis Eschenbach
Since at least the days of Da Vinci, people have been fascinated by perpetual motion machines. One such “perpetuum mobile” designed around the time of the civil war is shown below. It wasn’t until the development of the science of thermodynamics that it could be proven that all such mechanisms are impossible. For such machines to work, they’d have to create energy, and energy cannot be either created or destroyed, only transformed.
I bring this up for a curious reason. I was reading the Jelbring hypothesis this afternoon, which claims that greenhouse gases (GHGs) are not the cause of the warming of the earth above the theoretical temperature it would have without an atmosphere. Jelbring’s hypothesis is one of several “gravito-thermal” theories which say the heating of the planet comes from gravity rather than (or in some theories in addition to) the greenhouse effect. His thought experiment is a planet with an atmosphere. The planet is isolated from the universe by an impervious thermally insulating shell that completely surrounds it, and which prevents any energy exchange with the universe outside. Inside the shell, Jelbring says that gravity makes the upper atmosphere colder and the lower atmosphere warmer. Back around 2004, I had a long discussion on the “climateskeptics” mailing list with Hans Jelbring. I said then that his theory was nothing but a perpetual motion machine, but at the time I didn’t understand why his theory was wrong. Now I do.
Dr. Robert Brown has an fascinating post on WUWT called “Earth’s baseline black-body model – a damn hard problem“. On that thread, I had said that I thought that if there was air in a tall container in a gravity field, the temperature of the air would be highest at the bottom, and lowest at the top. I said that I thought it would follow the “dry adiabatic lapse rate”, the rate at which the temperature of dry air drops with altitude in the earth’s atmosphere.
Dr. Brown said no. He said that at equilibrium, a tall container of air in a gravity field would be the same temperature everywhere—in other words, isothermal.
I couldn’t understand why. I asked Dr. Brown the following question:
Thanks, Robert, With great trepidation, I must disagree with you.
Consider a gas in a kilometre-tall sealed container. You say it will have no lapse rate, so suppose (per your assumption) that it starts out at an even temperature top to bottom.
Now, consider a collision between two of the gas molecules that knocks one molecule straight upwards, and the other straight downwards. The molecule going downwards will accelerate due to gravity, while the one going upwards will slow due to gravity. So the upper one will have less kinetic energy, and the lower one will have more kinetic energy.
After a million such collisions, are you really claiming that the average kinetic energy of the molecules at the top and the bottom of the tall container are going to be the same?
I say no. I say after a million collisions the molecules will sort themselves so that the TOTAL energy at the top and bottom of the container will be the same. In other words, it is the action of gravity on the molecules themselves that creates the lapse rate.
Dr. Brown gave an answer that I couldn’t wrap my head around, and he recommended that I study the excellent paper of Caballero for further insight. Caballero discusses the question in Section 2.17. Thanks to Dr. Browns answer plus Caballero, I finally got the answer to my question. I wrote to Dr. Brown on his thread as follows:
Dr. Brown, thank you so much. After following your suggestion and after much beating of my head against Caballero, I finally got it.
At equilibrium, as you stated, the temperature is indeed uniform. I was totally wrong to state it followed the dry adiabatic lapse rate.
I had asked the following question:
Now, consider a collision between two of the gas molecules that knocks one molecule straight upwards, and the other straight downwards. The molecule going downwards will accelerate due to gravity, while the one going upwards will slow due to gravity. So the upper one will have less kinetic energy, and the lower one will have more kinetic energy.
After a million such collisions, are you really claiming that the average kinetic energy of the molecules at the top and the bottom of the tall container are going to be the same?
What I failed to consider is that there are fewer molecules at altitude because the pressure is lower. When the temperature is uniform from top to bottom, the individual molecules at the top have more total energy (KE + PE) than those at the bottom. I said that led to an uneven distribution in the total energy.
But by exactly the same measure, there are fewer molecules at the top than at the bottom. As a result, the isothermal situation does in fact have the energy evenly distributed. More total energy per molecules times fewer molecules at the top exactly equals less energy per molecule times more molecules at the bottom. Very neat.
Finally, before I posted my reply, Dr. Brown had answered a second time and I hadn’t seen it. His answer follows a very different (and interesting) logical argument to arrive at the same answer. He said in part:
Imagine a plane surface in the gas. In a thin slice of the gas right above the surface, the molecules have some temperature. Right below it, they have some other temperature. Let’s imagine the gas to be monoatomic (no loss of generality) and ideal (ditto). In each layer, the gravitational potential energy is constant. Bear in mind that only changes in potential energy are associated with changes in kinetic energy (work energy theorem), and that temperature only describes the average internal kinetic energy in the gas.
Here’s the tricky part. In equilibrium, the density of the upper and lower layers, while not equal, cannot vary. Right? Which means that however many molecules move from the lower slice to the upper slice, exactly the same number of molecules must move from the upper slice to the lower slice. They have to have exactly the same velocity distribution moving in either direction. If the molecules below had a higher temperature, they’d have a different MB [Maxwell-Boltzmann] distribution, with more molecules moving faster. Some of those faster moving molecules would have the right trajectory to rise to the interface (slowing, sure) and carry energy from the lower slice to the upper. The upper slice (lower temperature) has fewer molecules moving faster — the entire MB distribution is shifted to the left a bit. There are therefore fewer molecules that move the other way at the speeds that the molecules from the lower slice deliver (allowing for gravity). This increases the number of fast moving molecules in the upper slice and decreases it in the lower slice until the MB distributions are the same in the two slices and one accomplishes detailed balance across the interface. On average, just as many molecules move up, with exactly the same velocity/kinetic energy profile, as move down, with zero energy transport, zero mass transport, and zero alteration of the MB profiles above and below, only when the two slices have the same temperature. Otherwise heat will flow from the hotter (right-shifted MB distribution) to the colder (left-shifted MB distribution) slice until the temperatures are equal.
It’s an interesting argument. Here’s my elevator speech version.
• Suppose we have an isolated container of air which is warmer at the bottom and cooler at the top. Any random movement of air from above to below a horizontal slice through the container must be matched by an equal amount going the other way.
• On average, that exchange equalizes temperature, moving slightly warmer air up and slightly cooler air down.
• Eventually this gradual exchange must lead to an isothermal condition.
I encourage people to read the rest of his comment.
Now, I see where I went wrong. Following the logic of my question to Dr. Brown, I incorrectly thought the final equilibrium arrangement would be where the average energy per molecule was evenly spread out from top to bottom, with the molecules having the same average total energy everywhere. This leads to warmer temperature at the bottom and colder temperature at elevation. Instead, at thermal equilibrium, the average energy per volume is the same from top to bottom, with every cubic metre having the same total energy. To do that, the gas needs to be isothermal, with the same temperature in every part.
Yesterday, I read the Jelbring hypothesis again. As I was reading it, I wondered by what logic Jelbring had come to the conclusion that the atmosphere would not be isothermal. I noticed the following sentence in Section 2.2 C (emphasis mine):
The energy content in the model atmosphere is fixed and constant since no energy can enter or leave the closed space. Nature will redistribute the contained atmospheric energy (using both convective and radiative processes) until each molecule, in an average sense, will have the same total energy. In this situation the atmosphere has reached energetic equilibrium.
He goes on to describe the atmosphere in that situation as taking up the dry adiabatic lapse rate temperature profile, warm on the bottom, cold on top. I had to laugh. Jelbring made the exact same dang mistake I made. He thinks total energy evenly distributed per molecule is the final state of energetic equilibrium, whereas the equilibrium state is when the energy is evenly distributed per volume and not per molecule. This is the isothermal state. In Jelbrings thought experiment, contrary to what he claims, the entire atmosphere of the planet would end up at the same temperature.
In any case, there’s another way to show that the Jelbring hypothesis violates conservation of energy. Again it is a proof by contradiction, and it is the same argument that I presented to Jelbring years ago. At that time, I couldn’t say why his “gravito-thermal” hypothesis didn’t work … but I knew that it couldn’t work. Now, I can see why, for the reasons adduced above. In addition, in his thread Dr. Brown independently used the same argument in his discussion of the Jelbring hypothesis. The proof by contradiction goes like this:
Suppose Jelbring is right, and the temperature in the atmosphere inside the shell is warmer at the bottom and cooler at the top. Then the people living in the stygian darkness inside that impervious shell could use that temperature difference to drive a heat engine. Power from the heat engine could light up the dark, and provide electricity for cities and farms. The good news for perpetual motion fans is that as fast as the operation of the heat engine would warm the upper atmosphere and cool the lower atmosphere, gravity would re-arrange the molecules once again so the prior temperature profile would be restored, warm on the bottom and cold on the top, and the machine would produce light for the good citizens of Stygia … forever.
As this is a clear violation of conservation of energy, the proof by contradiction that the Jelbring hypothesis violates the conservation of energy is complete.
Let me close by giving my elevator speech about the Jelbring hypothesis. Hans vigorously argues that no such speech is possible, saying
There certainly are no “Elevator version” of my paper which is based on first principal physics. It means that what I have written is either true or false. There is nothing inbetween.
Another “gravito-thermal” theorist, Ned Nikolov, says the same thing:
About the ‘elevator speech’ – that was given in our first paper! However, you apparently did not get it. So, it will take far more explanation to convey the basic idea, which we will try to do in Part 2 of our reply.
I don’t have an elevator speech for the Nikolov & Zeller theory (here, rebuttal here) yet, because I can’t understand it. My elevator speech for the Jelbring hypothesis, however, goes like this:
• If left undisturbed in a gravity field, a tall container of air will stratify vertically, with the coolest air at the top and the warmest air at the bottom.
• This also is happening with the Earth’s atmosphere.
• Since the top of the atmosphere cannot be below a certain temperature, and the lower atmosphere must be a certain amount warmer than the upper, this warms the lower atmosphere and thus the planetary surface to a much higher temperature than it would be in the absence of the atmosphere.
• This is the cause of what we erroneously refer to as the “greenhouse effect”
Now, was that so hard? It may not be the best, I’m happy to have someone improve on it, but it covers all the main points. The claim that “gravito-thermal” theories are too complex for a simple “elevator speech” explanation doesn’t hold water.
But you can see why such an elevator speech is like garlic to a vampire, it is anathema to the “gravito-thermal” theorists—it makes spotting their mistakes far too easy.
w.
Alexander Harvey says:
January 20, 2012 at 4:36 am
Alex, I’m sorry but I don’t have time to wander through all of that. My suggestion is to boil it down, then boil it down again, and re-post it.
w.
Willis says
” To believe that gravity can affect temperature, you have to have a weak grasp of physics, an unshakable belief in your correctness, and a willingness to ignore a bunch of folks who actually understand physics. That’s a bad combo.”
Yet only last week Willis believed in an adiabatic distribution for a thermally isolated column of gas in a gravitational field.
This week he has ‘seen the light’.
Don’t be so hard on yourself Willis.
Willis,
You contend that no one can explain the Jelbring gravito-thermal hypothesis clearly, which means that no one understand the Jelbring gravito-thermal hypothesis, which is prime facie evidence that it is incorrect. Moreover, you indicate in this post that if the Jelbring gravito-thermal hypothesis were correct, it would contradict the second law of thermodynamics, another good reason for assuming it to be false.
But then you chide Qark for ridiculing the discussion, of something no one can explain.
I can only conclude that you are merely trying to keep the pot boiling for no reason but the fun of it. In which case, I think Qark’s contribution was as worthwhile as most others.
But if that is not the case, I should be glad of your response to this seemingly simple plece of logic, which seems to settle the matter:
At equilibrium, planet-wide outgoing radiation at the top of the atmosphere matches planet-wide incoming radiation at the top of the atmosphere. But if the atmosphere is transparent (i.e., without significant GHGs), outgoing radiation at the top of the atmosphere must be the same as outgoing radiation at the surface of the planet, which means that the mean surface temperature must be the same with or without an atmosphere.
If that is correct, it means that gravity does not account for the greenhouse effect.
If it is incorrect, for the reason Jelbring contends, i.e., that gravity causes an atmospheric temperature gradient that accounts for the greenhouse effect, then planet-wide radiation at the top of the atmosphere must exceed planet-wide incoming radiation, meaning that the planet is luminous. However, we know that the planet is not luminous.
QED
I’m probably joining this discussion too late to add anything useful. To my simple mind there are two things to consider which I have difficulty applying to the atmosphere
First, the diurnal bulge/atmospheric bulge is a bit like a pump which compresses, and as a result heats, the atmosphere and then expands and cools the atmosphere? I assume the heating, however small is greatest at the earth’s surface.
Secondly (as a result of all the references to one molecule at time) I remember when we did a short course on Information Theory http://en.wikipedia.org/wiki/Information_theory we had to work out the theoretical maximum temperature we could heat a teapot to with a fixed amount of boiling water, in order to make a decent cup of tea. http://englishtea.org.uk/how_to_make_tea.html. The maximum temperature is achieved when water is added and removed from the teapot 1 molecule of H2O at a time. As we are dealing thermodynamics, presumably Information Theory is relevant but rarely if ever mentioned
Despite being described as a “gravito-thermal theorist”, Nikolov & Zeller seem to have gone to extraordinary lengths to actually mention the word “gravity”. It appears in the text of their Unified Theory of Climate precisely twice.
Gravity, by itself, does not produce heat – surface temperatures on the Moon for example would be identical regardless of whether it’s gravity is one-sixth or six times that experienced on Earth. So to that extent at least Willis, you are entirely correct.
Now consider this thought-exercise :
Introduce an atmosphere equivalent in mass to that of the Earth to the Moon. The vertical structures of those atmospheres would surely be profoundly different according to whether the Moon’s gravitational attraction was one-sixth or six times that of the Earth.
Now consider two “Moons” with identical incoming radiation, identical atmospheric mass and composition, but atmospheres with profoundly different structures due to their differing gravitational attraction.
Identical surface temperatures or not?
Hope that helps……..
I skipped most of the comments in this thread, my apologies if this has been said already.
Willis,
You are not going to get the elevator pitch explanation of N&Z that you demand because N&Z relies not on a single paradigm shift, but on several. No elevator pitch can encompass all of them while still articulating a cohesive whole. If you want to understand N&Z, your going to have to allow it to be broken up into pieces, the paradigm shift of each piece understood, and then put the whole thing back together.
I suggest you start with the constant and continuous misaplication of SB Law as it applies to this discussion as I think that is the single major hurdle to get passed. Every thread I see this topic being discussed, I see the same claims. 240 w/m2 = 253K and 288K = 390 w/m2. These numbers are totaly and completely wrong.
SB Law is valid for a very specific case, and that case only. It is valid for a body at equilibrium exposed to uniform radiance and which is at uniform temperature. The earth is NOT exposed to uniform radiance, it is exposed to radiance which ranges from 0 w/m2 to over 1,000 w/m2 and which fluctuates wildly in both space and time. The temperature of the earth as measured is similarly not uniform, it varies in space (latitude, longitude, altitude, time of day, season of year, and orbital variance).
Until we drop the notion that we can arrive at meaningful numbers for earth temperature based upon averages of insolation and temperature compared via SB Law, there is no value whatsoever in discussing the balance of the N&Z hypothesis.
I note in closing Willis that your approach to questioning N&Z has been much more “attack mode” than anything else, and I think that is becoming a stumbling block in terms of having a productive discussion.
dmh
Robert Brown says:
January 20, 2012 at 9:34 am
Final overall comment and off to work.
“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.”
Well, if you have read my paper I am not talking about an PM. Willis does so it his problem. I just want to know what is wrong with my paper. For your information an energy generating machin has been constructed to use the energy difference in the oceans. It will of course diminish the temperature difference as time is passing. I don´t see theoretical problem to do the same between the surface temperature and the temperatur at the top of Mount Everest. It is a practical problem of course.
In the case of my model atmosphere there is a temperature difference that can be used for energy extraction. That can only be done by moving energy outside the closed insulated atmosphere. In such a case energy will be removed from the inclosed atmospherea and its average temperature would sink. However such a machine is not allowed since the atmosphere was inclosed and no energy at all was allowed to enter or leave the system. You and Willis seem unable to recognise the assumtions that has been made in the text.
The theory tells that no energy can be extracted within a system that is at maximum entropy and that is also my opinion as long as we stay within the closed system. Willis is favouring a PM and I am not, he has been doing so for 8 years. To avoid more irrelevant comments I want to make clear that ALL content within the closed system consists of ideal gases as is told in the assumptions.
An Elevator Speech to prove isothermal result using two tubes of different gases.
The situation we analyze is a uniformly insolated ground in a spherically symetric system with some gravitational gradient. The ground is at a constant temperature T(r=ground). We erect TWO vertical tubes, insulated from the environment and each other, except at two points r=ground, and r=B. We put a different gas (ideal or non-ideal) in each tube. The only difference we require is that they have different specific heat values (Cpx and Cpy). The system must be at equilibrium by definition.
Let us assume that at equilibrium the atmosphere is NOT isothermic, but is a function of r. If so, there must be a real lapse rate in each tube. The Lapse rate (dT/dr) is a function of the Specific Heat of the gas(Cp(i)) and the gravitational accel (g). Both tubes experience the same g, but they have different Cp gasses. Therefore, there must be Difference Equilibrium Lapse rates in the two tubes. At point A, they can have the same temperature, but at point B they must have different temperatures. If they have different temperatures at B, then you can have heat flow at B, which means the system is NOT in Equilibrium. If not isothermal, then not in equillibrium if Cp’s are different.
Only if the gases are isothermal at all z, can the system stay in Equilibrium.
capt. dallas says:
January 20, 2012 at 9:51 am
mkelly said, “Gravity has NO AFFECT ON TEMPERATURE.”
It was actually Jeremy that said “Gravity has no affect (effect) on temperature.” I was asking him to put it in the form of the first law Q=U+W.
Tallbloke said:
I don’t think so Tallbloke. I have spent the latter half of my 60+ years on Earth discovering that what I “knew” is often enough false. That is, my ignorance has increased. Whenever someone says to me “you are ignorant” I take it as a compliment 🙂
That said, a very great deal of what I know has been well-tested and therefore I currently take to be true. In order to learn, we must continually test what we believe to be true.
Additionally, in order for any significant amount of comments on this thread to be not-ignorant we would have to discard the Law of Contradiction.
Embellishment to Rasey 11:09 Two tube example.
Modification 1: Both tubes are optically transparent, but thermally insulated. Fill them with different NON-greenhouse gases, different Specific Heats (Cp). Result must be isothermic.
Modification 2: Now fill one of the tubes with a strong Greenhouse gas. It is optically transparent so it should be absorbing and emitting lots of IR. By the same argument as 11:09, if that tube is not isothermal, then there will be different temperatures at B and non-equilibrium heat flow. So this GHG tube must also be isothermal. But how can it be so if the pressure of the GHG varies with r, and therefore its alleged Greenhouse capacity varies by r. How can it remain isothermal?
(shhh… unless GHG doesn’t matter?)
“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. ”
This is true.
But two things.
One it is gravity which causes more density near surface and less density higher- that would be a difference of temperature.
Two: the atmosphere isn’t creating heat. But gravational body can create heat- it will have radioactive elements which create heat and with “an impervious thermally insulating shell”
there isn’t temperature limit, heat keeps building.
I suppose if got rid of all radioactive elements [or only used elements with extremely long half-lives] one would lower the amount of heat generated. I think a pure sample with no radioactive elements wouldn’t be easy to make or find- not sure if or what this could done- or if it would remain so.
Now if you have atmosphere so large it enter the realm of being a planetary type mass, then the atmosphere itself could generate heat. But Earth type atmospheres or Venus type atmospheres are insignificant in regard to planetary masses. Whereas neptune’s mass is mostly “ocean” and “air”- Neptune and other gas giants do have enough atmosphere to have planetary scale atmospheres.
So with this “impervious thermally insulating shell” one could get endless energy from a planet with an atmosphere.
Willis,
With some trepidation I offer this change of your thought experiment…
Assume a long, perfectly insulated tube. One end is anchored on a planet’s surface the other end extends to vacuum ( where it is also perfectly insulated). Assume the tube contains an ideal gas. Assume also that the planet’s surface gravity equal s earth’s (1 g ) and the planet’s radius is also equal to earth’s. No energy is added to the tube, and no energy escapes the confines of the tube. assume the density of the gas is equal to the the density of earth’s air at sea level. Last assumption: Assume the ideal gas is already at vertical (and horizontal) thermal equilibrium.
So the initial conditions are the tube is at the same temp for all altitudes and the density profile is similar to earth’s atmosphere.
Rhetorical question: What happens to the temp as a function of time, and altitude?
Here’s my answer: The temp says constant throughout the length of the tube forever.
here’s how I look at the situation…Consider a plane P at, say, 1Km above the surface (and parallel to the surface) that divides the tube into 2 sections, A and B. The plane does not hinder (or aid) the gas molecules.
In order for the temp to change so that there is higher temp in section A, the average kinetic energy of the molecules in A must somehow increase (that’s the definition of increased temp). However this would be equivalent to Maxwell’s Demon setting up shop at plane P, only allowing fast molecules into A, while only allowing slow molecules into B. Since that cannot happen, the temp in A can not change (also true for B).
I look at this Thought Experiment as your T.E. running backwards in time.
Thanx for all your postings. You are an inspiration.
Tom M.
quondam said @ur momisugly January 20, 2012 at 6:57 am
Thanks for that insight, Quondam.
Johan i Kanada says:
January 20, 2012 at 4:09 am T
“This argument should be possible to resolve in 5 min by any reputable physics professor.”
Unfortunately, whatever this physics professor said, he would be immediately overwhelmed by lots of commentators here saying that it wasn’t true.
You have now entered the twilight zone, where idiotic comments far outweigh the occasional science that you may come across. The denizens of this zone do not believe in the greenhouse effect, because they don’t want to. They do not understand science (but that doesn’t matter) and so latch on to any passing pseudo- science – as promulgated by various anti-science blogs. As Willis Eschenbach said ” you are fighting basic ignorance of science, you will be deluged with ignorant people”. And in this twilight zone, ignorance swamps knowledge,
Having said that, the problem here is that not easy to solve. There is no empirical test which can resolve it. I think that different physicists could easily arrive at different conclusions based on mind experiments.
From an earlier post:
“The water at the bottom of the ocean is under great pressure. Does 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.”
Luke says this is because the oceans are heated from the top. But this wouldn’t explain why the water in a domestic hot water tank is hotter at the top. So, good guess Luke, at the obvious wrong answer, but null points.
Tallbloke says that “Not only that but water is incompressible”. The right answer! – have a cigar.
!
Robert Brown says:
January 20, 2012 at 9:11 am
Robert, I don’t provide long answers to condescending replies so I’ll just repeat my earlier request:
tallbloke says:
January 19, 2012 at 4:34 pm
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).
And while your checking those out, would you be so kind as to consider my refutation of your ‘slices’ argument:
“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.
Thank you.
I read the contribution by George Turner:
“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.”
And Willis’ reply that there is more than half the (mass) of the atmosphere near the bottom. I was thinking as I read George that I would have flipped it at the centre point of mass in which case the objection does not apply. Flip a cylinder of atmosphere that is well above the surface about its centre of mass and allow it to float vertically (as it wll tend to do). The mass remains the same, the centre of mass will remain the same distance above the surface at all times even if the (‘mechanical’) flipping point rises or falls, the flipping requires no energy. The same compression and decompression mentioned by George applies and there will not longer be an isothermal state. Having now perturbed the initial isothermic condition, it will not re-establish itself even if perfectly insulated.
Why? As the atmosphere is not a solid, gas molecules will move up and down randomly. As a parcel of molecules rises the temperature will drop due to expansion. Yes, the potential energy with respect to the surface rises, but the temperature drops and this is about temperature which is a measure of only one type of energy. The thesis states that there will be a difference in temperature, top and bottom, it does not make claims about a difference in total energy with respect to the surface of a gravitational object. Work accomplished heating a falling molecule has to be accounted for by cooling taking place elsewhere in the system. It cannot come from the bottom of the system.
One can make an argument that the total energy in any molecule is constant at all heights but I doubt that applies to any molecule in a spherical atmosphere. If it applies to a particular sphere (because of a perfect balance between sperical expansion and elevation) it cannot also apply to a ‘flat planet’ with a cylinderical sample of atmosphere because the volumeetric expansion rate is different (trumpet v.s. clyinder). Because it cannot be correct for both, I suspect it is generally correct for neither save in special cases.
From an initial isothemal state all molecules falling will warm and all molecules rising will cool. The heat will accumulate at the bottom. There is no work done. Gravity does not do any work. The heat will shift towards the bottom because gases move without input of energy and cool or heat adibatically.
The idea of using the temperature difference between the hot and cold zones to generate power is a good one. It will work, but will cool the whole atmosphere in the process. It was written above as if all the heat from below would be vented near the top of the atmosphere, therefore that would allow the heat to migrate down again and this be recycled, but this description is incomplete. Energy extracted in the form of energy would be subtracted from the heat processed, providing net cooling by exactly the amount of the energy extracted (including friction). So it would work for a while, converting the atmosphere’s heat into electrical or mechanical energy. It is exactly the same as using the temperature differential between the surface and the ocean deeps to generate electricity. It works (quite well) but it cools the ocean in the process and it is not perpetual.
In the Elevator:
1. Gas molecules move about with no external input of energy. Therefore they may rise or fall in the atmosphere over time.
2. It is well established that gases cool when decompressed and heat when they are compressed. In a free atmosphere above a spherical, insulated planet, molecules are free to compress and decompress as they move vertically. There is no work performed during this process because they are drifting in free space. The total heat content of the system remains constant.
3. If an atmosphere was initially isothermal, the higher elevation gases would have to have been artficially heated to be at the same temperature while also being in a decompressed state. The lower gases would have to have been artificially cooled to be as the same temperature and simultaneously in a compressed state.
4. As the gases move randomly about the vertical column, the hot molecules dropping from above will carry heat downwards, increasing in temperature above the initial average. Lower gases rising will cool by adiabatic expansion below the initial average. There is no net heating or cooling in the atmosphere.
5. After a time, when equlibrium is established (no net change in temperature of any horizontal slice of the atmosphere) it will be warmer at the bottom and colder at the top. The direct cause for this temperature difference is gravity and the effect is observed because of the size of the system (large) and the lack of any external, gravitational perturbations.
6. If gravity is increased, or if the total volume of atmosphere is increased, the equilibrium temperature at the bottom will increase. An average temperature can be calculated, as can an elevation at which this temperature will be observed.
Very interesting discussion Willis, and nicely done.
The only thing that gets me is the idea that the gas would be isothermal (temperature being kinetic energy) violates the conservation of energy. As a gas molecule moves away from the gravity source, it MUST lose kinetic energy to potential energy. As it falls back down, it’ll convert that potential energy back to kinetic energy. Ergo, energy is conserved. But -temperature- is the observation of kinetic energy, not potential energy.
In that regard, a higher elevation must be cooler in -temperature-, even if the heat content (total energy) is the same. I think that’s the problem. We conflate temperature with heat, when they are not the same thing.
You can have two objects at different temperature, but if they are equal in heat, so that energy cannot transfer one way or the other, this temperature difference must be maintained. And we can do this by turning kinetic energy (temperature) into potential energy. No heat is lost.
I’m not defending the gravity thermal theories, but I am expressing how I cannot understand this thought experiment in terms of energy conservation. And I wonder if the ideas about heat and temperature have gotten crossed. Or maybe I am fundamentally misunderstanding?
But still, raising up means losing kinetic energy to potential energy, and temperature is kinetic energy not potential energy. Heat transfer can only happen through kinetic energy, not potential energy… So to conserve energy, temperature must decline while raising above a gravity source… Likewise, if you stand in a gas close to the gravity source you’ll get hit by more collisions than if you sit above where more energy is locked in potential energy. And, if you used your body’s temperature (kinetic energy) to push you upwards against gravity, you’d cool your body down as more energy was put into potential, right? You’d still have the same amount of energy in you, but you’ve transformed it. That’s the only logical conclusion I can come to. Isothermal (temperature wise) while moving in a gravity well doesn’t make sense to me at all, and nor do we ever see that in nature in atmospheres.. to my knowledge.
Again, maybe I am missing something.
I have to disagree here. It is possible to make energy between the ground and the top of the atmosphere because the ground is warmer than space from the point of view of the atmosphere. The atmosphere does not see the Sun because it does not absorb in the UVs. So space is very cold for it. If there was a blob of nitrogen in orbit around the Earth, it would be cold. So it would be possible to make energy between this blob of gas and the ground. Don’t forget, the ground is warmer than space in the IR.
Think about a one molecule atmosphere. It receives or gives energy to the ground every time it hits it. The vertical kinetic energy of the molecule near of the ground can be different every time. But each time, it slows down as it goes up and then it speeds up when it comes back down. If you make an average over multiple hits to the ground, you will find these 2 facts:
1- It is more often near of the ground(higher pressure at the ground level).
2- It has more kinetic energy near of the ground(Higher temperature at the ground level).
If you increase the number of molecules, each of them will still lose kinetic energy as it goes up.
Now, let’s make a little thought experiment. Let’s imagine an invisible layer around the Earth at a certain altitude. The number of molecules passing from under to over the layer has to be the same as the number of molecules going the other way at equilibrium. The amount of kinetic energy also has to be the same at equilibrium. Now let’s put a second layer very near of the first to look at the derivative. What’s been said in the first part of this paragraph still holds true. But sometimes, a molecule will pass through the lower layer and come to vertical halt between the layers and it will go back down through the lower layer without passing the higher layer. This is where the differential of pressure appears. Every time a molecule passes through both layers, it either loses kinetic energy on its way up or gain kinetic energy on its way down. If 2 molecules hit each other, you have to look at the pair of molecules. The center of mass can turn around between the two layers, pass the two layers in an upward or downward motion. And the pair of molecules will act like a single molecules if you calculate the differential of pressure or the differential of kinetic energy between those two layers.
John Marshall says: “I also ask my Jupiter question again. Why does this gas giant radiate more heat than it receives from the sun. your argument above makes this impossible.
My astrophysics instructor said he believed there were decaying fissionables at the core.
Stephen Rasey says:
January 20, 2012 at 11:09 am
“An Elevator Speech to prove isothermal result using two tubes of different gases.
Let us assume that at equilibrium the atmosphere is NOT isothermic, but is a function of r. If so, there must be a real lapse rate in each tube. The Lapse rate (dT/dr) is a function of the Specific Heat of the gas(Cp(i)) and the gravitational accel (g). . If they have different temperatures at B, then you can have heat flow at B, which means the system is NOT in Equilibrium. If not isothermal, then not in equillibrium if Cp’s are different.
Only if the gases are isothermal at all z, can the system stay in Equilibrium.”
I certainly don´t believe that an elevator speach is the way to perform scientific work.
You are free to express your opinion whatever it is but in this case it is not based in scientific reasoning and definitly not based on first principle physics.
The adiabatic temperature lapse rates that will develope (if long time enought will pass) in your examples are given by dT/dZ = -g/Cp1 and the other will be given by dT/dz= -g/Cp2. A remarkable fact is that both these laps rates are independant of the absolute amount of energy that was inclosed in each tube. In both cases the energy in two arbitrarily chosen equal mass units will carry the same amount of energy. Remember that the 1:st a and 2:nd law of thermodynamics apply to energy, not to temperature. When gravity is not included the second law can be formulated in terms of temperature even if it is not recommended (but very common in anglo litterature).
davidmhoffer says:
No…They are not “totally and completely wrong”. The 288 K = 390 W/m^2 is in fact quite accurate for the Earth’s present temperature distribution to a good approximation (introducing about 2K of error with a generous estimate).
The 240 W/m^2 = 255 K is a bit dicier since it is for a hypothetical world that is a little hard to specify and could have a somewhat broader temperature distribution. However, what can be said rigorously is that a blackbody radiating an average of 240 W/m^2 could have an average temperature no higher than 255 K. It could have an average temperature lower than that (which is what N&Z show with their T_sb calculation that assumes an extremely broad temperature distribution since the local instantaneous temperature is determined by radiative balance with the local instantaneous solar insolation). [To the extent that the Earth is not exactly a blackbody in the mid- and far-infrared, the average temperature could be higher, but for the terrestrial surface, we are talking about 3 K at about the outside limit. And, the fact that the “non-uniform effect” and the “not exactly a blackbody effect” go in opposite directions means the two effects tend to offset each other to some degree.]
By the way, for those who want a more precise quantification, I have derived a formula for the difference between the fourth root of the average of T^4 and the direct average of T. The formula is that this difference is given by
difference = (3/2)*(sigma^2)/T_ave
where sigma is the standard deviation of the distribution of T and T_ave is the average value for the distribution (in absolute temperature units, like Kelvin). [Although this formula is an expansion good for small sigma/T_ave, I have verified that it gives answers within 2% of the actual difference for two distributions (Gaussian and flat “box” distributions) for sigma/T_ave < 0.10 (which is larger than any reasonable estimate I can make of the relevant value for Earth).]
Dave, we all know that you have become completely obsessed with this particular issue…but you have failed to refute both my and Willis's rough quantifications of its magnitude and hence you are continuing to "make a mountain out of a molehill" on this subject.
ShrNfr says onJanuary 19, 2012 at 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??”
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If it can help – my advice to you – is to go back in history and look up where it all originates and how “Global Warmists” or “CAGW” alarmists get it wrong, even right from the start, with written history.
The 18th and 19th Centuries saw many famous Philosophers/researchers. (They did not all live long enough to be called Scientists – as that title is fairly new)
Let me quote, if I may, Timothy Casey B.Sc. (Hons): Consulting Geologist who has put the papers of some of them online: “According to Weart (2003, Flannery (2005) and Archer (2009) the “Greenhouse Effect” originates with Fourier, ——.” – And further on: “Arrhenius claimed:
Fourier maintained that the atmosphere acts like the glass of a hothouse, because it lets through the light rays of the sun but retains the dark rays from the ground.”
Nothing could be more wrong – or further from the truth – Put “Fourier (1824) as translated by Burgess (1837)” into your “Computer search engine” or http://geologist-1011.net and see what comes up. You will learn a lot – including, maybe, why davidmhoffer says what he says on January 20, 2012 at 10:49 am.
Reading Fourier’s paper from 1824 really is worth the effort and Timothy Casey B.Sc is a pretty good teacher too.
O H D
Oh, I think I should also point out that I was ignoring radiative transfer for heat, since that isn’t part of the thought experiment. But that necessarily energy is lost to space as radiation which cools everything over time, and without energy input, there will be no energy to propel gas molecules up against gravity. So then, after a certain amount of time, the entire atmosphere will settle down upon the surface with no more “bouncing” molecules jumping around.
But since the sun warms our surface, it acts to “bounce” molecules upwards, where they bounce against each other, etc, and act as a kinetic battery for storing energy. But again, as a ball, or molecule, bounces upwards, it loses energy and slows down (temperature decrease if temperature is the only thing driving this as it is in the atmosphere of our thought experiment), then plummets and warms back up, bounces again, and so forth. It’s just like watching balls bounce around a vibrator machine.
So… it seems to be you will have a thermal gradient, no matter what! It’s just will this gradient make apparent temperatures in the atmosphere at the surface higher than the S-B surface temperature?
Again, not defending these gravity-thermal theorems, but I do fully believe that gravity creates and maintains a thermal gradient for altitude above the surface (this also ignores the increasing volume of the sphere as we raise above the surface which decreases temperature and/or pressure).
I dunno, those are my thoughts, Willis. I actually think Dr. Brown was wrong then.
And could you generate energy from the atmosphere using a thermocoupler? Of course! But it would be ENORMOUS to have to reach high enough from the surface up to altitudes where the temperature drops (30,000 feet is pretty dang cold 😉 ).
Stephen Rasey good post.
For your first proposed experiment if you use argon and hydrogen you should get about 2K difference in 100m tubes which should be reasonably practical and measurable.
I like even better your second proposed experiment.
….” But how can it be so if the pressure of the GHG varies with r, and therefore its alleged Greenhouse capacity varies by r. How can it remain isothermal?
(shhh… unless GHG doesn’t matter?)”…..
Just goes to show that for isothermal/adiabatic distribution nothing can save the greenhouse effect.