Guest Post by Willis Eschenbach
Since at least the days of Da Vinci, people have been fascinated by perpetual motion machines. One such “perpetuum mobile” designed around the time of the civil war is shown below. It wasn’t until the development of the science of thermodynamics that it could be proven that all such mechanisms are impossible. For such machines to work, they’d have to create energy, and energy cannot be either created or destroyed, only transformed.
I bring this up for a curious reason. I was reading the Jelbring hypothesis this afternoon, which claims that greenhouse gases (GHGs) are not the cause of the warming of the earth above the theoretical temperature it would have without an atmosphere. Jelbring’s hypothesis is one of several “gravito-thermal” theories which say the heating of the planet comes from gravity rather than (or in some theories in addition to) the greenhouse effect. His thought experiment is a planet with an atmosphere. The planet is isolated from the universe by an impervious thermally insulating shell that completely surrounds it, and which prevents any energy exchange with the universe outside. Inside the shell, Jelbring says that gravity makes the upper atmosphere colder and the lower atmosphere warmer. Back around 2004, I had a long discussion on the “climateskeptics” mailing list with Hans Jelbring. I said then that his theory was nothing but a perpetual motion machine, but at the time I didn’t understand why his theory was wrong. Now I do.
Dr. Robert Brown has an fascinating post on WUWT called “Earth’s baseline black-body model – a damn hard problem“. On that thread, I had said that I thought that if there was air in a tall container in a gravity field, the temperature of the air would be highest at the bottom, and lowest at the top. I said that I thought it would follow the “dry adiabatic lapse rate”, the rate at which the temperature of dry air drops with altitude in the earth’s atmosphere.
Dr. Brown said no. He said that at equilibrium, a tall container of air in a gravity field would be the same temperature everywhere—in other words, isothermal.
I couldn’t understand why. I asked Dr. Brown the following question:
Thanks, Robert, With great trepidation, I must disagree with you.
Consider a gas in a kilometre-tall sealed container. You say it will have no lapse rate, so suppose (per your assumption) that it starts out at an even temperature top to bottom.
Now, consider a collision between two of the gas molecules that knocks one molecule straight upwards, and the other straight downwards. The molecule going downwards will accelerate due to gravity, while the one going upwards will slow due to gravity. So the upper one will have less kinetic energy, and the lower one will have more kinetic energy.
After a million such collisions, are you really claiming that the average kinetic energy of the molecules at the top and the bottom of the tall container are going to be the same?
I say no. I say after a million collisions the molecules will sort themselves so that the TOTAL energy at the top and bottom of the container will be the same. In other words, it is the action of gravity on the molecules themselves that creates the lapse rate.
Dr. Brown gave an answer that I couldn’t wrap my head around, and he recommended that I study the excellent paper of Caballero for further insight. Caballero discusses the question in Section 2.17. Thanks to Dr. Browns answer plus Caballero, I finally got the answer to my question. I wrote to Dr. Brown on his thread as follows:
Dr. Brown, thank you so much. After following your suggestion and after much beating of my head against Caballero, I finally got it.
At equilibrium, as you stated, the temperature is indeed uniform. I was totally wrong to state it followed the dry adiabatic lapse rate.
I had asked the following question:
Now, consider a collision between two of the gas molecules that knocks one molecule straight upwards, and the other straight downwards. The molecule going downwards will accelerate due to gravity, while the one going upwards will slow due to gravity. So the upper one will have less kinetic energy, and the lower one will have more kinetic energy.
After a million such collisions, are you really claiming that the average kinetic energy of the molecules at the top and the bottom of the tall container are going to be the same?
What I failed to consider is that there are fewer molecules at altitude because the pressure is lower. When the temperature is uniform from top to bottom, the individual molecules at the top have more total energy (KE + PE) than those at the bottom. I said that led to an uneven distribution in the total energy.
But by exactly the same measure, there are fewer molecules at the top than at the bottom. As a result, the isothermal situation does in fact have the energy evenly distributed. More total energy per molecules times fewer molecules at the top exactly equals less energy per molecule times more molecules at the bottom. Very neat.
Finally, before I posted my reply, Dr. Brown had answered a second time and I hadn’t seen it. His answer follows a very different (and interesting) logical argument to arrive at the same answer. He said in part:
Imagine a plane surface in the gas. In a thin slice of the gas right above the surface, the molecules have some temperature. Right below it, they have some other temperature. Let’s imagine the gas to be monoatomic (no loss of generality) and ideal (ditto). In each layer, the gravitational potential energy is constant. Bear in mind that only changes in potential energy are associated with changes in kinetic energy (work energy theorem), and that temperature only describes the average internal kinetic energy in the gas.
Here’s the tricky part. In equilibrium, the density of the upper and lower layers, while not equal, cannot vary. Right? Which means that however many molecules move from the lower slice to the upper slice, exactly the same number of molecules must move from the upper slice to the lower slice. They have to have exactly the same velocity distribution moving in either direction. If the molecules below had a higher temperature, they’d have a different MB [Maxwell-Boltzmann] distribution, with more molecules moving faster. Some of those faster moving molecules would have the right trajectory to rise to the interface (slowing, sure) and carry energy from the lower slice to the upper. The upper slice (lower temperature) has fewer molecules moving faster — the entire MB distribution is shifted to the left a bit. There are therefore fewer molecules that move the other way at the speeds that the molecules from the lower slice deliver (allowing for gravity). This increases the number of fast moving molecules in the upper slice and decreases it in the lower slice until the MB distributions are the same in the two slices and one accomplishes detailed balance across the interface. On average, just as many molecules move up, with exactly the same velocity/kinetic energy profile, as move down, with zero energy transport, zero mass transport, and zero alteration of the MB profiles above and below, only when the two slices have the same temperature. Otherwise heat will flow from the hotter (right-shifted MB distribution) to the colder (left-shifted MB distribution) slice until the temperatures are equal.
It’s an interesting argument. Here’s my elevator speech version.
• Suppose we have an isolated container of air which is warmer at the bottom and cooler at the top. Any random movement of air from above to below a horizontal slice through the container must be matched by an equal amount going the other way.
• On average, that exchange equalizes temperature, moving slightly warmer air up and slightly cooler air down.
• Eventually this gradual exchange must lead to an isothermal condition.
I encourage people to read the rest of his comment.
Now, I see where I went wrong. Following the logic of my question to Dr. Brown, I incorrectly thought the final equilibrium arrangement would be where the average energy per molecule was evenly spread out from top to bottom, with the molecules having the same average total energy everywhere. This leads to warmer temperature at the bottom and colder temperature at elevation. Instead, at thermal equilibrium, the average energy per volume is the same from top to bottom, with every cubic metre having the same total energy. To do that, the gas needs to be isothermal, with the same temperature in every part.
Yesterday, I read the Jelbring hypothesis again. As I was reading it, I wondered by what logic Jelbring had come to the conclusion that the atmosphere would not be isothermal. I noticed the following sentence in Section 2.2 C (emphasis mine):
The energy content in the model atmosphere is fixed and constant since no energy can enter or leave the closed space. Nature will redistribute the contained atmospheric energy (using both convective and radiative processes) until each molecule, in an average sense, will have the same total energy. In this situation the atmosphere has reached energetic equilibrium.
He goes on to describe the atmosphere in that situation as taking up the dry adiabatic lapse rate temperature profile, warm on the bottom, cold on top. I had to laugh. Jelbring made the exact same dang mistake I made. He thinks total energy evenly distributed per molecule is the final state of energetic equilibrium, whereas the equilibrium state is when the energy is evenly distributed per volume and not per molecule. This is the isothermal state. In Jelbrings thought experiment, contrary to what he claims, the entire atmosphere of the planet would end up at the same temperature.
In any case, there’s another way to show that the Jelbring hypothesis violates conservation of energy. Again it is a proof by contradiction, and it is the same argument that I presented to Jelbring years ago. At that time, I couldn’t say why his “gravito-thermal” hypothesis didn’t work … but I knew that it couldn’t work. Now, I can see why, for the reasons adduced above. In addition, in his thread Dr. Brown independently used the same argument in his discussion of the Jelbring hypothesis. The proof by contradiction goes like this:
Suppose Jelbring is right, and the temperature in the atmosphere inside the shell is warmer at the bottom and cooler at the top. Then the people living in the stygian darkness inside that impervious shell could use that temperature difference to drive a heat engine. Power from the heat engine could light up the dark, and provide electricity for cities and farms. The good news for perpetual motion fans is that as fast as the operation of the heat engine would warm the upper atmosphere and cool the lower atmosphere, gravity would re-arrange the molecules once again so the prior temperature profile would be restored, warm on the bottom and cold on the top, and the machine would produce light for the good citizens of Stygia … forever.
As this is a clear violation of conservation of energy, the proof by contradiction that the Jelbring hypothesis violates the conservation of energy is complete.
Let me close by giving my elevator speech about the Jelbring hypothesis. Hans vigorously argues that no such speech is possible, saying
There certainly are no “Elevator version” of my paper which is based on first principal physics. It means that what I have written is either true or false. There is nothing inbetween.
Another “gravito-thermal” theorist, Ned Nikolov, says the same thing:
About the ‘elevator speech’ – that was given in our first paper! However, you apparently did not get it. So, it will take far more explanation to convey the basic idea, which we will try to do in Part 2 of our reply.
I don’t have an elevator speech for the Nikolov & Zeller theory (here, rebuttal here) yet, because I can’t understand it. My elevator speech for the Jelbring hypothesis, however, goes like this:
• If left undisturbed in a gravity field, a tall container of air will stratify vertically, with the coolest air at the top and the warmest air at the bottom.
• This also is happening with the Earth’s atmosphere.
• Since the top of the atmosphere cannot be below a certain temperature, and the lower atmosphere must be a certain amount warmer than the upper, this warms the lower atmosphere and thus the planetary surface to a much higher temperature than it would be in the absence of the atmosphere.
• This is the cause of what we erroneously refer to as the “greenhouse effect”
Now, was that so hard? It may not be the best, I’m happy to have someone improve on it, but it covers all the main points. The claim that “gravito-thermal” theories are too complex for a simple “elevator speech” explanation doesn’t hold water.
But you can see why such an elevator speech is like garlic to a vampire, it is anathema to the “gravito-thermal” theorists—it makes spotting their mistakes far too easy.
w.
Willis Eschenbach;
But heck, let’s play it your way. You say you can do it if we break it up into pieces. OK, give me the elevator speech for the first piece of the lot, we’ll start with that.>>>
Already did. Several times.
John Mason says:
January 20, 2012 at 5:56 am
Despite repeated calls, no one has yet given the “elevator speech” about how N&Z actually works. Someone above said it’s all far too complex to be explained simply … riiight.
My point is that I don’t know how the N&Z model works, and if you do, please give us the elevator speech so we can all understand how it’s supposed to go.
w.
PS—I also don’t know what you are calling a “delay model”.
RE: Jelbring at 12:15 pm
You criticize my use of elevator speech (or verbal proof, take your pick) without addressing its conclusion. You say that there should be two different lapse rates, then go on to say something about equal masses. I never specified equal masses, in fact with two different gasses, with different Cp and probably different densities, there is no reason to expect equal masses or densities at intervals r from A to B.
You agree with me that there will be different lapse rates, so therefore, there can be only one point C along the tubes where they have the same temperature. At all other points (not C), the temperatures will be different between the tubes. Different temperatures means heat flow at the window at point B. Heat flow is not equilibrium, therefore there is a contradiction. Modus tollens.
The tubes must remain isothermal, same temperature at all r.
It problem is the uniform insolation, dead planet, without day-night, assumption. There isn’t a planet in the universe above 3 deg K that fits that assumption. Because planets are not uniformly heated, have a night and day, some deg of radioactive internal heating, they have non-zero real lapse rates, so we feel that it must also be so in the dead planet case. That is was the bugaboo that haunted me. Until I realized that uniform insolation requires a uniform radiator at distance at the same temperature.
My take away from these long threads this week is that the uniform insolation case requires an isothermal atmosphere (zero real lapse rate ) regardless of composition. Isothermal atmosphere is worthless to study in climate science. Therefore uniform insolation cases are worthless to study. [Watch the fur fly now!]
JJThoms says:
January 20, 2012 at 6:03 am
Quite true, many thanks.
I first read about the Hilsch Vortex Tube in the “Amateur Scientist” column back in the sixties when “Scientific American” used to actually be about science. I machined one up a decade or so ago out of a block of aluminum, they are amazing. I could get about 100°F difference between the hot and cold ends.
w.
Wrong. The mechanism of heat conduction cares nothing about gravity. It only cares about a temperature difference (gradient). Is the temperature at the opposite ends of an insulated (say enclosed in a high vacuum chamber) bar of copper different if it’s vertical rather than horizontal? The gravitational potential energy of the copper atoms at the top of the bar is higher than for the atoms at the bottom of the bar.
Exactly the opposite. It is only possible if work is being done, i.e. something is moving the air up and down in the column to establish the adiabatic profile. At the adiabatic profile, the work done would be very small, but even with neutral buoyancy at all altitudes, you can’t move something without doing some work. Since work is being done, the average temperature in the volume will also increase over time Conduction does no work. It simply increases the entropy of the system.
OzWizard says:
January 20, 2012 at 6:43 am
Great! You understand it! So give us the clear, concise version of their theory called an “elevator speech”, that not only says what it does, but how it does it.
I’ve asked a lot of people but you’re among the first to claim to understand it, and the other claimants haven’t come through with their elevator speeches, so you could be the first off the blocks.
w.
PS—please don’t mention atmospheric radiation in the elevator speech, as N&Z say the following:
In other words, their theory doesn’t require GHGs to work … and so neither can your explanation.
All the best,
w.
DirkH says:
January 20, 2012 at 6:57 am
Say what? QUOTE MY WORDS. I have no recollection of anything even remotely resembling that. I say the column will be isothermal, meaning all at the same temperature top to bottom. If not, you could pull work out of it, and that would be perpetual motion.
w.
JJThoms and Willis,
You can often see Hilsch Vortex tubes in use in Formula 1 pits between sessions. They use them to keep the drivers cool while they’re waiting in the cockpit to go back out on the course. The air hose connected to the middle of a metal tube with a small diameter tube on one end and a large diameter tube on the other end is a dead giveaway.
davidmhoffer says:
Dave, repeat after me, 100 times if you have to: “The local value of the insolation does not determine the local temperature of the Earth. It does not even come close…It does not even come sorta, a little bit close! It is freakin’ ridiculous!” I don’t know about where you live, but where I live I’ve never seen the temperature drop down even close to the 3deg background temperature at space at night. In fact, the coldest temperature recorded on Earth isn’t even close to that!
There is absolutely no justification for using the variation in local insolation to determine an effective blackbody temperature of the Earth…None, whatsoever. Nada! It is an extremely silly thing to do. What could possibly be your justification for thinking this number is at all useful? Even on the airless moon, where the diurnal cycle is much longer and the heat capacity is much lower and convective transport of heat is practically non-existent, this is not all that good approximation for what the local temperature is going to be…at least once you get just a few cm down below the surface.
I think the problem with this experiment, the more I read it, is that it’s being forgotten for a gas to be a gas it has to be receiving a source of energy. Otherwise, it would cease being a gas and settle on the bottom of its containing (i.e. Pluto’s atmosphere); as it would lose all its energy to its surroundings (which ultimately lose their energy to space, which ultimately spreads out across the universe as the CMB, which will ultimately lead to the heat death of the universe according to Entropy and how we currently understand physics). The atmosphere’s temperature difference could do work, as that difference is captured energy from the Sun, and thus can be recaptured if one figured out a way to do so.
Basically, we cannot create a rational situation where energy input, and thus energy gradients, are separated out from the system. We can’t just say “here we have an isothermal gas doing nothing”. Shoot it off into space and it’ll soon turn solid! The container its in itself would act as a heat exchanger, as there is no perfect insulator.
In short, are we saying anything logical or reasonable about reality with these thought experiments I see people running?
Robert Clemenzi says: “The only way to transfer heat to space is via radiation, and the only way for the atmosphere to loose heat to space is to have greenhouse gases that radiate energy.”
Robert – not so. All gases radiate. Search for “emissions spectrum”. wikki will give you a good introduction.
“DeWitt Payne says:
January 20, 2012 at 2:14 pm
Alan Millar says:
January 20, 2012 at 1:39 pm
Lets be clear a closed system with an atmospheric temperature gradient present could exist indefinitely without breaching thermodynamic laws.
Wrong. The mechanism of heat conduction cares nothing about gravity. It only cares about a temperature difference (gradient). Is the temperature at the opposite ends of an insulated (say enclosed in a high vacuum chamber) bar of copper different if it’s vertical rather than horizontal? The gravitational potential energy of the copper atoms at the top of the bar is higher than for the atoms at the bottom of the bar.
However, that is only possible if absolutely no work is being done at all. If work is being done, and I cannot imagine a system, with a temperature gradiant, that could prevent work being done, then entropy must increase.
Exactly the opposite. It is only possible if work is being done, i.e. something is moving the air up and down in the column to establish the adiabatic profile. At the adiabatic profile, the work done would be very small, but even with neutral buoyancy at all altitudes, you can’t move something without doing some work. Since work is being done, the average temperature in the volume will also increase over time Conduction does no work. It simply increases the entropy of the system.”
Are you bereft of understanding?
Did I not say that I could not imagine any system with a temperature gradiant that could stop work taking place?
You have just said the same thing using different words!
Sheesh!
Alan
davidmhoffer says:
We know the explanation of the other ~100K: The explanation is simply this – Different temperature distributions will have different average temperatures. Any temperature distribution that emits 240 W/m^2 into space is compatible with the energy balance of the Earth. Hence, you can have all sorts of temperature distributions that will have average temperatures less than 255 K. Which one is chosen for the Earth or for any other celestial body depends on things like the variation (in space and time) of solar insolation on the body, the heat capacity of the solid and liquids at the surface, the heat capacity of the atmosphere, the heat transport in the atmosphere and in the solids and (especially) liquids at the surface.
You think there is some great mystery to explain…but there is not.
The more and more I think about this…
“If not, you could pull work out of it, and that would be perpetual motion.”
But Willis, all gases can do work. To be a gas means it has to have stored energy in kinetic motion, making the molecules move too much to stick together as a liquid and then a solid.
You can get energy back out of any gas when it condenses, and from any liquid when it solidifies. The heat of condensation and heat of fusion. It would not be perpetual motion, because any energy we take out of a non isothermic gas will simply drive the entire column towards condensation, and eventually the “atmosphere” will simply settle as a solid. And, if we drag out every ounce of kinetic motion, we can get all the energy from it till it hits 0 K.
I think this is where the logic is going awry. There is always a kinetic energy difference between each molecule in a gas (a distribution as you point out), and that difference turns to potential energy as one moves against a gravity field. But if you try to use this difference to do work, you lower the average temperature of the entire column, even if there is a temperature gradient in the column (the top colder than the bottom). The top will cool fastest, and the gas will begin to settle, forming condensate on the sides of the container. The bottom would stay warmer and condense last, allowing some molecules to continue zipping around (the highest energy part of the distribution); but the pressure of the gas would steadily decrease.
Isothermal has nothing to do with anything from what I see the more I think of it. Work is done by the entire column or not; any gradient itself does and cannot do work, as affecting the gradient changes the entire average distribution and removes energy from the entire column of gas.
Again, perpetual motion comes in nowhere; because gas is a high energy phase of matter, and matter can change states.
Alan Millar,
That’s not at all what your words said. You said:
And that bolded part of your statement is still wrong. Unless you meant “could not exist indefinitely” instead of could. I’m commenting on what you actually posted, not what you may have meant.
Surely centripetal force has also to be taken into account?
Joel Shore said:
“Which one is chosen for the Earth or for any other celestial body depends on things like the variation (in space and time) of solar insolation on the body, the heat capacity of the solid and liquids at the surface, the heat capacity of the atmosphere, the heat transport in the atmosphere and in the solids and (especially) liquids at the surface.”
Hey Joel, I think you are nearly there but not quite.
This is how it works:
The oceans control air temperatures as per my Hot Water Bottle Effect.
I’ve also said that the oceans should be considered as part of the atmosphere and I have explained in detail why the ocean heat content and the rate of energy flow from ocean to air is also pressure dependent just as is the ATE of Nikolov and Zeller.Therefore both being pressure dependent the oceans cannot alter the ATE. In fact they are an important part of setting it on our particular planet.
The ATE effect is dominant in the atmosphere and governs the temperature gradient from surface to space. We could adopt the term Ocean Temperature Effect (OTE) for the region below the ocean surface but I prefer the term ATE to cover both, with the oceans just being considered as a part of the atmosphere. Obviously there is a discontinuity at the water/air interface but the evaporative process deals with that to leave ATE in the air undisturbed.
ATE is far more powerful than the misleadingly named and probably non existent GHE from GHGs because the former involves the entire atmospheric mass whilst the latter involves only GHGs which are a not a sizeable proportion of total mass.
What I think happens is that ATE is in complete control and all the other features of the system from the bottom of the oceans to the top of the atmosphere organise themselves around ATE to maximise system entropy (the tendency of any system to become less organised over time). In the case of an irradiated planet the concept of it becoming less organised over time involves the removal of energy to space as fast as possible given the constraints of basic physics.
The system always responds negatively to any factor that tries to alter the surface temperature fixed by the ATE because any deviation from the ATE represents a reduction in efficiency as regards the rate of energy loss to space. As far as we can tell it always succeeds leaving ATE unaltered.
The way that the system organises itself depends on the composition of the component elements but due to the dominance of the ATE the only effect from composition differences is to change the rate of energy throughput within each section of the system so that the surface temperature does not change.
However a faster throughput of energy within a particular section of the atmosphere will result in higher temperatures wherever more warm air passes more often across sensors situated within that section but that is a result of energy redistribution and not a sign that the equilibrium temperature of the system has changed.
The ability to redistribute energy in that way (differentially in different sections of the system) is in fact what makes the system flexible enough to maintain the ATE.
Thus pressure and energy input give us the ATE but everything else including GHGs only affects the rate of energy throughput and not the ATE itself.
If GHGs increase then the energy throughput increases to leave the ATE stable and if GHGs decrease then the energy throughput decreases to leave the ATE stable.
N & Z are carefully collating data to verify that proposition. If they do indeed get accurate enough planetary surface temperaures to prove the dominance of the ATE from planet to planet then all that other factors can achieve is to work around the ATE just as I suggest.
So far they have firmed things up by getting a more accurate lunar surface temperature and corrected an apparent error in the application of the S -B equations.
The resulting figures are in supprt of the proposition that ATE governs the surface temperaure regardless of all other potentially confounding factors.
DeWitt Payne says: “The mechanism of heat conduction cares nothing about gravity. It only cares about a temperature difference (gradient)”
I know what you mean – but are you missing something?
Imagine a heat engine with a low altitude heat source (extract heat here) and high altitude sink (dump heat at the assumed cold upper atmosphere). The plan is to exploit a temperature difference. The link between the source and sink is solid (e.g. electrical conduction through copper).
To simplify things, consider operation in terms of a single molecule of the atmosphere. The heat sink adds kinetic energy to the molecule at altlitude. The molecule (in the fullness of time) falls towards the heat source, and gains kinetic energy. At the source, it has the capacity to pass an additional chunk of kinetic energy to the machine.
As you’ll know, this doesn’t work. We appear to have passed energy from the sink to the source to create a boost for the engine.
What went wrong?
And therein lies the problem, that you’re talking about perpetual motion and you don’t know it. Hans, you are indeed proposing perpetual motion. You are saying that gravity separates the warm and cold molecules.
Don’t expect maths terms used correctly, but, isn’t weight a ‘function’ of gravity? Molecules only have weight because of gravity, which is why the ideal gas law doesn’t have gravity, the ideal gas doesn’t have weight or volume, so, a hotter real molecule has weight and will become less dense and therefore lighter as it heats up and so will spontaneously rise unless work is done on it to stop this, and as it rises into the colder regions it cools, becoming heavier it sinks where it will again gain some heat and so the cycle continues, doesn’t it?
Isn’t the Earth as is a fairly good approximation to this if one takes out the spin? All the spin does is put in a some interesting routes for volumes of air, which with or without the spin naturally rise as heated and gravitate to the colder poles (heat flows spontaneously from hotter to colder). Did you like the use of gravitate… 🙂 I only noticed after I’d typed it. Anyway, this is what I read when looking up how our winds work.
Our weather is very energetic because we have the Sun’s imput, but that only exaggerates what gets it all moving, which is the difference in temps between land and seas and so cold air moving in to under hot air rising such as coastal regions, morning and evening differences, and cold air compressing the molecules beneath as it descends again after being for a while hot air rising, both these create winds. Without the ocean one of the wind systems would be out, but, I suppose, as long as there is a temp difference among the rocks or whatever is on the surface, there should be winds created from the temp differences of the volumes of air above them.
If all the surface was of the same material, the same kind of rock, I suppose it would just, somehow, rise and fall simply from the effects of gravity, that is, weight of the molecules, as they changed densities on becoming hotter and colder.
Perhaps one could design an optimum mix of gases to exaggerate these differences in weight of gravity..?
Anyway, gravity separates molecules by weight, hot or cold doesn’t make any difference to gravity, that just makes a difference to the molecule – expanding, becoming less dense with heat, contracting, becoming more dense with cold. the molecules have a different weight relative to each other at the same temperature anyway.
I think I have an answer that I actually believe.
1) Temperature, BY DEFINITION, is the inverse of the rate of change of entropy with respect to energy (with a proportionality constant). That means, when a unit of energy is transferred from a relatively warm object to a colder one, the entropy of the warmer object decreases, but by a relatively small amount, because high temp means low rate of change of entropy, and the entropy of the colder object increases by a larger amount (low temp means high rate of entropy change). So, the total entropy increases.
2. The total entropy of an isolated system must stay the same or increase (2nd law of thermodynamics).
3. If we make the Earth an isolated system by putting a perfect, reflective bubble around it, then it must obey the 2nd law: its total entropy can remain the same or increase; it can never decrease.
4. We neglect the interior of the Earth, and the oceans, because the effect we’re discussing should apply on a planet with a cold interior and no water.
5. If we initialize the atmosphere of this world with regions of unequal temperature, then occasionally, through simple conduction or via radiation, net energy will get transferred from a warmer region to a colder region and when it does, the total entropy of the system will increase IRREVERSIABLY – the system as a whole will never be able to return to the lower entropy state.
6. Therefore, there is an inevitable process by which temperatures will equalize, pushing entropy up, or there is a state with regions of unequal temperature but no possible means for net energy transfer between them – a highly improbable scenario and certainly not the general case.
7. Willis is right. Gravity won’t produce any temperature gradient. It does, of course, produce gradients in pressure and total energy content (as a function of temperature), but not temperature.
I think this thread has jumped the shark.
A physicist says:
January 20, 2012 at 8:53 am
This to me is the fundamental argument.
This is why any and all arguments about the means of how gravity supposedly separates by temperature, or the strong arguments from various people about why it clearly must separate by temperature, are meaningless. Not because the means are wrong or falsifiable, but because the outcome is impossible. Robert Brown has capably and clearly given (and continues to give) the “why it is isothermal” speech. He has done the best job to date of explaining the means and the whys.
But set all of that aside:
IF GRAVITY ACTUALLY SEPARATES TEMPERATURE, WE HAVE FREE ENERGY FOREVER!
If sealed thermally isolated containers of air were to gravitationally separate, with warm air at the bottom and cool air at the top, then we could build tall insulated cylinders and pull power out of them forever.
Does anyone really, in their heart of hearts, regardless of the logic of any and all arguments, believe that we can constantly and unceasingly pull energy out of a thermally insulated column of air?
Because make no mistake about it. That is what Hans Jelbring is claiming.
w.
Gravity generates the adiabatic lapse rate by converting kinetic energy to potential energy. If the atmosphere was full with greenhouse gases, it would equilibrate with radiative transfer. The only reason the atmosphere would have an adiabatic lapse rate with greenhouse gases is if the ground was warmer than space. Because with radiative transfer, different bodies will equilibrate to an identical temperature.
Now, I think it is a question of optical thickness to IR. Space does not emit a lot of IR, so there is a differential of temperature at the radiative level between space and the ground. Now, here’s a small piece of thinking that is probably wrong, but I don’t know why. The mass of the atmosphere is equivalent to 5m of ground. The interior of the Earth is very warm and, I guess, optical thickness is probably the reason why the ground is not has warm. The highest variation of temperature you can find in the ground is about 30K/km. This is equivalent to 0.15K for 5 m. So, if the atmosphere is able to generate 33K for the whole atmosphere, it would mean that a molecule of a greenhouse gas is around 220 times more optically thick than a molecule of the ground.
From that I have 2 questions:
1- Are greenhouse gases 220 times more optically thick than the ground?
2- Why?
Gravity does not separate by temperature. It separates by mass.
Jelbring, Nikolov and Zeller (and me) accept that in the absence of an energy source the column will become isothermal.
It is only when energy is added that the temperature gradient forms as a result of more densely packed molecules converting a greater proportion of the incoming radiation to kinetic energy.
davidmhoffer says:
January 20, 2012 at 1:55 pm
If you calculate a realistic surface temperature for earth based on actual variance of insolation, you arrive at a value of about 140K.
That is a totally unrealistic surface temperature as it assumes the dark-side of the planet is at absolute zero, which is a totally unrealistic case and far from what is observed, it isn’t even realistic for the moon which has a 14-day ‘night’ and no atmosphere!