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.
jae says:
January 22, 2012 at 7:09 pm
jae, don’t you not have following the thread?
w.
jae said @ur momisugly January 22, 2012 at 7:09 pm
You ask: “Why is it not getting warmer these days, when CO2 emissions are increasing drastically?”
Answer: Because Willis invented this wonderful “regulation of incoming radiation through changes in albedo (primarily in the tropics) is consistently neglected in climate science. It is the single largest factor. When the clouds form in the late tropical mornings around the ITCZ, incoming solar is cut by 40 W/m2. This implies that the variation of the time of tropical onset is a major regulatory factor, overwhelming any small changes from” CO2. Just be grateful he invented it otherwise we would all be dead from malaria, heat stroke, increases in prostitution, obesity, decreasing biodiversity etc.
You also ask: “Why do other planetoids with atmospheres show about the same amount of “warming, DESPITE the amounts of GHGs present?”
Maybe, just maybe, I’m surmising here, Willis isn’t interested in the issue, or lacks the time, would prefer to go fishing, hitch-hiking, paying attention to the missus… Why don’t you prepare a paper on this and ask Anthony to post it? Or would that be too much like work?
Willis Eschenbach: “Sirrah, that is vile mendacity. I read the paper at your behest, and I responded to you in detail. My opinion was, you didn’t understand Velasco. You can take your ball and go home with my blessing, but by gosh, you can’t blame me for it after I did exactly what you are now saying no-ne has done.”
Willis, believe me, I appreciate your looking at the paper. And I recognize that the passage you seized upon does not lend itself to ready comprehension. But you’re forcing me to be blunt here. One could arrive at the conclusion you did only by failing to read or understand the equations that preceded it.
I quite understand how someone hurriedly skimming the paper might do that. But your perception of reality is distorted if thus merely tossing off the first comment that comes to your head after such a superficial review–and then ignoring the explanation I gave in response–is what passes in your mind for “serious discussion from the many physicists here.”
“Temperature does not depend on potential energy, it depends on degrees of freedom. ”
I don’t see why anyone would think temperature is related to potential energy. A rock on a hill has nothing to do with it’s temperature. Or the temperature gasoline and oxygen [potential energy] isn’t related to temperature.
“That’s why a jar full of air at 300K riding in the space shuttle will have precisely the same velocity/kinetic energy distribution as a jar full of air at 300K sitting on the surface of the earth. It does not depend on pressure.”
Well the air molecules are changing vector every nanosecond- or they are “pulling *huge* gees”
so 3 gees from a space shuttle, is rather trivial to a single molecule. Though 3 gees will affect all the molecules- creating pressure
“A jar full of air at 2 atmospheres and at 300K has the same velocity/KE distribution as a jar at 1 atmosphere. ”
Not sure what you mean by “velocity/KE distribution”.
But you seem to be suggesting that if you 1/2 volume/double pressure you would not effect the molecules average velocity.
It seems to me the initially molecules velocities are not affected, but with more molecules in a smaller volume with molecules travel the same velocity- it is higher temperature.
So, two cubic meters of 1 atm gas at room temperature forced into 1 cubic meter, initially retain their velocity [and are hotter than room temperature] and has it cools to room temperature the average velocity of gas decreases.
Obviously the 2 atm container of gas could have more Potential Energy, but that’s not important in regards to it temperature- If container is place in environment of 2 atm- it has no Potential Energy, if put in a vacuum it more Potential energy as compared to 1 atm.
It seems to me if you talking about x amount of gas molecule- the temperature is directly related to the velocity of the molecules. Increase their speed, warmer temperature. Decrease their speed
lower temperature. Hence a hot quantity of gas which cools, has the molecules of gas slowing down- or one changing the volume. With the atmosphere which isn’t in a container one can have expansion or contraction of volume of the atmosphere.
As for a jar on space shuttle- the air has little mass/weight and will not be not affected significantly from 3-4 gees [or 50 gees].
“It does not depend on the number of molecules (although you can get into trouble for very low numbers of molecules because your jar can get to where it only has one or a very few molecules in it, in which case “distribution” of velocities and “temperature” become shaky concepts). A jar with N molecules at pressure P and temperature T has the same average kinetic energy per molecule as a jar with 2N molecules at pressure P/2 and temperature T, whether or not one of them is floating in intergalactic space and the other is sitting (well insulated) in a balloon floating at rest in the atmosphere of Jupiter.”
The KE of molecules gas is 1/2 mass and velocity squared. Gravity only changes weight not mass.
But if double the mass of molecules- double the pressure you will increase temperature of gas and after it’s cooled to ambient temperature, the molecules would seem to have to have lost velocity from the point in time when the gas was heated from the added pressure.
Bart says:
January 20, 2012 at 6:04 pm
Phil. says:
January 20, 2012 at 5:02 pm
“…the only way that conduction can reduce the radiation loss from the surface is by cooling the surface.”
No, that is not the only way. Stefan-Boltzmann is an equilibrium relationship. You do not know the radiation loss from the surface in non-equilibrium conditions.
Amazing, you keep coming back with the same nonsense!
You have a situation of constant heat input to a surface in contact with a finite atmosphere heat capacity and the only method of heating that atmosphere is by conduction. Eventually the atmosphere will reach the surface temperature and the atmosphere cannot exceed that temperature. At that point the situation is equilibrium so your repeated objection doesn’t hold!
Explain to us how the atmosphere and surface temperatures exceed the equilibrium surface temperature, let’s have some equations and facts instead of the mumbo-jumbo hand waving that we’ve had from you hitherto.
You know, it is really annoying when someone proclaims they know everything about a phenomenon which is actively under investigation.
I agree it’s really annoying when someone asserts a non-physical model without any justification and pontificates about laws named after himself. Try using accepted physical laws and explain how the presence of a non-absorbing gas can increase the surface temperature above the equilibrium value.
Stephen Wilde says:
January 22, 2012 at 10:35 am
The Ideal Gas Laws have never been falsified.
If that were the case then Van der Waals wouldn’t have needed to develop his equation:
http://en.wikipedia.org/wiki/Van_der_Waals_equation
Joe Bom, I note that above you say:
Joe Born says:
January 22, 2012 at 8:13 pm (Edit)
Joe, you claimed above that you misunderstood it until you read the equations that preceded it. I went back and read them. I could not see how they changed the conclusion in any way, much less in the way that you claimed.
You quoted Velasco’s conclusion, which was:
Here are the two possible answers as stated in the paper:
Answer 2 was the adiabatic case. Answer 1 is the isothermal case. THEY SAID THE ANSWER WAS “ISOTHERMAL”. You went on to to argue that they did not say what they plainly said, for reasons that are still not clear to me, and made no sense.
So I did not answer your post, Joe. You are unable to read clear english. Read the conclusion above. In neither case is answer (2) right. Answer (2) is adiabatic lapse rate. They said three times in their conclusion that the final rate is isothermal, and you want to tap-dance around that.
Sorry, not interested. You want a rational discussion, but I can only provide half of the rationality required.
w.
@ur momisugly Trick 1/22 at 5:56 pm
“ Rasey: No,… There is no acceleration…”
Merely trying to point out (me – poorly) whether the cup is accelerating or not depends on the reference frame. Cannot merely say the cup is not accelerating. Consider all ref. frames. Not just the familiar one.
Trick, the definition of acceleration is the second derivative with respect to time of the equation of position. Define Positions P in some coordinate system as a function of time. Velocity V is the first derivative, dP/dt. Acceleration is the second derivative of position, d^2P/d^2t, the first derivative of velocity, dV/dt. Gravity acts as a force, one of many forces at play, not an acceleration.
If you choose a reference frame of the table or corner stone of your building or the nearest USCGS Benchmark, the Position of the coffee cup on the table is constant with time, its velocity is zero, its acceleration is zero.
If you choose a reference frame based upon the Moon, a Celestial frame, a non-inertial frame, Sun-Galactic Coordinate System, or the SupergalacticCordinate system, then, yes, the coffee cup has non-zero acceleration that is hopelessly difficult to calculate, but at least you know the USCGS benchmark and the center of the Earth has the same acceleration difficult to calculate acceleration. Feel better?
Your life is a lot less complicated as a scientist or engineer by picking the frame of reference and the coordinate system that makes the math the easiest. Zeros are good things in math. That’s why we have multiple frames of reference and coordinate systems. That’s why tensor analysis was developed. Just ask Einstein.
Stephen Rasey says at 9:35pm:
“…yes, the coffee cup has non-zero acceleration… Feel better?”
Yes! It is all relative. Thanks, Stephen
PS: I’m just hanging out here last few days while sporting a head cold, interested in the science conversation. But I do feel better now, LOL.
Joel Shore;
The point is that the greenhouse effect alone accounts for about 33 K or more…and it is the only thing that explains the important part of the warming>>>
Since you don’t even know what the actual baseline temperature sans GHE is in the first place, you cannot possibly know how much of the observed temperature is due to other effects, nor, without being able to quantify each and every one of them, can you possibly calculate how much is GHE.
Here is the gold-standard of reference frames: the JPL ephemeris. http://www.cv.nrao.edu/~rfisher/Ephemerides/ephem_use.html
Prediction and reduction of pulsar pulse times of arrival… on the earth’s changing distance to a pulsar as it moves around the sun. … working at the level of a few hundred nanoseconds over long periods of time…. implies that the observer’s position with respect to the solar system barycenter be known to about 100 meters. Necessary if you want to shoot Cassini through the gap between Saturn and its rings seven years from launch. That’s science and engineering!
Keeping this climate related, here is the North Polar hexagonally shaped vortex of Saturn. Its been there for decades. A deep mystery.
Say you want to make Mars, have warm atmosphere as earth does?
The N&Zers and the CAGW could have different approaches.
Suppose what is wanted is ability for a human operate on Mars
without a spacesuit/pressure suit.
At the present, if given a oxygen mask, you can’t breathe on Mars-
there isn’t enough pressure. At 45000′ on earth, you can’t breathe
that air- well you can breathe it, it won’t give you enough oxygen to
remain conscious. If you use an oxygen mask you can breathe the air and
remain functional. But at 100,000′ an oxygen mask won’t help you.
And Mars atmosphere is similar to earth at 100,000′.
So on Mars or earth starting above 45,000 you need a pressure suit.
So what wanted is something as good as Mt Everest in term of pressure
and preferable a bit warmer than Mt Everest.
Now, for N&Zer, we can’t increase Mars gravity, but could use heavier
gas. And CAGWer would probably want some super greenhouse gas.
“Following these first proposals a variety of other partially even more ambitious concepts to terraform Mars were published. The include (1) changing the orbital eccentricity of Mars’ orbit around the Sun and (2) changing the obliquity of Mars’s spin, (3) channelling of volatile-roch cometary nuclei into the Martian atmosphere, (4) seeding of Martian atmosphere with heat-absorbing, cloud-forming particles, (5) heating the polar caps using large spaceborne mirrors, (6) devolatising of the carbon within the Martian crust, (7) inducing large-scale drainages of potential Martian aquifiers, (8) the introduction of microbes, bioengineered to survive the harsh environment on the Martian surface, (9) the addition of bioengineered plants to lower the surface albedo and (10.) the introduction of super-greenhouse gases (GHGs)”
http://journalofcosmology.com/Mars149.html
And:
“According to the Intergovernmental Panel on Climate Change, SF6 is the most potent greenhouse gas that it has evaluated, with a global warming potential of 22,800 times that of CO2 when compared over a 100-year period. Measurements of SF6 show that its global average mixing ratio has increased by about 0.2 ppt per year to over 7 ppt. Sulfur hexafluoride is also extremely long-lived, is inert in the troposphere and stratosphere and has an estimated atmospheric lifetime of 800–3200 years.”
http://en.wikipedia.org/wiki/Sulfur_hexafluoride#Greenhouse_gas
And Sulfur hexafluoride is 5 times denser than air, and non-toxic- you can watch Y-tube of people breathing it to get a deep voice [opposite of Helium].
Fluorine and sulfur are fairly abundant. There is more Fluorine than carbon or sulfur in earth crust:
http://en.wikipedia.org/wiki/Abundance_of_elements_in_Earth%27s_crust
Existing Mars atmosphere is 2.5 x 10^16 kg or about 25 trillion tonnes- mostly CO2.
One would need to do this economically. Assume less the 1 trillion dollars.
Assume costs are about $100 per kg for anything made, oppose to naturally occurring- such as water or CO2 in comets. Assume naturally occurring could be $1-10 per kg. One could get cheaper costs if whatever needed is “waste product” or by product of some other needed commodity.
With this constraint, one get about 10 billion kg of Sulfur hexafluoride. Let’s give a round number of 25 billion kg- or 1/millionth of Mars atmosphere.
Would such a small trace gas have a significant effect upon Mars temperature?
Good thread!
Having ignored your 100 km column height initially, I had a stupid hang-up about constituent stratification of air in a full atmosphere height column. I see now that would make no difference, the entire column must still be isothermal. Thanks Willis, Dr Brown, Anthony et al, I learned a lot of detail new to me.
davidmhoffer says:
January 22, 2012 at 9:58 pm
Actually the facts we have do allow us to draw some conclusions. Let me define the “theoretical S-B temperature” as the temperature of a blackbody with a uniform surface temperature corresponding to the amount of incoming radiation. Here’s what we know.
1. For a given incoming radiation, any variation in surface temperature from the isothermal state will lower the mean surface temperature.
2. An atmosphere, with or without greenhouse gases, can reduce the temperature drop from variations in temperature. It does this by reducing the amount of day / night ∆T and equator / polar ∆T.
3. A transparent GHG-free atmosphere cannot warm the surface above the isothermal state of the theoretical S-B temperature.
Therefore: at a minimum, the greenhouse effect of GHGs and clouds must be responsible for at least the thirty degrees C that the earth is above the theoretical S-B temperature.
In addition, since the greenhouse effect undoubtedly reduces the day/night temperature swings, some additional amount of the warming beyond the 33°C is also due to the greenhouse effect.
Finally, the rest of the warming is due to the atmosphere itself reducing things like the equator / polar temperature differential through the physical export of heat from the tropics to the poles. This is a separate and independent effect from the greenhouse effect.
w.
Joel Shore says:
January 22, 2012 at 11:02 am
@Joules Verne and tallbloke: The average surface temperature of the moon is the perfect debating point if your goal is to never resolve anything. You can debate this all day but unless you carefully define how the average is taken (e.g., are you looking at the first fraction of a mm or at the first meter of the surface), you’ll get all sorts of different answers!
And, this is precisely because there are lots of different temperature distributions having lots of different average temperatures that are all compatible with the moon being in radiative balance.
And the range is?
On another thread where I addressed your concern around this issue, you started waffling about average temperature a metre down in the regolith and asked where the surface is. On the surface was my reply. DIVINER carries an MSU instrument and it measures the radiation leaving THE SURFACE, not the temperature 5cm 50cm or 100cm below the surface.
I submit that you are the one wishing to make the debate endless, in order to delay the inevitable, preferably forever.
davidmhoffer says:
January 22, 2012 at 10:26 am
Tallbloke;
I’ll be providing a mathematical proof of the misapplication of S-B on my site soon. Watch this space.>>>
To limit my misuse of time on the internet I long ago made a deal with myself to participate in one an one only forum. Please provide that mathematical proof as soon as you can and I will break my three year old deal with myself on the spot.
David, thanks for all your excellent application of reason on this thread. If you just sign up to follow my blog, you can ignore the intervening posts you will be notified of via email, and you can be in early when the S-B law misapplication post comes up.
Cheers
TB.
Willis Eschenbach: “Joe, you claimed above that you misunderstood it until you read the equations that preceded it. I went back and read them. I could not see how they changed the conclusion in any way, much less in the way that you claimed.”
Those of you who, like me until today, tended to give Willis’s conclusions a good deal of weight, would do well to look at Velasco et al.’s Equation 8 and see for yourself whether it supports the conclusion that Velasco et al. found a non-zero lapse rate. You may revise your assessment of Willis’s ability to do the math.
I know I did.
I must also emphasize that this system (Jelbring) does not represent a perpetuum mobile – it is strictly a result of elementary thermodynamics. If this is a perpetuum mobile, then the rotation of the planets around the sun in the solar system is a perpetuum mobile – I don’t think Newton would approve! He understood gravity.
Of course it does, because it violates elementary thermodynamics.
At this point, the demonstration has been made many, many times. I will repeat it. Pay attention.
First, reference has been made to one textbook with the proper thermodynamic argument for the specific case of gravity given in the text itself.
Second, reference has been made to another textbook where proving that there is no lapse rate in the specific case of a gas in gravity is a student exercise.
Third, the example of Maxwell’s Demon has been given repeatedly — any time a natural force is asserted to cause the spontaneous separation of an isolated system into reservoirs at different temperatures, one can build a heat engine that does nothing but convert heat into work with no other effect, violating the second law.
Fourth, both Willis and I have undertaken — repeatedly — to show that this is the case with specific examples. Examples include:
* Two different columns of gas with different lapse rates. Place them in good thermal contact at the bottom, so that the bottoms remain at the same temperature. They must therefore be at different temperatures at the top. Run a heat engine between the two reservoirs at the top and it will run forever, because as fast as heat is transferred from one column to another, (warming the top) it warms the bottom of that column by an identical amount, causing heat to be transferred at the bottom to both cool the column back to its original temperature profile and re-warm the bottom of the other column. The heat simply circulates indefinitely, doing work as it does, until the gas in both columns approaches absolute zero in temperature, converting all of their mutual heat content into work.
* A single, isolated column of gas with a different temperature at the bottom and the top that is maintained by gravity as the stable thermal equilibrium. Since the temperatures at the bottom and top are different, one can run a heat engine between them. Examples of heat engines that could be run that have been given include a Carnot Cycle (ideal) engine, an electrical thermocouple, a precisely balanced “dippy bird”. All of these are normal thermodynamic heat engines that take heat from any reservoir at high temperature and deliver some of that heat to a cold reservoir at a lower temperature, converting the rest into work.
If the heat engine is located completely inside the insulated column of gas, it will do work that is ultimately transformed back into heat inside the column. Since the stable lapse rate is given as g/C_p (where I have no idea why you are using C_p in your example above, since P is varying along the gas column, but it doesn’t really matter) no matter how much heat you deliver to the top of the column from the bottom in this way, no matter how much heat is transformed into work (and ultimately back into heat) the energy sorts itself out again so that the stable lapse rate is maintained. The heat engine (of any sort) will run forever, literally converting heat into work over and over and over again.
Or, one can run a heat engine that removes the work done from the reservoir and releases it into the outside environment regardless of its temperature. In this case the heat content of the gas column will be gradually transformed into work until it reaches absolute zero in temperature. Congratulations! You’ve now violated the refrigerator statement of the second law as well!
For some reason, nobody in this thread wants to confront this head on. They continue to write absurdity after absurdity, basically stating that the gas columns they describe are in thermal equilibrium because they satisfy some equation or another that they pretty much made up and asserted as the definition of thermal equilibrium. They do not bother to take ordinary and elementary precautions and determine whether or not this assertion is consistent with the laws of thermodynamics and actual definition of equilibrium in terms of heat flow. They ignore well over 100 years of physics and laws that every physicist knows cannot be broken, by asserting a system that is a textbook example of violation of the second law. Any bright undergraduate, given this as a homework problem without being told what mechanism causes the “miraculous” spontaneous separation of a gas column into hotter and colder gas in equilibrium should be able to demonstrate that it violates the second law!
As I said, IMO Jelbring shouldn’t waste his intellect on trying to explain the warming of planets. He should go ahead and patent “Jelbring’s 100% efficient heat engine”. All he needs is a tower full of, say, Xenon, a km high. Then there are any number of designs for a heat engine that take up heat at the bottom and deliver it to the top as long as there is a temperature difference between the bottom and top, and of course there will always be such a temperature difference because as fast as heat is delivered to the top, gravity will sort it back out so it falls to the bottom to maintain the thermal gradient.
That patent can join the vast list of similar patents for PMMs, at least as soon as one builds a working model. The patent office no longer accepts applications for PMMs without a working model.
BTW, it is absolutely trivial to test the Jelbring hypothesis, and for that matter the N&Z variant (which I’m still working through, as N&Z’s applies to an open system where Jelbring’s is closed by assertion and hence easier to instantly contradict, thanks Anthony for the new post of N&Z with more detail and annotation). It is asserted that air will have an approximate static lapse rate of C_p/g in thermal equilibrium. The actual atmosphere is never, of course, in anything like thermal equilibrium — heat is always flowing from the ground out to space over 80-90% of the Earth’s surface at any given time, and where it isn’t it is only because there is a thermal inversion that is “impossible” according to both N&Z and Jelbring, e.g. over Antarctica during its winter.
However, it is a tabletop experiment to equip a simple centrifuge with recording thermistor buttons glued into the “top” and the “bottom” of a Dewar cylinder containing ordinary air and leave it long enough to reach thermal equilibrium inside the cylinder. We’re talking undergraduate science here, something you could very likely manage with items purchased at Wal Mart. Spin the radially aligned Dewar up to 100 to 1000 g and you should be able to get an easily measureable permanent thermal gradient in the pseudogravitation of the centrifuge.
You won’t, of course. If you could, once again such a system could be used to build a PMM — build large toroidal disk at a Lagrange point, spin it up to 1000 g’s, run a series of thermocouples between the inner and outer thermal reservoirs, and it will generate electricity until it cools the gas in the cylinder to zero without energy input (or if the thermocouple runs inside of the adiabatically isolated torus, it will drive a motor forever).
Looking forward, therefore, to easily reproducible tabletop verification of Jelbring’s hypothesis, followed by any number of PMM patents.
rgb
jae says:
January 22, 2012 at 7:09 pm
Willis, don’t you not have anything to say about the empirical evidence? Why do other planetoids with atmospheres show about the same amount of “warming, DESPITE the amounts of GHGs present? “Why is it not getting warmer these days, when CO2 emissions are increasing drastically? The “bottom line” is always empirical evidence, but you just seem to shake it off!
I keep wondering just WHY you will not address this issue. You have no problem addressing other issues. Come on!
Could you have a case of confirmation bias?
jae, I think you’re being a little hard on Willis. Think of the wrongly named GHE this way. The atmosphere is like an electrical wire. The energy absorbed by the surface travels through the atmosphere to the effective radiating altitude where it is emitted to space. The warming of the atmosphere is like the resistance in the wire.
Now, what allows the energy to flow are the GHGs. They allow the atmosphere to conduct the energy. Without them there would be no way to the energy to flow. Hence, GHGs are required to close the circuit if you will. It would do no good for Willis to deny that GHGs are required.
I think this analogy may be more realistic than many think. If the effective radiation altitude is set by the relationship found by N&Z (i.e. the turbulence of gases in a gravitational field) then you have the empirical evidence that increases in CO2 would do little to change the temperature and yet still require GHGs like CO2 to be present to enable the flow of energy.
tallbloke says:
Frankly, that is just a very silly statement. I have been the one who has consistently said that the debate over the temperature of the moon is a distraction from the discussion…from the very first time I commented on it over two weeks ago: http://wattsupwiththat.com/2011/12/29/unified-climate-theory-may-confuse-cause-and-effect/#comment-857787 And, I have very clearly explained why this is the case.
I have also predicted that a lot of time would be wasted arguing about irrelevancies such as the average surface temperature of the moon: http://wattsupwiththat.com/2011/12/29/unified-climate-theory-may-confuse-cause-and-effect/#comment-860185
Joel Shore says to Tallbloke
“Frankly, that is just a very silly statement. I have been the one who has consistently said that the debate over the temperature of the moon is a distraction from the discussion”
Well in the Halpern et al paper that Joel signed up to section 3.3 starts
“The Moon is a good example to contrast with the Earth”
Perhaps a little consistency is required here!
Or maybe like everyone else you realise that the Halpern et al paper is riddled with mistakes.
gbaikie says at 1/22 8:30pm:
“I don’t see why anyone would think temperature is related to potential energy.”
If temperature is not related to molecule’s PE then can construct a Perpetuum Mobile!
Consult Caballero text top post link for ideal gas p. 12: ” The number of molecules can be expressed as a density, and, as we will see, the mean speed can be expressed as a temperature….Temperature is just another name for the mean kinetic
energy density of molecular motion.”
Consider Willis’ premise of a GHG-free atmosphere air in adiabatic (insulated) tall cylinder in earth’s gravity field g at room avg. temperature. Zoom in on one air molecule speeding around in that cylinder (an ideal control volume allowing no energy in or out).
This molecule has a mass m and speed v. As gbaikie writes, the molecule’s kinetic energy KE is 1/2mv^2.
This molecule is of mass m & at any height h has potential energy PE of m*g*h.
The molecule’s total energy is KE + PE.
The thermo 1st law tells us total energy cannot be created or destroyed but it can be changed from one form to another (thermal to potential to chemical and back – if this process is irreversible 2nd law deduces entropy increases).
The molecule’s total energy = KE + PE which therefore must = constant always since energy can’t be created or destroyed.
Hence as the molecule speeds around in the cylinder & colliding w/o energy loss (an ideal gas!) 1st Law tells us molecule must conserve total energy changing PE into KE and back & forth w/no entropy increase ideally since their sum always = constant for each molecule. The molecule’s thermal energy must change with PE introduced by changing height in the gravity field. Why?
Consider molecule happens to move up against the gravity field or h increases. Compute molecule’s PE = m*g*h so it increases.
The molecule’s speed decreases as it moves up against gravity field so its KE decreases as 1/2mv^2 decreases.
This is consistent with 1st Law: PE up, KE down so KE + PE = 1/2mv^2 + mgh = constant & unchanged or conserved. Focus on KE decreasing here.
Robert Brown & Caballero tell us the thermal energy of the molecule is its KE and ideal gas law tells us PV = nRT. In the cylinder: V,n,R are bulk constants. So P ~ constant * T in the cylinder. If KE decreases with height thermal energy decreases with height.
Air is compressible gas & since P is higher at bottom of cylinder due to weight of molecules above in the gravity field, T must be higher because P proportional constant * T.
Robert Brown (and thus Willis’) ignores the upward moving molecule’s decreasing thermal energy thus decreasing T (from decreasing KE and increasing PE) and thus they ignore 1st Law of thermo. This enables Robert and Willis’ to construct a Perpetuum Mobile by inserting a silver rod in the gas cylinder.
Again, that is why it is important that temperature is related to potential energy of the molecules w/gravity.
If you don’t do the KE + PE = total energy math right, a Perpetuum Mobile looks possible to construct. It is not possible; Robert and Willis’ haven’t done the total energy math right & thus they don’t apply thermo physical laws correctly in the presence of gravity field.
In real life, I can really construct a highly (but not perfectly) insulated cylinder of air. I can really drop in an (insulated or not, superconducting or not) silver wire. No Perpetuum Mobile results. Not even close.
Why? 2nd thermo Law tells us “differences in temperature, pressure, and chemical potential equilibrate in an isolated physical system”, no heat energy flows in Willis’ premise one cylinder in equilibrium. Why is this so hard?
Since apparently even the past thermo grand masters & their non-ideal real experiments could not agree whether the T and P fields are ideally stratified or isothermal, that can & will be debated all you want. Have at it.
NB: if Willis’ premise air column really is isothermal as Robert Brown claims, buoyancy disappears from Willis’ premise – a story for another day.
Ideally stratified or isothermal answer really doesn’t matter much in real life since the atmosphere is agreed to really have a lapse rate. Real air molecule KE & thus air thermal energy or temperature generally decrease with height as the air molecules move up against gravity, generally decreasing KE and increasing PE keeping their total energy constant.
(I write generally atmosphere T decreases with height – lapses – but that is not always true b/c the real atmosphere has very complex heat flowing & V is not constant unlike in Willis’ premise.)
For my view, entropy inside Willis’ ideal air column is constant & there is a stratified P & T field since ideally pressure and temperature decrease w/increasing height. Makes it easier to think thru at least.
This became important to consider recently because of the discussion of the new N&Z paper(s) and how much of the real atmosphere lapse rate is due to P&T field gradients and how much lapse rate is due to earth’s atmosphere radiating to very cold space.
No matter what you drop into Willis’ control volume, thermocouple, silver wire, drinking bird, movable open or closed jars positioned anywhere, heat or chemical energy cannot be made to flow in this one reservoir at equilibrium due to 2nd Law. There is no possible Perpetuum Mobile in Willis’ premise.
Willis’ air column is only one block of energy! Put two of Willis’ premise “cylinders” together and then heat will flow if Tavg. is different. As Robert points out repeatedly.
Apologies if the following has already been pointed out, but if I wait to reply until I’ve read the whole thread I’ll forget what I wanted to say! I’ve been following the discussion on previous threads but only now on my new computer am I again able to post comments.
First, I’m delighted that someone has at last realised that an atmosphere in thermal equilibrium must be isothermal. “Same temperature” and “thermal equilibrium” are just different ways of saying the same thing.
Jelbring erroneously “thinks total energy evenly distributed per molecule is the final state of energetic equilibrium”; however, Willis is also mistaken in saying “the equilibrium state is when the energy is evenly distributed per volume and not per molecule”. There is no such requirment at equilibrium (in an isothermal atmosphere there is a lot more energy per unit volume at low altitudes, where the air is denser).
Willis is also mistaken in claiming that Jelbring’s model violates energy conservation. It does not violate the First Law of Thermodynamics (permitting the operation of a Perpetual Motion Machine of the First Kind), but the Second Law (a Perpetual Motion Machine of the Second Kind, which destroys entropy). The power from Willis’s thermopile, doing work within the model environment, will endlessly dump its waste heat back into that atmosphere. Still impossible, of course.
Jelbring’s hypothesis founders on that basic error, but, like Willis, I am unable to make sense of the Nikolov & Zeller theory. It reads like gibberish. So I’m not sure if they’re making the same main mistake, or a different one.
Caveat 1: A planet can continuously radiate more power than it receives from the sun due to the release of gravitational potential energy in its atmosphere. Jupiter is an example. It has been doing so for billions of years, gradually shrinking in size (since it has no real “surface” we can consider it all atmosphere, for present purposes). Such gravitational collapse can even heat the core of the very largest planets to the point at which thermonuclear fusion ignites (we call such planets “stars”!). Energy can also be released by tidal friction (Io is a good example). Or, as in the case of the Earth, by radioactive decay (fission is negligible), which contributes some four orders of magnitude less power than the sun, and is therefore considered climatalogically insignificant.
Caveat 2: In General Relativity, an equilibrium state is possible in which the temperature is higher at the bottom of a gravitational well than at the top. Consider a large gravitating body, surrounded at a distance by shell at uniform temperature T1. Let the red shift climbing out of the well from the surface to the shell be Z. Then the temperature of the surface, at equilibrium, will be T1.Z. The surface radiates Z**4 times as much power as the shell.
So how is this equilibrium? First, every outgoing photon drops in energy by the same factor Z. Second, time runs Z times more slowly at the surface. Third and fourth, only some of the photons manage to reach the shell, the rest following trajectories that curve back down to the surface, a factor of 1/Z in each of two orthogonal directions (other ways of looking at this are to note that the aberration of light compresses the sky into a cone, or that the horizon curves up into bowl). And that makes up the Z**4.
It is not possible to use this gravitational temperature “difference” to drive a perpetual motion machine because any connection between surface and sphere has to deal with this same fundamental time differential or change of reference frame. Convert the proper temperature from one frame to the other (by means of the factor Z), and there’s no temperature difference any more. [This is in sharp contrast to the nonrelativistic Jelbring model, in which the top and bottom of his atmosphere could be connected in parallel by two columns of differing scale height and lapse rate (eg, air and helium).]
This is my closing comment. I have already shown explain my view about a static atmosphere here: Marc77 says: January 22, 2012 at 8:59 am
Said shortly, back-radiation of IR photons is a back-radiation of momentum and kinetic energy. The phenomenon is similar to how gravity “back-radiates” momentum and kinetic energy of gas molecules. Gravity also cool photons as they get out of a gravity field based on general relativity. The gradient of cooling as a particle goes up in a gravity field is proportional to the ratio of momentum to kinetic energy. So heavier the gas molecule will lead to a higher lapse rate. This effectively leads to the possibility to generate energy from the differential of temperature at different heights. This means that a static atmosphere under gravity is highly unstable. So gravity alone is enough to generate convection cells.
That’s it. My model of a static atmosphere is right in predicting an exploitable differential of temperature. It means that convection cells spontaneously appear on nearly every planets, even if the surface is uniformly heated and the atmosphere is perfectly transparent. These convection cells are necessary to come close to an isothermal equilibrium. But don’t forget that a planet with a temperature is not in thermal equilibrium with space, so it is normal to never have an isothermal equilibrium.