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.
davidmhoffer says:
January 22, 2012 at 4:57 am
If they’ve erred in their calculation of mean surface pressure, then by all means, point out the error and suggest a fix. But don’t throw the baby out with the bath water.
I don’t think this is relevant. It’s not the variables in equations 7 and 8 that are the free parameters. It is the constant values they specified (those values could be anything). I also didn’t look close enough at the equation to see what was being done. So, on this point Willis and Joel are right.
However, if we look closely at the curve and also at Figures 5 and 6, we see something interesting. The curves match fairly closely. This means the so-called free parameters did not have to vary over a wide range to fit the curve. I think N&Z did themselves a disservice by trying to make a perfect fit. There is clearly a relationship that bears further investigation. This is the baby that needs to be viewed with more scutiny.
Nick Stokes says:
Nick,
Interesting…but I am still having trouble completely coming to grips with your argument. I understand how it is possible in principle for parts of the atmosphere to act as a heat pump…but I am having trouble understanding why you think that this drives the atmosphere up from a lower lapse rate to the adiabatic one. What is the driving force? (For an engine, I tend to think that the driving force is simply that heat wants to flow from hot to cold but it seems to me that a heat pump doesn’t have anything driving a certain temperature distribution…I turn on my air conditioner and what determines the final temperature in my house is simply the amount of electricity I run it with, e.g., the power of the air conditioner, its efficiency, and how long it runs.)
Also, how does this jive with the observed fact that the stratosphere is not being driven to the ALR? Or, are you saying that it is necessary to have things, such as in the troposphere, where part of it would be working as a heat engine (because convection is driving the lapse rate down) in order to have the part where it is acting as a heat pump?
John Marshall says:
Are you suggesting that coconuts migrate? (http://thinkexist.com/quotation/are-you-suggesting-that-coconuts-migrate/761764.html )
Srtioudly, are you saying that the Earth and its atmosphere are undergoing gravitational collapse and that this is producing 150 W/m^2? (And, that somehow all the satellite measurements that show that the Earth, as seen from space, is only emitting ~240 W/m^2 are wrong?)
tallbloke says:
January 22, 2012 at 3:41 am
“Independent of the question about the effect of gravity on temperature, N&Z have shown using empirical data and a better application of S-B that the average temperature of the surface of the Moon is ~90K cooler than previously thought. This is a mortal blow to Joel’s scientific beliefs, and he is desperate to get N&Z buried on any pretext.”
The avarage surface temperature of the moon was measured by two different Apollo missions in mid-latitude locations. It’s exactly what everyone thought it would be and what theory still predicts it should be which is 250K.
How do you explain your apparent discounting of experimental data? Do you believe both Apollo experiments were somehow flawed or what? In a nutshell – two different Apollo missions to the moon bored 3 meter deep holes in the regolith and then placed thermocouples at various depths from surface to bottom of the hole. The intent was to measure thermal conductivity of the regolith which is uber-important in the design of any habitats that may be constructed on the moon as it tells them how deep the structure needs to go to be immune from the large diurnal temperature swings and what the temperature of the regolith is once you’re deep enough so that it becomes constant.
As it turns out the constant temperature is 250K which is precisely what S-B predicts the average surface of the moon should be and the depth at which the temperature becomes constant is anything greater than 50 centimeters. The experiments continued transmitting temperature data to the earth for 4 years.
When some new hypothesis comes along from an undistinguished source that defies both long established laws of thermodynamics as well as repeated experimental data there’s invariably an explanation and that explanation is that the new hypothesis is wrong. This is crank science. Please stop dallying with it. It’s making you look bad.
That stratifying seems to square with 0th,1st, 2nd Law and ideal gas law. I don’t think Maxwell-Boltzmann distribution can be invoked in a gravity field since it deals with statistics of molecular movements w/o external forces. Here gravity is an external force. M-B can only be invoked if gravity is turned off.
That would be fine except that click through references to one straight up algebraic proof that you are incorrect has been offered, one reference to a textbook (Caballero) has been offered that both derives/explains the adiabatic lapse rate and has as an explicit end of section homework problem to prove otherwise, and finally your answer is inconsistent. If MB statistics were not valid in gravitational fields, how would they ever have been discovered? Is there somewhere Maxwell or Boltzmann could go where they were absent?
Therefore consider the “jar” argument once again. Bear in mind that the jar in question is one that is differentially small but large enough that it contains enough molecules that they can achieve “thermal equilibrium” (large compared to the mean free path). Grab a jar of air at the bottom of your “equilibrium” room with a DALR. Its pressure is a bit higher and temperature is a bit higher than air at the top. Grab a second jar of air at the top, where pressure and temperature are both a bit lower.
So far, we know nothing about the density of said air. Nothing in fluid dynamics requires a fluid to be compressible. Real fluids range from nearly incompressible water to highly compressible air — I don’t know how you want to idealize your “air” but let’s assume that it is moderately compressible. Even ideal fluids will almost certainly have a positive thermal expansion coefficient across the temperature range as well (a factor in the DALR) so we can assume safely enough that even an idealized fluid with a temperature lapse will have a density lapse as well.
So in the end, J_b from the bottom has T_b, P_b and N_b in volume V, where jar J_t from the top has T_t, P_t and N_t. T_b > T_t, P_b > P_t and N_b > N_t.
Gravity, however, is the same at the top and at the bottom. Moving the jar at the top to the bottom (remember, the fluid is in jars with rigid sides) does not change anything about the state of the fluid. Moving them anywhere does not change their state, as long as it is done gently enough that one doesn’t slam the fluid molecules around inside their jars (this is called “quasi-static” motion in thermodynamics, and is assumed for anything like an adiabatic process so we haven’t really introduced new assumptions there).
The fluid in the two jars is not in thermal equilibrium. Surely you agree? They are at two different temperatures. If the two jars have any sort of thermal pathway” opened between them, they will come to thermal equilibrium at a temperature in between T_b and T_t, one we can actually compute as it will depend on their heat capacities at constant volume which depend on N only (and in fact are equal to e.g. 3/2 Nk or 5/2 Nk for ideal monatomic or diatomic gases respectively).
Note well — extremely well, if you please — that the heat capacity of the gas gets no contribution from gravity. Moving a jar of air up or down in gravity does not change its ability to store heat. From this alone you should be able to see that gravity is decoupled from the problem, because your belief that dT/dh (where h is the height of a jar) gets a contribution from gravity at equilibrium is incorrect. dT/dh = 0 (where the derivative should be a partial derivative btw). Adiabatic lapse is a non-equilibrium state.
We surely agree that the two jars are not in equilibrium. Even if we leave them where they were in the first place and simply run a heat-superconducting wire between them, we expect heat to flow in the wire because they are not in thermal equilibrium and thermal equilibrium does not depend on where you are! The whole point of the zeroth law is that if I carry a thermometer with me it will predict whether or not heat would flow between any two reservoirs whose temperature I measure no matter where they are and no matter what the state is of each reservoir and whether or not the two systems are at all similar. I can measure air temperature in the Swiss Alps and water temperature in the North Carolina ocean, and if they are the same then I know that if I placed an “ideal” thermal conduit between the Alps and the Ocean no heat would flow.
Once again, you are stuck. You have a closed system that — you claim — is in thermal equilibrium with two different temperatures, one at the top and one at the bottom. Yet that means that an ordinary thermometer carried from the bottom to the top would read two values, and, just as would be the case for any two systems whose temperature is measured, means that heat would flow between them if it could.
a) It can. Air is a conductor of heat and heat will flow from the bottom to the top until the system is in equilibrium.
b) If you persist in arguing that it cannot, then you have established gravity as a Maxwell’s Demon for air. Please read about Maxwell’s Demon as it would greatly improve your understanding of detailed balance and why this argument ultimately microscopically fails.
c) Given the stable thermal gradient in this case, one can trivially construct a heat engine that does perpetual work moving heat from the bottom to the top and then “re-using” this energy after gravity sends it back to the bottom. That’s again a simple fact. One could run one of those little bobbing ducky things with a fluid with a high expansion coefficient in glass inside your container forever. Head down, it warms and squirts fluid through a tube to the other end (which is higher, hence cooler). Eventually the tail is heavier than the head, so it falls. Now the head cools and the tail warms to squirt the fluid back the other way. It falls again. Each cycle carries heat from bottom to top, but no matter, gravity will re-partition the heat again so you can use it over.
rgb
Drinking Bird:
http://en.wikipedia.org/wiki/Drinking_bird
rgb
@Robert Brown
In your isothermal arguments you are conflating temperture and energy. Shame on you. In the absence of gravity the column would be isothermal. However gravity induces a pressure gradient and this introduces a temperature gradient along with it. Total energy in the column however does not change and neither does the total energy in any horizontal layer. Total energy is a mix of gravitational potential energy and kinetic energy. As you move further up the column total kinetic energy declines and gravitational potential energy increases commensurately. “Heat” is energy of motion, measured by thermometers (“sensible”) but it isn’t the only kind of energy. The books balance just fine with a thermal gradient produced by a gravitational field. Gravity does not produce or reduce total energy, it doesn’t change the distribution of energy, it merely changes the form the energy takes on at different altitudes.
The isothermal/adiabatic distribution of a thermally isolated gas in a gravitational field has never been tested experimentally.
I was aware that the usual suggestions (such as a thermocouple or several thousand thermocouples with their real copper or silver connectors) don’t stack up when real values are calculated.
Stephen Rasey proposed to use two columns each with a different gas with widely different values of Cp.
I suggested two and realised that you could get a 2K difference between the two 100m tubes.
DeWitt Payne improved the model by suggesting another two gases that gave 7Kdifference.
It seemed all very practical and measurable.
I was convinced and did not need much persuading (as I tend toward the isothermal camp).
Why did someone not think of this test before, I thought?
However on reflection the test is questionable .
If the gases are allowed to mix at the top you have a one off heat transfer which cannot be repeated.
If the gases are kept separate by say copper plugs with a thermocouple in between I would like to see practical figures for gas to copper heat transfer before the matter becomes part of “settled science”.
William Gilberts post to Robert illustrated the wider context where he says:
“First, you talk extensively about “equilibrium” and “thermal equilibrium”. But I believe we should be talking specifically about “thermodynamic equilibrium”. Thermal equilibrium is but a subset of thermodynamic equilibrium. A system is in “thermodynamic equilibrium” when it is in thermal equilibrium, mechanical equilibrium, radiative equilibrium and chemical equilibrium. Thermodynamic equilibrium equals thermal equilibrium only when a system’s internal energy can be described by
U = CvT (1)
In this case the system’s internal energy is thermal energy and thermal equilibrium is all that matters. Your statement “Thermal equilibrium is isothermal, period” only applies to such a system. But that is not the system of a planetary atmosphere under the influence of a gravitational field.
Second, we need to better define where the classical laws of thermodynamics and equilibrium are valid. They are valid with a homogeneous system where all the locally defined intensive (e.g., per unit mass) variables are spatially invariant. But a system is not homogeneous if it is also affected by a time invariant externally imposed field of force, such as gravity. Thus in a gravitational field the laws of thermodynamics have to be applied in a manner that reflects the external field. This is a paradigm buster in itself.
Third, the thermodynamics of an atmosphere cannot be described wholly through considerations of heat transfer only (Trenberth diagram, anyone?). The atmosphere must be treated as a system undergoing both heat and mass transfer. Mass transfer is the reason that gravity is so important in understanding atmospheric thermodynamics. This gets to the mechanical equilibrium part of thermodynamic equilibrium.
Fourth, chemical equilibrium is also very important in atmospheric thermodynamics. But if you assume uniform molecular diffusivity in a horizontal layer (gravitational potential energy handles the vertical diffusion) we are left with latent heat and that is beyond our discussion here.”
Robert Brown and Joel Shore both pointed out that at times of an atmospheric inversion the atmosphere above the earth surface can be at a higher temperature than the surface.
But what happens then?
the radiative flux from the surface is more intense than the radiative flux from the atmosphere and so the atmosphere fails to stop the surface cooling further.
The heat flow is still from the surface to the atmosphere.
Radiation is not heat.
Temperature is not heat.
Until a fully implemented experiment or at least fully calculated presentation with real figures is supplied I for one will keep an open mind.
A Physicist;
(1) Nikolov & Zeller erred in neglecting radiative transport in the atmosphere.
(2) The symptom of the Nikolov & Zeller error is that (as is generically true of “gravito-thermal” formalisms) their model exhibits one of the following two flaws (depending upon details):
(a) the model either predicts an isothermal atmosphere
(which at odds with observation), or else
(b) the model violates the second law of thermodynamics
(3) The fix for the Nikolov & Zeller error is to incorporate radiation absorption and emission.
(4) Working through the details of this change, the standard GHE mechanisms are recovered.
——————
A grandiose case of circular reasoning. Your position is pretty simple. In your mind it is impossible for the earth surface to be higher than the effective blackbody temperature without back radiation (GHE). You conclude from your belief system that any formula that doesn’t attribute the higher than effective blackbody temperature of earth to GHE must therefore by default be wrong and to violate the laws of thermodynamics. Wrong.
Consider a nice hot day in the tropics. The sun comes up at dawn and the temperature is already at 20C or 293K. Over the course of the day, the temperature increases by 20K to 313K. After it peaks, it begins to cool again, falling back to 293K by the following morning. Do we need back radiation to explain this? No. Note that I’m not saying that back radiation isn’t part of the equation, but I am saying that you do not need back radiation to explain this. If you try an stick to “average” insolation and “average” temperature to understand what happens every single day, you will get large numbers to attribute to GHE and they will be wrong. The following is illustrative.
If we assume an average insolation of 240 w/m2, then insolation couldn’t possibly maintain the temperature in the scenario above at 20C,let alone increase it during the course of the day to 40C. 240 w/m2 equates to only -18C, so if all we were relying upon was “average” insolation, the earth would actually cool, not warm, even during the day. Do we need back radiation or GHE to explain this rise in temperature that occurs every day on earth despite this? We do not.
The insolation that the tropics is exposed to every day ranges from 0 w/m2 at night, to 1,000 w/m2 at noon. What is the blackbody equilibrium temperature of earth at 1,000 w/m2?
Answer: 364K or 91C
Question: Does the earth surface ever get to 91C?
Answer: No
Question: If GHE raises the temperature of earth surface to a temperature higher than the blackbody temperature expected from insolation, why doesn’t the temperature go even higher than 91C?
Answer: I know what you are thinking right now. You can blame this conundrum on conduction and convection cooling the earth surface. Back to circular reasoning again. You can’t claim that the surface of the earth is at a temperature higher than blackbody because of GHE and also claim that it doesn’t get to blackbody at all DESPITE GHE. Further, there is a far simpler explanation: heat capacity.
Explanation:
The earth surface does not and cannot respond to changes in insoltion instantaneously. The earth surface has a heat capacity, and for any given change in insolation, there must be a time constant applied to determing how long it will take to warm the earth surface to equilibrium.
The temperature of the earth surface in the tropics when exposed to 1,000 w/m2 never gets to 91C because it doesn’t have TIME to get to 91C. Further, at night when insolation is zero, it doesn’t cool off to absolute zero because it doesn’t have TIME to cool that much. The “average” daily temperature can easily be maintained at well above the non existant imaginary 255K without a single watt from GHE provided that we STOP averaging insolation and treating it like a fixed number and instead accept that it varies wildly every single day and when combined with the heat capacity and time constant that governs warming and cooling, explains most if not all the the surface temperature over and above the supposed 255K.
Do convection, conduction, and back radiation get involved in the process? Of course they do. But is GHE required to raise the temperature of the earth above 255K?
No.
N&Z did not break the laws of thermodynamics, and what they showed is NOT that they ignored GHE, but that properly calculated, GHE is insignificant.
Joel Shore says:
January 22, 2012 at 6:56 am
“It is not smearing opponents. It is trying to make you guys understand how incredibly ignorant and silly you are making the “skeptic” community look in the eyes of the scientific community.”
Really. And who exactly is this “scientific” community and how does its defintion manage to exclude the “skeptic” community. There are many scientifically literate people who are skeptical of the alarmist narrative. Some of those skeptics even have the politically correct credentials that inbred academic bigots regard as credibility markers. I find you characterization insulting and a disservice science everywhere. Science is a discipline that may be practiced by anyone at any time and it is also a discipline which can be abandoned by anyone at anytime especially when power and tribal politics are a factor in the practioner’s behavior.
RichardM;
I don’t think this is relevant. It’s not the variables in equations 7 and 8 that are the free parameters. It is the constant values they specified (those values could be anything). I also didn’t look close enough at the equation to see what was being done. So, on this point Willis and Joel are right.>>>
The point is that if you arrive at the mean surface pressure of the various planets by another means, and plug those values into N&Z, you should either get the same results at they did, or, if you get different results, then either the way you calculated mean surface pressure is wrong, or the way they did is. Or I suppose, both could be wrong.
But I don’t see anyone jumping up and showing that the mean surface pressures of the various planets are appreciably different from what they calculated. Oddly, would that not be the easiest way to falsify at least that part of their work?
But allow me to suggest an alternative. If you understand what they are trying to get at over all, is there any reason they could not have used atmospheric weight (note that I said weight, not mass) instead of mean surface pressure?
Joel Shore;
The same logic applied to the calculation of 255K however, yields a value about 100K lower, a matter that Joel Shore refuses to engage in regard to.
That is even more untrue. I have engaged in discussing this in considerable detail, including why I believe your “100 K lower” claim is pure fantasy for any reasonable definition of and Earth without greenhouse gases but otherwise similar.>>>
Sir, I have provided you with sample insolation curves and the blackbody calculations derived from them by doing the calculation over time and shown quite conclusively that it is easily possible to have a daily fluctuation of insolation from 0 to 850 w/m2 that averages 240 w/m2 and yields an average temperature over time of 140K. Your rebuttal amounted to screaming “that’s impossible”. Hardly a refutation. Read my comment upthread about heat capacity and time constants.
Robert Brown says at 1/22 8:04am:
“We surely agree that the two jars are not in equilibrium.”
Robert – Thank you for the well prepared & thought out reply. It is excellent & consistent with your earlier discussion. It will take a bit to compose a prepared response with the given reading assignments – I will have to double check them.
My view continues that the jars are in energy equilibrium with Willis’ gas system 1 before they are sealed, T stratified & no energy flows in the equilibrium cv up to the instant of sealing – after sealing their energy equilibrium becomes a second & third body equilibrium w/gas & as such energy can be made to flow thereafter. Basically, count the control volumes, there are two more cv.s after jar sealing. Willis’ premise only allows 1 cv, the answer has to be consistent with 1 cv and nothing ever crosses the 1 cv whilst forming conclusions. This is always hard.
This thread made me aware that apparently even the thermo grand masters had different views of Willis’ premise prior to the sealing of the jars. As Tallbloke wrote – that’s science. Might be a l-o-o-o-ng thread for good reason – “Waiting for Godot “ Act II quote: “In the meantime let us try and converse calmly, since we are incapable of keeping silent.”
Heat can be emitted by the ground has IR or has a transfer of momentum to the gas above. IRs can be back-radiated by certain gases. The upward momentum of a particle will be back-radiated by gravity. In the end, the heat emitted by the ground in both forms will be back-radiated to the ground. Can anyone tell me the difference between the 2 kinds of back-radiation?
Also, if a gas particle is accelerated downward and hits a CO2 particle, this CO2 particle is more likely to emit an IR photon.
The way to calculate the adiabatic lapse rate in a no emissivity atmosphere is to define to invisible surface at a slightly different height, and calculate the amount of momentum that goes through these layers. You have 4 cases:
1- A particle passes through the lower layer, does not interact in between, and then goes through the top layer.
2- A particle passes through the top layer, does not interact in between, and then goes through the lower layer.
3- A particle passes through the lower layer, does not interact in between, does not have enough momentum to make it to the top layer, so it goes back through the lower layer again.
4- Multiple particles hit each others in between.
If you calculate the amount of momentum that goes through those 2 layers. You will find that 1, 2 and 3 show a higher sum of momentum at the lower layer. 4 is more tricky, but I believe it can be simplified by taking the center of mass the multiple particles. But in reality, you also have to consider the individual amount of momentum in relation to this center of mass. But I think it is inconsequential, I might be wrong.
In the case of a planet with no sun and a no emissivity atmosphere. The planet would slowly cool to space. The top of the atmosphere would always be cooler than the surface of the planet. Eventually, the top of the atmosphere would rain down to the ground. In the end, the planet would get to a very low temperature. Using a thermocouple in this atmosphere could potentially accelerate the cooling because most thermocouple are made of materials with a non-null emissivity.
tallbloke says:
January 22, 2012 at 2:22 am
Think of a metal rod with a heat source at one end and something very cold at the other. If you divide this rod into slices, you could make the same argument – that heat can not flow because “adjacent ‘surfaces’ are at the same temperature”. Yet, we know that heat does flow. This is because each “slice” is not at some temperature, but because all slices have a temperature gradient.
Using the numbers provided by Scot Allen, January 22, 2012 at 12:27 am
Average speed surface is 500m/s
Average distance between molecules at surface is 10^-5 cm.
10^-5 cm * (1 m/ 100 cm) / (500 m/s) = 2E-10 seconds between collisions
2E-10 s * 9.8 m/s2 = 1.96E-9 m/s — the maximum change in speed due to gravity
(1.96E-9 m/s) / (500 m/s) = 3.92E-12
(500 m/s + 1.96E-9 m/s) ^2 – (500 m/s) ^2 ~= 2 * 500 * 1.96E-9 = 1.96E-6
Assuming 1/2 kT = 1/2 mv^2, then T = m/k * v^2 and
T2/T1 = v2^2 / v1^2
T2 = T1 * (v2^2 / v1^2)
So the question becomes – What is v2? A linear sum of the maximum velocity difference is obviously wrong since more energy will be transferred by molecules traveling parallel to the surface than by those traveling perpendicular to it.
Assuming a linear sum of the maximum values (the wrong approach)
(1.96E-9 m/s) / (1,000 m / 1E-7 m) = 19.6 m/s change every kilometer
T2 = 300K * (500 + 19.6)^2 / 500^2 = 324K – whoa, that’s humungous
Some other examples, just moving the decimal point
T2 = 300K * (500 + 1.96)^2 / 500^2 = 302.4K
T2 = 300K * (500 + 0.196)^2 / 500^2 = 300.2K
Arcsin(0.10) = 5.74 degrees
Arcsin(0.01) = 0.573 degrees
Granted, half a degree is a pretty small skim angle, but this at least puts numbers to how I understand the problem. Over a long enough period of time, an even shallower angle would transfer enough energy to create an isothermal atmosphere (at least in the limit of infinite time and no turbulence).
Bryan says on January 22, 2012 at 8:21 am:
“The isothermal/adiabatic distribution of a thermally isolated gas in a gravitational field has never been tested experimentally.”
Hmmm. Lets see what history tell us:
“Fourier (1824, p. 153)
It is difficult to know how far the atmosphere influences the mean temperature of the globe; and in this examination we are no longer guided by a regular mathematical theory. It is to the celebrated traveller, M. de Saussure, that we are indebted for a capital experiment, which appears to throw some light on this question. The experiment consists in exposing to the rays of the sun, a vessel covered with one or more plates of glass, very transparent, and placed at some distance one above the other. The interior of the vessel is furnished with a thick covering of black cork, proper for receiving and preserving heat. The heated air is contained in all parts, both in the interior of the vessel and in the spaces between the plates. Thermometers placed in the vessel itself and in the intervals above, mark the degree of heat in each space. This instrument was placed in the sun about noon, and the thermometer in the vessel was seen to rise to 70°, 80°, 100°, 110°, (Reaumur,) and upwards. The thermometers placed in the intervals between the glass plates indicated much lower degrees of heat, and the heat decreased from the bottom of the vessel to the highest interval.The effect of solar heat upon air confined within transparent coverings, has long since been observed. The object of the apparatus we have just described, is to carry the acquired heat to its maximum; and especially to compare the effect of the solar ray upon very high mountains, with what is observed in plains below. This experiment is chiefly worthy of remark on account of the just and extensive inferences drawn
Fourier (1824, p. 154)
from it by the inventor. It has been repeated several times at Paris and Edinburgh, and with analogous results”
By the way Tallbloke has done us all a big favour by posting “Fourier 1824 as translated by Burgess 1837” on his blog, so go read it and perhaps learn – a lot.
His (Fourier 1824) pagenumbers may not match mine, but that should not be a big issue
davidmhoffer says: 1/12 at 8:30 am
Keep it up, David. One very minor correction: “what happens every single day” isn’t really correct because in the average insolation, there is no night and there is no day. 😉
All this analysis based upon a “divide by 4”, average insolation, must stop. It is a dead end on a dead planet. Heat capacity is vital to the study of the temperature history of the earth. Here is a link to arguments I have made before on WUWT with traceback to climateetc since summer 2011.
It is time to bury the Dead Planet Model.
David, the short answer is “Yes, only back-radiation can explain this.”
Because if we miraculously turned-off all back-radiation in the atmosphere, then the first night would be very cold (as it is in the dry desert at night), then during the following days and nights each new cumulus cloud, thunderstorm, or hurricane, would dump heat into the upper atmosphere that could *never* radiate away, with the result that within a few weeks all such storms would cease, with new clouds formed during the day at ground-level unable to rise through the now-heated upper air.
New patterns of global air circulation would then emerge, between the (now-cold) tropic latitudes and the (now even colder) polar latitudes … the resulting global weather patterns on such a non-GHE planet might be very interesting, but they would not much resemble the weather patterns of our planet.
The weather, I think, would end up looking very much like the weather of Snowball Earth a world of cold foggy days and colder nights even at the equator, a world without hurricanes or thunderstorms, a world with ever-growing polar ice caps, progressing until the entire world was locked in ice.
Robert Clemenzi says:
January 22, 2012 at 9:03 am
tallbloke says:
January 22, 2012 at 2:22 am
The two packets would have different average temperatures commensurate with the g/Cp relationship, but since the adjacent ‘surfaces’ are at the same temperature, no heat will flow because energy is in equilibrium.
Think of a metal rod with a heat source at one end and something very cold at the other. If you divide this rod into slices, you could make the same argument – that heat can not flow because “adjacent ‘surfaces’ are at the same temperature”. Yet, we know that heat does flow. This is because each “slice” is not at some temperature, but because all slices have a temperature gradient.
Sure, if you create an energy differential between the ends, heat will flow. My point is that Jelbring’s hypothesis (and Loschmidt and Laplace and Lagrange and all of classical mechanics) say that there will be a thermal gradient at energy equilibrium. If energy is in equilibrium, then no heat will flow, despite the fact that there is a thermal gradient.
dynamic equilibrium means there is a flux.
static equilibrium means there is no flux.
this simple device called a ‘word’ can really help sort out thing if you don’t post normally contort it at whim.
a rubber ruler can’t be a useful standard.
davidmhoffer says:
January 22, 2012 at 8:30 am
Skin temperature measured by satellite reaches 70C. Nice global maps in the link below. Soil temperature can get much warmer than that below the surface and reaches a maximum about a quarter inch deep in dry sand. FYI.
http://www.cienciayclima.es/files-pdf/Hot-places-on-earth.pdf
O H Dahlsveen
I said
“The isothermal/adiabatic distribution of a thermally isolated gas in a gravitational field has never been tested experimentally.”
You said
“Hmmm. Lets see what history tell us:
“Fourier (1824, p. 153)”
Your interesting passage from Fourier did not deal with a thermally isolated gas .
Which means no heat enters or leaves the gas sample.
Re: Joules Verne -9:34 am Mildrexler 2011 map.
Cool Map! Uh.. Hot Map!… Uh.. A keeper in any case.
Joules Verne says:
January 22, 2012 at 7:59 am
The avarage surface temperature of the moon was measured by two different Apollo missions in mid-latitude locations. It’s exactly what everyone thought it would be and what theory still predicts it should be which is 250K.
So it wasn’t the average temperature of the Moon which was measured, it was two mid-latitude locations. Extrapolating from that using a misapplication of the S-B law doesn’t give you the average temperature.
How do you explain your apparent discounting of experimental data? Do you believe both Apollo experiments were somehow flawed or what?
Not at all. N&Z use the old apollo data as well as the new data which shows colder than expected high latitudes. Have you read their paper?
“Data obtained during the LRO commissioning phase reveal that the Moon has one of the most
thermal environments in the solar system. Surface temperatures at low latitudes soar to 390K
(+117C) around noon while plummeting to 90-95K (-181C), i.e. almost to the boiling point of liquid
oxygen, during the long lunar night (Fig. 2). Remotely sensed temperatures in the equatorial region
agree very well with direct measurement conducted on the lunar surface at 26.1o N by the Apollo 15
mission in early 1970s (see Huang 2008). In the polar regions, within permanently shadowed areas
of large impact craters, Diviner has measured some of the coldest temperatures ever observed on a
celestial body, i.e. down to 25K-35K (-238C to -248C). ”
When some new hypothesis comes along from an undistinguished source that defies both long established laws of thermodynamics as well as repeated experimental data there’s invariably an explanation and that explanation is that the new hypothesis is wrong. This is crank science. Please stop dallying with it. It’s making you look bad.
They bullied people who supported the discoverers of the ulcer causing stomach bacteria too. The discoverer of plate tectonics was told he was a crank as well.
I’ll be providing a mathematical proof of the misapplication of S-B on my site soon. Watch this space.