Guest post by Robert G. Brown
Duke University Physics Department
The Problem
In 2003 a paper was published in Energy & Environment by Hans Jelbring that asserted that a gravitationally bound, adiabatically isolated shell of ideal gas would exhibit a thermodynamically stable adiabatic lapse rate. No plausible explanation was offered for this state being thermodynamically stable – indeed, the explanation involved a moving air parcel:
An adiabatically moving air parcel has no energy loss or gain to the surroundings. For example, when an air parcel ascends the temperature has to decrease because of internal energy exchange due to the work against the gravity field.
This argument was not unique to Jelbring (in spite of his assertion otherwise):
The theoretically deducible influence of gravity on GE has rarely been acknowledged by climate change scientists for unknown reasons.
The adiabatic lapse rate was and is a standard feature in nearly every textbook on physical climatology. It is equally well known there that it is a dynamical consequence of the atmosphere being an open system. Those same textbooks carefully demonstrate that there is no lapse rate in an ideal gas in a gravitational field in thermal equilibrium because, as is well known, thermal equilibrium is an isothermal state; nothing as simple as gravity can function like a “Maxwell’s Demon” to cause the spontaneous stable equilibrium separation of gas molecules into hotter and colder reservoirs.
Spontaneous separation of a reservoir of gas into stable sub-reservoirs at different temperatures violates the second law of thermodynamics. It is a direct, literal violation of the refrigerator statement of the second law of thermodynamics as it causes and maintains such a separation without the input of external work. As is usually the case, violation of the refrigeration statement allows heat engines to be constructed that do nothing but convert heat into work – violating the “no perfectly efficient heat engine” statement as well.
The proposed adiabatic thermal lapse rate in EEJ is:
where g is the gravitational acceleration (presumed approximately constant throughout the spherical shell) and cp is the heat capacity per kilogram of the particular “ideal” gas at constant pressure. The details of the arguments for an adiabatic lapse rate in open systems is unimportant, nor does it matter what cp is as long as it is not zero or infinity.
What matters is that EEJ asserts that 
in stable thermodynamic equilibrium.
The purpose of this short paper is to demonstrate that such a system is not, in fact, in thermal equilibrium and that the correct static equilibrium distribution of gas in the system is the usual isothermal distribution.
The Failure of Equilibrium
In figure 1 above, an adiabatically isolated column of an ideal gas is illustrated. According to EEJ, this gas spontaneously equilibrates into a state where the temperature at the bottom of the column Tb is strictly greater than the temperature Tt at the top of the column. The magnitude of the difference, and the mechanism proposed for this separation are irrelevant, save to note that the internal conductivity of the ideal gas is completely neglected. It is assumed that the only mechanism for achieving equilibrium is physical (adiabatic) mixing of the air, mixing that in some fundamental sense does not allow for the fact that even an ideal gas conducts heat.
Note well the implication of stability. If additional heat is added to or removed from this container, it will always distribute itself in such a way as to maintain the lapse rate, which is a constant independent of absolute temperature. If the distribution of energy in the container is changed, then gravity will cause a flow of heat that will return the distribution of energy to one with Tb > Tt . For an ideal gas in an adiabatic container in a gravitational field, one will always observe the gas in this state once equilibrium is established, and while the time required to achieve equilibrium is not given in EEJ, it is presumably commensurate with convective mixing times of ordinary gases within the container and hence not terribly long.
Now imagine that the bottom of the container and top of the container are connected with a solid conductive material, e.g. a silver wire (adiabatically insulated except where it is in good thermal contact with the gas at the top and bottom of the container) of length L . Such a wire admits the thermally driven conduction of heat according to Fourier’s Law:
where λ is the thermal conductivity of silver, A is the cross-sectional area of the wire, and ΔT=Tb–Tt . This is an empirical law, and in no way depends on whether or not the wire is oriented horizontally or vertically (although there is a small correction for the bends in the wire above if one actually solves the heat equation for the particular geometry – this correction is completely irrelevant to the argument, however).
As one can see in figure 2, there can be no question that heat will flow in this silver wire. Its two ends are maintained at different temperatures. It will therefore systematically transfer heat energy from the bottom of the air column to the top via thermal conduction through the silver as long as the temperature difference is maintained.
One now has a choice:
- If EEJ is correct, the heat added to the top will redistribute itself to maintain the adiabatic lapse rate. How rapidly it does so compared to the rate of heat flow through the silver is irrelevant. The inescapable point is that in order to do so, there has to be net heat transfer from the top of the gas column to the bottom whenever the temperature of the top and bottom deviate from the adiabatic lapse rate if it is indeed a thermal equilibrium state.
- Otherwise, heat will flow from the bottom to the top until they are at the same temperature. At this point the top and the bottom are indeed in thermal equilibrium.
It is hopefully clear that the first of these statements is impossible. Heat will flow in this system forever; it will never reach thermal equilibrium. Thermal equilibrium for the silver no longer means the same thing as thermal equilibrium for the gas – heat only fails to flow in the silver when it is isothermal, but heat only fails to flow in the gas when it exhibits an adiabatic lapse in temperature that leaves it explicitly not isothermal. The combined system can literally never reach thermal equilibrium.
Of course this is nonsense. Any such system would quickly reach thermal equilibrium – one where the top and bottom of the gas are at an equal temperature. Nor does one require a silver wire to accomplish this. The gas is perfectly capable of conducting heat from the bottom of the container to the top all by itself!
One is then left with an uncomfortable picture of the gas moving constantly – heat must be adiabatically convected downward to the bottom of the container in figure 1 in ongoing opposition to the upward directed flow of heat due to the fact that Fourier’s Law applies to the ideal gas in such a way that equilibrium is never reached!
Of course, this will not happen. The gas in the container will quickly reach equilibrium. What will that equilibrium look like? The answer is contained in almost any introductory physics textbook. Take an ideal gas in thermal equilibrium:
where N is the number of molecules in the volume V, k is Boltzmann’s constant, and T is the temperature in degrees Kelvin. n is the number of moles of gas in question and R is the ideal gas constant. If we assume a constant temperature in the adiabatically isolated container, one gets the following formula for the density of an ideal gas:
where M is the molar mass, the number of kilograms of the gas per mole.
The formula for that describes the static equilibrium of a fluid is unchanged by the compressibility (or lack thereof) of the fluid – for the fluid to be in force balance the variation of the pressure must be:
(so that the pressure decreases with height, assuming a non-negative density). If we multiply both sides by dz and integrate, now we get:
Exponentiating both sides of this expression, we get the usual exponential isothermal lapse in the pressure, and by extension the density:
where P0 is the pressure at z=0 (the bottom of the container).
This describes a gas that is manifestly:
- In static force equilibrium. There is no bulk transport of the gas as buoyancy and gravity are in perfect balance throughout.
- In thermal equilibrium. There is no thermal gradient in the gas to drive the conduction of heat.
If this system is perturbed away from equilibrium, it will quickly return to this combination of static and thermal equilibrium, as both are stable. Even in the case of a gas with an adiabatic lapse rate (e.g. the atmosphere) remarkably small deviations are observed from the predicted P(z) one gets treating the atmosphere as an ideal gas. An adiabatically isolated gas initially prepared in a state with an adiabatic lapse rate will thermally equilibrate due to the internal conduction of heat within the gas by all mechanisms and relax to precisely this state.
Conclusion
As we can see, it is an introductory physics textbook exercise to demonstrate that an adiabatically isolated column of gas in a gravitational field cannot have a thermal gradient maintained by gravity. The same can readily be demonstrated by correctly using thermodynamics at a higher level or by using statistical mechanics, but it is not really necessary. The elementary argument already suffices to show violation of both the zeroth and second laws of thermodynamics by the assertion itself.
In nature, the dry adiabatic lapse rate of air in the atmosphere is maintained because the system is differentially heated from below causing parcels of air to constantly move up and down. Reverse that to a cooling, like those observed during the winter in the air above Antarctica, and the lapse rate readily inverts. Follow the air column up above the troposphere and the lapse rate fails to be observed in the stratosphere, precisely where vertical convection stops dominating heat transport. The EEJ assertion, that the dry adiabatic lapse rate alone explains the bulk of so-called “greenhouse warming” of the atmosphere as a stable feature of a bulk equilibrium gas, is incorrect.
Correction: That should read …
“FROST on the ground (shaded from direct Sunlight) can remain there all day (even when ground and air are above 0 deg.C) so why doesn’t backradiation melt it?”
Note (in the link* below) that both the ground beneath and the air just above the frost were each just above freezing point, so there should be some conduction into the frost, but no radiation out of it. However, if the backradiation really does have about a quarter of the power of the Sun at noon and the backradiation from a cooler atmosphere really is able to impart thermal energy into the frost, then that frost should have melted at least as quickly as it would have in the Sun for a couple of hours. After all, water molecules should absorb IR radiation, shouldn’t they?
Well Prof Claes Johnson has shown why they don’t when they are warmer than the source.
And if backradiation all day long can’t even melt a bit of frost, how much warming will it cause in the oceans?
* http://climaterealists.com/index.php?id=9004
Crispin: Whilst I trust you know my position on all this, I do not like pushing the “CO2 saturation” concept. Firstly, bands only appear blank at TOA because CO2 scatters radiation and hence, when you point an instrument at some place on Earth, very little appears to come directly towards you from that point. Warmists will argue that the bands just get wider,
None of this matters anyway, because the energy will be mostly converted to thermal energy which can then transfer to other molecules (by collision) and end up being emitted by water vapour for example. Any emission to the surface will not be absorbed and converted to thermal energy (because it comes from a cooler source) and so all radiation from the atmosphere eventually ends up going to space. Hence carbon dioxide molecules have a cooling role radiating away that thermal energy which they acquire from oxygen and nitrogen molecules that cannot radiate themselves. It also absorbs and sends back to space some of the Sun’s incident radiation which is in the IR spectrum, hence also having a cooling effect in this manner.
Dr. Brown, George E. Smith, Willis, and a couple of others, Thank You.
I want to thank you for this educational opportunity. I have read all the comments that have been presented on this thread as well as other threads. Thank you for explaining the physics as I learned it. Now I feel much better that I could not fully grasp the gravitational temperature effect.
If one can’t follow the thought experiment presented by Dr. Brown, then an understanding will likely be very difficult, a tough nut to crack. Some who like myself are the slowest to grasp something may be most likely to become the greatest supporters of if when we do because we fought tooth and nail not to believe in it. Hence my learning process, quite skeptical with regards to anything concerning ‘climate related’. WUWT and the open discussion here is the greatest venue to acheive that type of learning experience. When every conceivable argument is presented as well as the facts, I feel confident with my knowledge when I walk away. Thanks to all.
robr says:
January 24, 2012 at 9:32 pm
The DALR is defined as g / Cp, where g is gravity and Cp is the specific heat of the atmosphere at constant pressure. Since I see no pressure term in there, I’m gonna say no.
(Bear in mind, however, that if you double the gravity, you’ll double surface pressure more or less. And so both pressure and “g” will change, and also DALR will change … but DALR will change because of the “g” term, not because of the pressure.)
Unfortunately, there is no simple answer to that one, as you are talking about a complete planetary climate system on an imaginary planet, and the pressure would have a host of different effects on winds, evaporation, all kinds of things.
So if anyone gives you a yes or no answer to the second question, they’re blowing smoke.
All the best,
w.
don penman says:
January 24, 2012 at 9:42 pm
Cool. Step out of a window, and tell gravity you’ve decided not to obey the law. There’s big money in it … selling tickets. Like getting energy from gravity, however, it’s a one-time thing.
w.
The problem outlined by Dr. Brown is interesting but largely irrelevant to the issue of whether the surface would be warmer in the absence of greenhouse gases.
Here is my reasoning on that.
It’s the analogy to the passive solar water heating system. First lets get a few things clear on that.
A good passive solar system does not need a greenhouse for the collectors to operate well. Often they use just plain black piping. It works nearly as well as pipes in a greenhouse because the 1,000 plus watts of solar radiation far exceeds radiation losses without the greenhouse. The pipes do not ever get warm enough due to the convection occurring in the water system bringing constant cooler water to the inside of the pipes.
Greenhousing the pipes only adds a few degrees to the system and is often not done as that’s the most expensive part of the system. (convection also ensures the surface does not equilibriate to the average daily temperature reading above the surface. Error is greatest at night.)
The heat you get in a passive system is far in excess of the daily average temperature.
Its important to understand this as well. We are looking at incremental warming not warming from the greenhouse effect itself which is already incorporated in the ambient local temperatures.
Finally, we should note that a favorite tactic of folks arguing this point is they want to simplify it by applying uniform radiation. These are analogies like Willis was using to argue against the gravitational effect. But uniform radiation would cause our passive water heating system to fail. All we would have would be water at the ambient local temperature.
The passive system uses gravity and convection but it entirely depends upon a diurnal cycle to obtain a higher average and in no depends upon the radiative effect of the medium in the storage system.
Thus it doesn’t matter a whit if after we invent an atmosphere isolated from any external interactions what it does in those states. The world of Jelbring is only relevant for ruling out external effects from explaining the actual state of the atmosphere at the moment the world is imagined. Thus what it does afterwards is truly irrelevant. It is relevant to how gravity does it but not to whether gravity does it or not.
The AGW advocates would like for us to believe that convection is caused by a radiative atmosphere but the atmosphere inside the pipes of the water system is not radiating, yet it warms and it warms purely by convection and acceptance of radiation at the surface (the collector level)
So what are the results? Well if Jelbring’s conclusions are correct that the adiabatic lapse rate is stable and it probably has a 50% chance of being so (or 49% if you really want to argue it) then gravity causes the surface all by itself to be warmer than it would be without an atmosphere.
And what would be the case if it weren’t stable like Dr Brown claims? Well then it would be like the passive solar hot water system that does not have a defined lapse rate but does convect under a varying heat source and averages a greater temperature than the ambient local temperature (which has the GHG effect included already). Indeed the system would equilibriate as soon as you either turn off the sun or set it at a uniform level of radiation.
So the conclusion is there is 1) Jelbring’s lapse rate is not stable so some great portion of the ATE (redefined GHE) comes from gravity enabled by the variability of downward surface radiation.
Or 2)
Jelbring’s lapse rate is stable so the ATE comes from gravity and variability of the downward surface radiation can be averaged and you get the same result.
What will be interesting is in the details of how this is being correlated to other worlds. And of course Dr. Brown and crew are certainly welcome and encouraged to do the same as one should be able to tease out the differences implied by the two different theories.
Better get that space program back on steroids is all I can say.
Bill Hunter says
“First lets get a few things clear on that. A good passive solar system does not need a greenhouse for the collectors to operate well. Often they use just plain black piping. It works nearly as well as pipes in a greenhouse because the 1,000 plus watts of solar radiation far exceeds radiation losses without the greenhouse. The pipes do not ever get warm enough due to the convection occurring in the water system bringing constant cooler water to the inside of the pipes. Greenhousing the pipes only adds a few degrees to the system and is often not done as that’s the most expensive part of the system. (convection also ensures the surface does not equilibriate to the average daily temperature reading above the surface. Error is greatest at night.) ”
Thanks for this practical information it backs up another practical investigation from Penn State Uni on ethylene polytunnel greenhouse.
Basically the project was to find if it made any sense to add Infra Red absorbers to polyethylene plastic for use in agricultural plastic greenhouses.
Polyethylene is IR transparent like the Rocksalt used in Woods Experiment.
The addition of IR absorbers to the plastic made it equivalent to “glass”
The results of the study show that( Page2 )
…”IR blocking films may occasionally raise night temperatures” (by less than 1.5C) “the trend does not seem to be consistent over time”
http://www.hort.cornell.edu/hightunnel/about/research/general/penn_state_plastic_study.pdf
When matter heats up due to compression or from falling into a gravity field, where does the extra thermal energy come from?
What standard model particle delivers the additional energy?
The matter heats up but where does the energy come from.
We know photons or EM radiation can deliver energy through the Electro-Magnetic Force. We know energy is added from the Weak Force in nuclear reactions according to E=M*C^2, the Strong Force does not operate unless Neutron Stars are Black Holes are involved. The Gravitational Force may compress space-time so the molecules themselves may just be more energetic in a space compressed 3-D environment.
But I have never seen an explanation of where the extra energy comes from when matter is heated up due to compression or when matter falls into a gravity well.
It IS coming from somewhere. It is already there, it is just a question of what is the ultimate source of this thermal energy.
Bill Illis says
“When matter heats up due to compression or from falling into a gravity field, where does the extra thermal energy come from? ”
If the falling is at constant speed it comes from the work done by atmosphere at that level (PdV work).
Its the opposite of the work done by a rising expanding parcel of air which does PdV work ON its surrounding atmosphere.
DeWitt Payne says: January 25, 2012 at 4:13 pm
Silver Ralph says:January 25, 2012 at 2:57 pm
If, on the other hand, he means the temperature of the total airmass, as measured by a standard thermometer, then he should know that you could never get the air at 50,000 ft to be +30oc. Just not possible. Never going to happen. So Dr Brown cannot mean this.
Not on Earth. But on a hypothetical planet with an isothermal surface and a transparent atmosphere or a very tall insulated cylinder, sure. You just need a surface temperature of 30C (the degree symbol is unnecessary) and a lot of time.
__________________________________________________________
Thank you for the scientific definition of temperature.
However, this is hardly explaining our atmosphere. We have a surface that is sort of isothermal (within a band of, say, +40 to -40oc); we have a fairly transparent atmosphere; and we have had a lot of time to run the experiment (several million years).
Yet the average temperature at 50,000 ft is around -80 oc. And there is no chance of the ‘temperature’ at 50,000 ft ever equalling the suposed average surface temperature of +15oc (ISA defined atmosphere), no matter how sensitive your thermometer. So if your explanation is correct, then why is the Earth so unlike the idealised system?
In short, I still cannot see the difference between the silver wire experiment, and the normal atmosphere. Ok, so the silver wire has greater conductivity to transport het to the upper atmosphere, but the less conductive real atmosphere has had several million years to transport surface heat to the top of the atmosphere and it would appear that it has still not achieved anything like equilibrium temperature.
Some basic explanations without the math is required, I feel.
PS In science you may use ‘c’ as opposed to ‘oc’, but in the rest of the world ‘c’ means ‘cents’ (dollars and….).
.
Bill:
One component of total thermal energy is gravitational potential energy. Thus a portion of total thermal energy can interchange with potential energy.
The assumption is that the compression occurs when the body of gas is physically lowered closer to the Earth and thus loses PE. That loss of PE transfers into a gain of KE which contibutes to thermal energy raising the temperature. (Compare the interchange between PE and KE with a pendulum, or when you car starts to roll down a hill.) The opposite occurs when warm air rises.
PS As you probably know, this is a reason for using the term “thermal energy” rather than “(ocean) heat content” as used by you-know-who. There is no fixed thing which is “heat content” and heat is energy in transit as distinct from energy itself.
As a “layman” I find this very interesting.
Fig 2 doesn’t really convince me of anything. I like the analogy of the spinning wheel. Let’s say we have a spinning ring in a vacuum with no gravity. The ring will spin forever right? Now imagine we attach a couple gears and a shaft from a fixed point. The gears will simply connect the shaft to the inner ring causing it to spin. If the gears are all frictionless the shaft will rotate forever.
I know the analogy doesn’t fit but it’s close. Obviously if we apply any friction to the shaft (a generator) the ring will stop spinning. Saying any heat runnin through the wire is a perpetual motion machine just doesnt ring true.
Having said all that I think the temperature will equalize in the cylinder and no heat will flow through the wire.
Applying this to our atmosphere is the hard part for me. So we have an atmosphere with a hot side and a cold side. This seems to easily explain the temperature gradient.
What I wonder about is the effect of doubling or tripling the nitrogen thereby increasing pressure. I can’t see this making the hot aide hotter. I imagine the cold side will just move farther out. The atmosphere would be a greater reservoir of heat but the temp wouldn’t be higher.
Taking into account day/night, the rate of conduction at the surface and the differences between surface and atmospheric temperatures oh and GHGs all make things more confusing!
As I suspected this notion that gravity produces a lapse rate goes WAY back. James Clerk Maxwell hisself proposed it in 1866. If I’m wrong I’m in very good company. Here’s a nice writeup on the history. Many physicists to the present day have carried Maxwell’s torch. It is not settled science. Maxwell himself collaborated with Boltzman to formulate the Maxwell-Boltzman distribution law that made the column isothermal. Maxwell continued to question its validity though and many since then have also questioned it. At least Maxwell was a good scientist skeptical of his own work his entire life.
http://philosophyfaculty.ucsd.edu/faculty/ccallender/index_files/maxwell.doc
much more at link above
“”””” Bill Illis says:
January 25, 2012 at 8:22 pm
When matter heats up due to compression or from falling into a gravity field, where does the extra thermal energy come from?
What standard model particle delivers the additional energy?
The matter heats up but where does the energy come from “””””
Bill there really is not much to it. Imagine a humungous cloud of gas but assume the individual moelcules are separated far enough in space. that they basically never (or extremely seldom) ever see each other, so there ar no collisions. Jeans showed that any such cloud no matter how uniform in properties, if the total mass exceeds some threshold value, becomes unstable, and a region of slightly higher density appears. That becomes a gravitational “magnet” attracting every molecule towards that region, which will simply increase the density inhomogeneity.
So your “gravity field”, is the mutual self attraction of all of those molecules to each other, and each molecule will start to move in the direction of the center of mass of all the molecules. So every molecule will be headed towards the same point. Now it is also possible even likely, that the initial velocity vector for each molecule is not directedf exactly at the CM point, but to slightly off center points; and this will result in a rotary momentum, in addition to the linear momentum towards the CM.
Initially there are basically no collisions, so the Temperature is essentially zero (kelvins).
As the molecules move towards each other the density increases, and the inverse sqare law causes the gravity to increase, so the molecules are accelerating towards the CM, ever faster, andf also starting to show signs of a net cloud rotation, depending on the initial state.
Eventually the density will get high enough, and the initial directional non uniformity sufficient to allow molecules to start banging into each other. These collisions are random events, and so they start to change the directed collapse towards a common focal point, into a more chaotic pattern, and the directed acceleration starts to get attenuated by the chaotic scattering of the colliding particles. This is the first sign of both pressure (change in momentum of particles in collision) and also Temperature. The Temperature represents the statistical distribution of individual molecular motions; relative to the common center of mass of the collapsiong cloud. The conversion from an orderly directed collapse to a more chaotic structure, represents the appearance of waste “heat” as the original work done by the force of gravity operating over the distance the molecule moves.
So the source of the energy is simply the work done by gravity forcr times distance. The potential energy of the molecules far removed from the CM of the entire cloud, is slowly being converted into kinetic energy of the onrushing molecular mass, but once collisions start occurring to disturb the uniform collapse, some of that kinetic energy gets converted to “heat” represented by the random distribution of the kinetic energies relative to the CM space co-ordinate frame. The density will continue to increase without limit, as the gravitational force increases due to the inverse square law of gravity, and the rotation will speed up, to conserve the angular momentum of the initial state, as the size decreases, so the moment of inertia continues to decline, and angular velocity increases to keep I. omega^2 constant.
It is the original potential energy of the distantly spaced gravitationally attracted molecules, that first converts to a directed kionetic energy and angular momentum, and finally start so dissipate as heat, once the molecules start to collide.
So the Temperature will increase without limit, until hydrogen thermo-nuclear “burning” starts. The energy released now heats the gas till it becomes an ionised plasma due to the high Temperature, the escape of this centraally generated energy to the suface of the “cloud” , now a proto star will eventually stop the collapse as the outer layers also heat, and the outer plasma will become opaque to the EM radiation generted at the million degree buring interface. So long as the hydrogen keeps converting to helium, the star will shine as a”main sequence star” and thr gravitational collapse will have been halted by the thermo-nuclear energy released.
The problem with the earth’s atmosphere is that there isn’t near enough gas to reach the density and Temperature to start hydrogen conversion, so the collapse stops when the pressure generated by gravitymatches the gravity force. The heating that occurs during collapse due to the work done by gravity, is eventually radiated away assuming no star is nearby, to supply new energy.
We hqppen to have such a star that delivers EM energy to the bottom of the transparent atmosphere, and that energy warms the bottom of the atmosphere by all the well known thermal processes, until the energy loss rate, eventually limited by radiation, matches the supply rate from the star. It is the heating of the atmosphere bottom, by the star light, that creates the outgoing Temperature lapse rate. It is NOT gravity that creates the Temperature gradient.
Silver Ralph and others:
I confess I have not read many posts on this thread, so I may be repeating something said by others. NASA data shows mean temperatures going down to around -60 deg.C in the troposphere, then back up by about 40 degrees in the stratosphere. Then I understand they go back down to around -100 deg.C at the mesopause, but then can be much warmer than the surface (even over +100 deg.C) in the thermosphere.
Any experiments in glass jars, cardboard boxes etc (including those of Arrhenius, Wood and Nahle) can never emulate an open atmosphere. One reason is that the inside surfaces of the containers absorb (and transmit) thermal energy, and can contribute to overall warming or cooling. Also pressure is nearly uniform, so downward conduction occurs and the Second Law applies. However, one “result” of the Second Law (see Wikipedia) is uniform pressure, and obviously that doesn’t apply in the atmosphere.
Hence, adiabatic temperature variations are a fact of life in the atmosphere. Furthermore, there will never be a stable state due to weather conditions. Energy is continually entering the atmosphere (probably more than 50% at the surface) and then of course it takes a finite time for warm air to rise by convection, cooling as it does so. In fact I understand that its motion is more cyclic, rising in equatorial regions and falling at the poles where inversion can prevail.
Then there are further complications when incident solar radiation causes some warming, and evaporation and radiation “springboard” some of the energy from the surface to somewhat higher altitudes.
The lapse rate is far from constant, there being a fall of roughly twice as much in the first 14,000 feet as in the next 11,000 feet for example, according to NASA data. This may be due to the springboarding of latent energy in evaporated water going up to cloud levels.
No one really has a hope of modelling it all accurately – ever.
Pick a good spot to live on this planet – and enjoy your weather!
@Bill Hunter. Thank you for that example where the diurnal day-night pumping is so essential for a passive solar hot-water system.
As I wrote earlier in the tread, the “average insolation” concept so often used to explain the climate energy balance misses so much. You have given us a great example: Solar Heaters don’t work without a night and day.
“”””” Eric Atkerson says:
January 25, 2012 at 7:02 pm
@ur momisugly George Smith
But tax gets boring at times so it is good to have a diversion… “””””
The short answer Eric is yes; but only for a short period of time.
Gravity provides a FORCE, that attracts the gas towards the ground. That force is m.g, where m is the mass of the molecule, and g is the acceleration due to gravity, so m.g is literally the WEIGHT in the gravity field of that molecule.
When that force pulls the molecule down some distance, the WORK done is the force times the DISTANCE moved . WORK is FORCE times DISTANCE (moved). ENERGY is the CAPACITY for DOING WORK.. Now of course the gravity will change with distance so you would have to do a calculus integration to get the correct answer.
As the gas drops under gravity and work is done by gravity compressing that gas; that work gets converted into heat as the molecular collisions increase at the higher density and the pressure goes up. The compression WORK gets converted to heat; BUT, once the collapse stops when teh pressure builds up enough to stop the fall, then the gas starts to lose energy and cool, by radiation, and eventually the whole thing would settle at a fixed Temperature. That assumes no other source of energy such as a nearby star. So yes gravity can create heat in compressing the gas but it is a transient event.
DeWitt Payne says: January 25, 2012 at 4:13 pm
So a thermometer reads according to the average kinetic energy of the molecules that hit it, not the rate that the molecules hit it.
_________________________________________________________
Sounds counter-intuitive, to me.
So an aircraft travelling at the normal TAS of 450kts (say, 900kph) at 40,000 ft, increases the measured temperature of the air by, say 30oc (-30oc TAT, as opposed to -60oc OAT). Are you saying that this measured temperature increase is solely due to an increase in the (relative) speed of each molecule hitting the probe, rather than the increased number of molecules hitting the probe? (The number of collisions with the temperature probe increases dramatically with increasing speed, as you might expect.)
I always thought that the surface warming of an aircraft (several hundred degrees-worth on Concorde), was due to the increased number of molecules hitting the airfame, and not the individual molecule’s increased velocity..
.
I don’t understand what all this commotion is about, this is not a novel problem!
This is not an appropriate application of thermodynamics, vis analysis of the atmospheric temperature lapse rate. The ideal gas atmosphere, or also the real atmosphere, isn’t isothermic. There is no “thermodynamic equilibrium” in the real atmosphere or even in an ideal gas atmosphere. There is no “heat flow”. There is no actual “heat”, anywhere at all, in this argument.
The atmospheric temperature lapse rate is a very simple statistical mechanical problem; it is energy partition, elastic molecules colliding in a gravitational field. A simple one dimensional model demonstrates it. Contrary to Dr Browns arguments, there are no Maxwell’s demons in the adiabatic lapse rate, and no other thermodynamic shibboleths. No “heat” is necessary, or even actually exists. There is no “perpetual motion” anywhere in the atmospheric temperature lapse rate, any more than the Laplacian elliptic operator, energy partition, and orbiting planets are “perpetual motion”. Gravity applies to molecules as well as to planets. Absent planetary gravitons, the atmospheric temperature lapse rate would still exist if little elastic strings were used to tie all the air molecules to the Earth.
addendum: The atmosphere temperature profile is described by bulk gas properties (ideal gas law) up to the tropopause, and gas radiative transport properties in and above the stratosphere.
addendum: The formalizations of the arguments here are very confusing; “heat”, “work”,
“equilibrium”, etc. The only real things involved here are electrons, photons and gravity (and extra inert mass proportional to electrons). This isn’t difficult!
Joules Verne. Thank you for your contributions on this thread.
You have been tenacious and your “temperature” was never raised. You have approached the issue from numerous angles to explain your reasoning and helped to improve my appreciation of all of the relevant points.
Others have presented their arguments forcefully too. But – despite it being described as a textbook case (an appeal to authority), I remain unconvinced by the arguments at the top of this thread.
http://philosophyfaculty.ucsd.edu/faculty/ccallender/index_files/maxwell.doc
Interesting link Joules Verne, Thanks.
Silver Ralph wrote “Sounds counter-intuitive, to me”
You should trust your intuition a little less it would seem. The plane warms by friction. The thermometer measures temperature, not the amount of friction. Temperature has nothing to do with the density of molecules. If it did, consider a near vacuum such as between the walls of a vacuum flask – does that have a temperature of near absolute zero? Hardly!
George E. Smith; Jan 25, 2012 at 9:23 pm
“It is the heating of the atmosphere bottom, by the star light, that creates the outgoing Temperature lapse rate. It is NOT gravity that creates the Temperature gradient.”
This simplistic summation really does not take into account all processes involved. For a start you ignore energy transfer by phase change. You appear to disregard the physical rate at which warm air rises by convection. When the warm air rises, I’m not even sure that you take into account the conversion of the change in gravitational potential energy to thermal energy, do you? If so, why isn’t gravity in your result?
What, may I ask, is wrong with this computation which gives a very different result?
http://claesjohnson.blogspot.com/2010/09/lapse-rate-vs-radiative-forcing.html
George, Robert G Brown (and others)
Please be sure to read the first linked item in the paper I linked above, namely http://www.nada.kth.se/~cgjoh/atmothermo.pdf
Of course I realise that this is leading to a very different result, but it is one which agrees quantitatively with reality and, in this case, I go with Professor Claes Johnson’s computations and obviously much more comprehensive coverage of the various processes in the atmosphere.
Bill Hunter said @ur momisugly January 25, 2012 at 7:48 pm
Gosh! I’ve been wasting money on putting greenhouse film on my greenhouse when I didn’t really need any. Whoda thunkit? People who use greenhouse film to raise the temperature around their crops are all idiots wasting their money? Don’t think so Bill…
Pompous said:
“Gosh! I’ve been wasting money on putting greenhouse film on my greenhouse when I didn’t really need any. Whoda thunkit? People who use greenhouse film to raise the temperature around their crops are all idiots wasting their money? Don’t think so Bill…”
Check and see if your fancy IR film is also moisture resistant. Reducing the thickness of the moisture layer on the inside of the cover has more effect than the IR coating.