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.
Oops, I mixed replies to the previous two comments. The paper was a separate suggestion. The answers are the same, however. Experiments talk, bullshit walks. And please, address the actual content of my argument above instead of invoking obscure stat mech or nonstandard axioms. Explain how a nonzero lapse rate does not enable second law violating, perpetual heat flow, if you would, right up to the point where real thermal equilibrium is achieved. Also remember, gravity is doing no net work while all of this is going on. If it were, things would actually be worse — you’d start violating the first law of thermodynamics as well.
rgb
Joe Born,
Please post a calculation of the Velasco lapse rate for a gas column with the surface at STP (101325Pa and 273.15K) and g = 9.81 m/s^2. The number density/cubic meter is ~6E23 molecules/mole/0.0224m^3/mole = 2.7E25.
One minor point. Since statistical mechanics is all about probabilities, it is possible to violate the Second Law. It’s just extremely unlikely. All the molecules of air in a room could migrate into one half of the room but the time for the probability of this event reaching 50% is really, really long. It’s many orders of magnitude longer than the age of the universe, depending on the size of the room and the air pressure in the room. I suspect Velasco’s calculation is something like that. For one molecule there’s a 50% chance it will be in one half of the room at any given time.
Robert Brown,
I’ve read a number of thermodynamics texts myself.
Not once did I see a proof of the Second Law that did not rely upon circular logic. I’ve seen plenty of empirical proof, that people have been unable to violate it, but no direct proof.
Relying upon the Carnot Cycle is pretty clearly circular logic. It’s more difficult to show, but assuming that the MB distribution remains uniform under gravity may also be circular.
If you have a proof of the Second Law that is not based on circular logic, I’d be happy to read it.
Failing that, all we have is that there are no publicly recognized or understood violations of the Second Law. It is empirical, and nothing more.
Poor engineering is not proof of impossibility.
” “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.”
I live half-way up a mountain at 6100 feet. The valley below is at 4500 feet. The temperature difference is nearly always the dry lapse rate 8 degrees F, whether it is calm or windy. Only if it is raining or snowing will it be different. It then goes to the moist lapse rate. Most of the time it is sunny, heating the ground equally, both in my back yard and in the valley below. What maintains the lapse rate temperature difference?”
Mostly gravity.
If you lived planet with 1/2 the gravity, the the temperature difference would about 1/2.
You could say you would be warmer. You could also say lower elevation would be cooler there would less difference temperature.
Less difference in temperature is undeniable.
With a silver rod, one could transfer heat from lower elevation to your elevation. Or one could use other material which cheaper and conducts heat better than air. But silver is one of best conductor of heat and air is one the poorest conductors of heat.
One can generate energy from differences in heat. Venus isn’t particularly good place to generate energy- despite being very hot.
Venus doesn’t even “have a lot of energy”- in terms of total joules of heat in it atmosphere, assuming one find a lot something which is colder one couldn’t create an extraordinary amount of energy.
Over a period of time, say 24 hours, earth absorbs more of the sun’s energy than Venus does- despite being closer to sun and getting around 2700 watts per square meter compared to Earth’s 1300 watts per square meter.
This can quickly seen: Venus is hot, it’s temperature near surface does not vary over time, and since Venus is hot, it can not be made hotter by the sun. The earth more distance and receiving less sunlight, is much cooler. And because it is cooler it can heated by the sun and there is daily variation in temperature. And on planetary scale, earth has large variation in equator and polar temperature. So earth is churning heat engine, whereas Venus is more stagnant.
So in terms of power, in terms of horsepower, earth is a more powerful engine.
It seems to me that in subject of climatology, there is measurement of the engine temperature, and there should more attention to how much power the engine produces- and what’s earth miles per gallon.
Robert G. Brown says
The dry adiabatic lapse rate determines how high thermals will go – usually, only a few kilometers. The actual lapse rate is normally significantly different from the DALR.
As this article argues, the lapse rate without IR emitters would be zero. It is the greenhouse gases that move the actual lapse rate (ELR) from zero to -6.5 K/km. The DALR is -9.8 K/km. To claim that anything “maintains” the DALR simply means that you have not looked at the data.
Related to the DALR is the concept of “potential temperature” – the temperature that a parcel of atmosphere would have if it moved adiabatically from some altitude to sea level. For instance, if the atmosphere at 10 km was -55C, its potential temperature is
The other meaning of this is that for air to convect from sea level to an altitude of 10 km, it must be at least 43C. A more typical value in the sub-tropics would be -70C at 17km
Since the surface temperature is typically a bit cooler than this, the bulk of the atmosphere does not follow the DALR. (Near the surface, the DALR is seen almost every day. But only near the surface.)
I suggest that everyone look at some real data.
“kuhnkat says:
January 24, 2012 at 2:33 pm
Alan Millar,
“The Sun will die and become a cold white dwarf with no solar wind to blow any atmosphere away.”
This is an assumption without much empiraical proof”
I hope your Mum isn’t reading that because even she would be embarrassed!!
Is this the level people will sink to just because they would like to have a new theory of Thermodynamics which will disprove the theory of CAGW?
Get a grip folks. These sort of statements are going to hold this well respected site up to ridicule.
Stick to facts and real physics and CAGW will be shown to be nonsense in any event.
It will take a bit longer but I will live to see it and I ain’t young! Have patience, trust in Gaia!
Alan
@ur momisugly Dr. Brown –
I’m curious, what if the gravity isn’t constant, but is fluctuating?
“Willis Eschenbach says:
Robert Brown says:
I have been seriously trying to follow this conversation. I have my Thermo text, my Heat Transfer text, my CRC handbook, the internet, and my calculator. For a dumb ass like me (tau beta phi), I wonder if one of you would answer give me your opinion to the following questions (2):
Does the atmospheric pressure, no GH gases, play a role in the dry adiabatic lapse rate?
Does the atmospheric pressure, no GH gases, effect the overall equilibrium temperature of the near surface of a planet?
Thank You,
Robert S Rider
I’m so dumb I can’t even spell Pi.
says: These two idealised adiabatic processes (like the adiabatic stages in the Carnot Cycle) will result in the parcel returning to Earth with nearly the same temperature as leaving (the slight drop being accounted for by radiation at TOA).
Carnot cycles are ISENTROPIC. By definition. Isentropic means adiabatic AND reversible.
Hmm, maybe we read different textbooks. Any cyclic heat engine — being cyclic — returns to its original state at the end of a cycle. All cyclic heat engines — being heat engines — increase the entropy of the Universe while operating. In particular the Carnot cycle absorbs heat \Delta Q at temperature T_H for a change of entropy of the hot-side reservoir of -\Delta Q/T_H, and then rejects it into the cold-side reservoir for a change of entropy of the cold reservoir of +\Delta Q/T_C.
The total entropy change — per cycle — is thus:
\Delta S = \Delta Q (1/T_C – 1/T_H) > 0
To correct you — and please, bear in mind that I’ve taught this for 30 years — Carnot cycles are NOT isoentropic. Isoentropic DOES mean adiabatic (\Delta Q = 0) and reversible, but Carnot cycles contain two isothermal expansion/compressions (also reversible). The isothermal parts are not isoentropic, as explicitly shown above.
Now, what drives the circulation cycle you describe? How about absorbing heat at constant temperature from the hot ground (reservoir) and delivering it to the upper troposphere where the heat is lost to radiation at much colder temperatures. Hmm, sounds like something that increases the entropy of the Universe to me. The air that is rising and the air that is falling are not at the same temperature. They may both be isoentropic processes, but they don’t occur at the same place and the same time, and it is the thermal variations of density with temperature that ultimately provides the lift (or lack thereof) that drives the cycle, positive or negative net buoyancy.
With all that said (filling in details), I think we agree. So what is the point?
rgb
Paul Birch:
“I have now read the Velasco et al article, and it agrees with what I said: in either the microcanonic (totally isolated) ensemble (with a reasonable number of particles in the gas) or the canonic ensemble (in thermal equilibrium with the surface or walls, irrespective of the number of particles), the gas is isothermal.”
Of course, what we’re talking about is the microcanonic ensemble, to which Equations 5-8 apply. If you read Velasco et al.’s Equation 8 for mean single-molecule kinetic energy K as a function of altitude z, you’ll see that the expression for K is the product of a constant and (1-mgz/E), where m is molecular mass, g is the acceleration of gravity, and E is total system energy. To me that looks as though K decreases with altitude z: the temperature decreases with altitude. Is there some different way you interpret that factor? As I read it, it says there will be a lapse rate that’s small for large numbers of molecules but stll finite and non-zero so long as the number of molecules is not infinite.
Presumably, you are basing your interpretation of Levasco et al. on its penultimate paragraph, in which they made an execrable attempt to state verbally what the equations express mathematically. Unfortunately, that passage is so abysmally opaque that any exegesis thereof matching the mathematical result is doomed to appear hopelessly strained. So I will forgo the attempt. The real question is, Does Equation 8 define an altitude-dependent temperature or not? If so, there’s a non-zero lapse rate at equilibrium.
If you can’t reach the answer by considering Equation 8 itself, consider the lead-up to it, where Velasco et al point out that the state density as a function of both velocity and altitude (Equation 5) is not the product of state density as a function of altitude alone (Equation 6) and state density of a function of velocity alone (Equation 7)–as it would be if temperature were independent of altitude. They also observed that the density distribution as a function of velocity is not, as one would expect of an isothermal configuration, the Maxwell-Boltzmann distribution.
That was the wind-up, and the pitch was Equation 8, which says that, indeed, the temperature is not isothermal.
Do you interpret those equations differently?
Mike, it was to address this specific objection that the Beach-House Block Story was conceived … this story shows that the length of the column is irrelevant.
Q. Daniels, please let me commend to your attention the Wikipedia page titled “Hamiltonian vector field”, and the references therein.
In particular, that page’s geometric theorem “the symplectic form ω is preserved by Hamiltonian flow” is equivalent to the dynamical principle “the state-space volume of a dynamical ensemble never decreases”, which in turn is equivalent to the thermodynamic principle “the entropy of a dynamical system never decreases”.
Whether or not this geometric reasoning conveys belief … at least it is not circular reasoning.
What a fun thread! I should be working but I’m reading it instead. (That is okay, it is 8:22 PM and I’m self-employed, so it’s not like the boss doesn’t know what I am doing.)
My thanks to Dr. Brown and Willis for their patience. I would have given up long ago. I liked Dr. Brown’s simple example.
My next comment is going to offend many people so, if you are sensitive, quit reading. The discussion in this thread reminded me of many of the discussions on RealClimate. Only the role of the climate scientists was taken by those who opposed Dr. Brown’s explanation—they knew what the truth was and they could figure out some theory to disprove it.
This thread is probably a healthy process—although somewhat painful to watch. But, it does show that one need to think hard about these issues.
I feel that this discussion is a reasonable model of how science often advances. Someone throws out a good idea. Many dump on it with facile but incorrect criticisms. A few offer support. Finally, after a long time and much confusion there is reasonable agreement that the idea is right (or wrong, depending). We now believe that bacteria cause many ulcers but that N-rays don’t exist. But, when the two theories were offered, the bacteria/ulcer theory was dumped on but the N-ray theory was not.
My guess it that a few who participate in this thread will actually learn something, which is probably more than you can say for most students in freshman physics in college.
Billy
Robert Brown says at 3:45pm:
“Tell me whether or not the system in figure 2 permits energy to flow in a circle forever.”
Robert Brown says in a top post verbatim quote, search on the text for context of his answer:
Yes. “Heat will flow in this system forever; it will never reach thermal equilibrium.”
Robert Brown at 3:45pm:
“If you answer “no, of course not” you are quite right.”
Now Robert Brown is going so fast he is not right with himself. S-l-o-w down again Robert, when you do, you are quite good. Maybe you really are struggling & working to line up with the past thermo masters to grok this stuff better like Joules Verne and Tallbloke handles.
Robert continues to struggle forward to equilibrium grokness by reading up on the subject:
“Thermal equilibrium does not equate the total energy. Read the equipartition theorem. Open a standard introductory physics textbook. Learn what temperature is. Then return.”
I have returned. Here is a quote from my standard introductory physics text book: “Equipartition gives the total average kinetic and potential energies for a system at a given temperature.”
Robert – You are advancing in your studies! This is good. You must now grok potential energy better. It is equipartitioned with kinetic energy at a given temperature. I have learned (long ago) that temperature is mean kinetic energy (reading your Caballero ref. was a cool refresher…).
So Robert is right here thermal equilibrium does not equate to the total energy. Thermal energy is equipartitioned with potential energy for the total energy. Good going Robert, I see advancement in this 3:45 post toward the thermo master’s laws.
Robert gave a little back with the two different answers to the same question but still see some progress.
Robert will be way better off moving to grokness equilibrium understanding the non-isothermal gas column upon reading Caballero section 2.3. Then return.
Venus atmosphere is ~4.8 x 10^20 kg
Average temperature: 737 K (464 C)
http://nssdc.gsfc.nasa.gov/planetary/factsheet/venusfact.html
Specific heat of CO2: [kJ/kgK]
600 K 1.075
650 K 1.102
700 K 1.126
750 K 1.148
800 K 1.168
http://www.engineeringtoolbox.com/carbon-dioxide-d_974.html
To lower one degree of K requires 1.148 times 4.8 x 10^20 kg
Earth ocean:
1.4 x 10^21 kg
278 K [5 C] 4.204 (kJ/kgK)
To lower or increase one degree of K requires 4.204 times 1.4 x 10^21 kg
To freeze or melt into ice requires 334 kJ/kg
To vaporize water 2,270 kJ/kg
http://www.engineeringtoolbox.com/water-thermal-properties-d_162.html
So how many joules does it take heat a Venus from say 20 K to it’s present
temperature?
The chart starts at:
175 K 0.709
So roughly .7 times 4.8 x 10^20 kg times [175minus 20K] 155 equals KJ
And from 175 to 375 .8 times 4.8 x 10^20 kg times 200 equals KJ
375 K to 600 K: 1.0 times 4.8 x 10^20 kg times 225 equals KJ
600 to 737 K: 1.1 times 4.8 x 10^20 kg times 137 equals KJ And sums:
5.2 x 10^22
7.68 x 10^22
10.8 x 10^22
7.23 x 10^22
Which is 30.9 x 10^22 kJ
With earth melt 1.4 x 10^21 kg ice is 334 kJ/kg times 1.4 x 10^21 which is
46.7 x x 10^22 KJ
So to heat ice from 273 K to 274 K require more joules than the atmosphere of Venus
requires to heat from 20 K to 737 K.
To warm the ocean from 276 [3 C] to 13 C
Requires 10 times 4.2 times 1.4 x 10^21 which is 5.88 x 10^22
In terms of ten millions of year, the earth oceans have had 10 C increase or difference
in ocean temperature. I don’t think many consider that Venus has had such swing
in temperature: 7.23 x 10^22 is amount joules required to heat from 600 to 737 K.
So about 100 K [or 100 C] change in Venus temperature.
In terms of ice age to interglacial periods there is about 10 C difference in average global
temperature [not ocean change in temperature- but atmospheric]. So in terms couple tens of thousands, earth temperature changes, still roughly close to comparable temperature of somewhere around 100 C change in Venus.
So it requires real absorption of energy [joules] to change “average temperature”, locally daily one can easily have more than 10 C change in temperature. Such changes reflect dynamic, and powerful heat engine.
So, we would expect the atmosphere at the surface of a planet to be warmer that it is at the top of the atmosphere. Of course, we can’t totally ignore conduction and radiation but, compared with convection, they are second order effects.
We might expect this if we didn’t understand convection. You’re getting things backwards, and amazingly, even though I derive the density of an ideal gas in thermal equilibrium above, you don’t even bother to read and understand it.
At a uniform temperature there is an exponential pressure and temperature gradient. If you warm the system at the bottom, the density of the fluid there decreases and there is a net buoyant force that lifts it up. Convection is cone-head complicated — I mean seriously complicated — in the general case. The equations that describe it are the Navier-Stokes equations, which are nonlinear partial differential equations so complex that mathematicians haven’t even been able to prove that a solution exists in the general case, let alone solve it. The idea is simple enough, and in simple geometries with e.g. uniform thermal gradients across the fluid one can predict some of the structure observed, e.g. convective rolls. But your base assumptions are completely false, and you have cause and effect completely reversed.
Undriven convection does not lead to warmer air on the bottom. Not ever. Heat a gas or liquid uniformly on top and you will have no vertical convection, because the density profile is stable. The stable undriven density profile is precisely what I derive, and is isothermal, with no convection. Only if you differentially heat a system on the bottom or on the sides (which is still part way to the bottom) do you get convection, and that only because the bottom is already warmer because of something else. Convection, in fact, cools the bottom!
A secondary comment is that radiation and convection make (from what I understand) roughly equal contributions to surface cooling. Either one can be dominant under different circumstances. During the day, convective cooling can be important — convection driven breezes can pick up a fair bit of heat from the surface. On a clear dry night, however, the ground temperature quickly inverts (becomes cooler than the bulk of the air immediately overhead) and radiation becomes far more important than convection.
The desert heats up to 45C or so during the day, but can still cool to 0C overnight. Not (primarily) from convection, not at all. By radiation.
Way back in boy scouts, winter camping in upstate New York, I learned about radiation and temperature. Cloudy nights are far warmer than clear nights. Clouds reflect a lot of heat back down and slow the cooling of the ground considerably. Water is a powerful contributor to the greenhouse effect. I also learned about a space blanket. A teensy thin layer of aluminized plastic, and yet it keeps you amazingly warm, because it reflects back your body’s radiant heat. You can feel it instantly if you put your hand into it. Your body loses roughly half of its heat from conduction/convection, and half from radiation. Air is a lousy conductor of heat, and often there is little or no wind. Radiation can easily be dominant, not just “second order”. I have no idea which one is dominant overall as far as surface cooling is concerned, but neither of them is negligible.
rgb
Robert Brown says:
January 24, 2012 at 8:28 am
Show me my mistake. Anybody. I won’t be offended.
[kdk33 says:
January 24, 2012 at 7:22 am ]
No, I think you are generally quite right, and this agrees rather well with Caballero’s argument. Isentropic because it is dominated by convection, not conduction, in an open system heated at the bottom. Isolate the system, or heat it at the top and explain to me how the bottom will end up warmer than the top.
Yeah, right. Just like the oceans. I wonder why the argument fails for the oceans? They seem to come into thermal equilibrium at, well, thermal equilibrium (constant temperature, independent of pressure, density, “gravity” etc), below the convection-dominated thermocline.
========================
The thermocline exists because of these, heated surface waters warmer and therefore less dense will sit on top of colder, denser water.
Because going through 4°C to lower temperatures water gets dense enough to sink and doesn’t freeze, freezing water floats, so not independent of density and pressure and as these are due to gravity, not independent of that either. Salt water has lower temperature before freezing, -1.9°C.
Some extra bits.
In this description of how oil is formed in the oceans, increased pressure means increased temperature:
“Other sediments continued to be deposited and further buried the oganic-rich sediment layer to depths of thousands of feet, compressing the layers into a rock that would become the source for oil. Over the years, as the depth of the burial increased, pressure increased, along with the temperature.”
“Water pressure at the deepest point in the ocean is more than 8 tons per square inch, the equivalent of one person trying to hold 50 jumbo jets.”
“Atlantic sea water is heavier than Pacific sea water due to its higher salt content.”
“The Antarctic ice sheet that forms and melts over the ocean each year is nearly twice the size of the United States”
“90% of all volcanic activity on Earth occurs in the ocean. The largest known concentration of active volcanoes (approximately 1,133) on the sea floor is located in the South Pacific”
“Under the enormous pressures of the deep ocean, sea water can reach very high temperatures without boiling. A water temperature of 400 degrees C has been measured at one hydrothermal vent.”
“The top ten feet of the ocean hold as much heat as our entire atmosphere”
The above from: http://www.savethesea.org/STS%20ocean_facts.htm
“90% of the total volume of ocean is found below the thermocline in the deep ocean. The deep ocean is not well mixed. The deep ocean is made up of horizontal layers of equal density.”
http://www.windows2universe.org/earth/Water/temp.html
And bearing in mind heat rises.., http://www.esr.org/outreach/glossary/insulation.html
“Ice is a great insulator. A lot of what causes climate and weather involves the exchange of heat and fresh water between the ocean and atmosphere. If the ice cover is high, very little heat escapes from the warm ocean to the cold polar atmosphere in winter. But the heat loss through open water is so high, maybe 10-100 times more than through ice, that even a small fraction of open water has a big effect on area-averaged heat loss. Typical heat loss values are ~10 W/m2 through thick sea ice, and ~1000 W/m2 in winter through open water (depending on wind speed, air temperature, etc.)”
Do you have a phobia about gravity? Just asking.
Robert Brown wrote:
I do not care about what generates the lapse rate. If the lapse rate is stable, so that heat delivered to the top redistributes to maintain a constant equilibrium temperature lapse between the top and the bottom — the sole case examined in the article above — then it violates the second law of thermodynamics.
Let me put it bluntly. If somebody presents a statistical mechanical computation that suggests that the second law is violated, I would knee jerk assume that the authors had made a terrible mistake unless and until proven otherwise, especially if I “could not understand” everything that they did.
Even then I would be doubtful.. To be honest, I would be doubtful if I did the work myself. I think that the paper you link has the right idea, and you will note that on other threads I propose precisely the same experiment. Show me, in other words. I’m a theorist, but I’m no fool. Experiments trump theory every time, …
I agree with this in detail, and find it a completely reasonable attitude. I will note that some people have difficulty understanding particular pieces of math, independent of their complexity. The Lorenz Transform is one such.
Graeff’s work is probably not sufficient proof for you. He believes he has successfully measured said temperature differential. http://www.firstgravitymachine.com
I also don’t think that a PMM2 machine violates TANSTAAFL. For one thing, the energy must come from somewhere, even if it’s just being exhausted as waste. For another, such a device would require an insight and a good deal of skill to build and use, even if it was as simple as rain. Doing takes effort, even if you’re just recycling waste.
The essence of this Robert Brown’s ‘refutation’ is that if the wire and the gas do not have the same thermal gradient i.e. if the wire is isothermal and the gas is not then, there is a violation of the laws of thermodynamics.
The problem with the refutation is that the wire is not isothermal for essentially the same reason as the gas is not: the atoms at the top of the wire will move slower than those at the bottom due to gravity and will therefore be at a lower temperature.
The atoms of the wire will lose velocity as they rise in the gravitational field just as those in the gas, thus there is less energy available transferred in interactions this will produce an gradient in the kinetic energy of atoms that make up the wire resulting in a temerature gradient due to gravity. That the distance covered between interactions is much smaller in the solid than it would be in the gas and that there are other interactions in a solid does not change this fact.
glen martin says:
January 24, 2012 at 2:07 pm
Phew … gravity slowing electrons in a wire … thought I’d heard everything.
In any case, even if your interesting theory about gravity slowing heat transfer in wires were correct, it doesn’t matter. That just slows down the transmission of heat, it doesn’t stop it. So it doesn’t mater for the disproof.
w.
@Robert Brown
OK, after pondering some more, I have identified a flaw in my reasoning. I think you and Willis and the others are correct – the column of gas does indeed eventually relax to an isothermal state if the column is in fact thermally isolated. It is still stratified, of course, but it would end up isothermal. Apologies for confusing everyone.
Here is where I was going wrong. I mentioned that gas near the bottom of the column has a smaller amount of potential energy than gas the top. While this is undoubtedly true, that potential energy only comes into play if the gas is being mixed or is otherwise dynamic, that is, if such energy is being released as a result of changing the height of some of the gas parcels. But of course the equilibrium state does not have any such mass motions, and so no work is being done on the fluid. As a result, the internal energy of the gas is the same everywhere, and thus the gas has the same temperature everywhere.
Of course, for a column of gas subject to heat exchanges at the top and at the bottom [such as a column of gas in a planetary atmosphere] but is otherwise thermally isolated, there will be a temperature gradient established in accordance with those boundary conditions. But that scenario is apparently off-topic in this thread.
Robert Brown says at 4:10pm:
“I am specifically proving that EEJ, a specific paper written by Jelbring and published in a journal (God help the referees, absent that day on vacation or something), violates the zeroth but especially the second law of thermodynamics when it asserts that there will be a thermal lapse rate in an adiabatically isolated column of ideal gas in thermal equilibrium in a gravitational field.”
Robert Brown needs to read Caballero sec. 2.3 that proves the zeroth is not violated & the 2nd is not violated for “adiabatically isolated column of ideal gas in thermal equilibrium in a gravitational field” which Caballero proves is non-isothermal & there will be a thermal lapse rate.
I imagine Caballero is just like every other thermo text book (but I have not read them all like Robert) & the thermo grand masters assert. Thus Jelbring EEJ is not in violation & not refuted if Jelbring asserts same as Caballero and Caballero is right.
Q. Daniels says:
Willis wrote: Will heat flow in the silver wire forever?
If you extract energy from the system, it will shut down as the entire system cools. Energy is conserved. If you extract energy, then it has to come from somewhere, and that somewhere is the thermal energy of the system.
If you do not extract energy, then yes, it will.
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LongCat says:
While I agree with the underlying point, I’m not sure why the wire would necessarily violate the laws of thermodynamics if it continuously transferred heat. Under normal circumstances, it would radiate some of this energy away and otherwise be an imperfect conductor. If, however, we’re assuming a closed system with a perfect conductor surrounded by a perfect insulator, why would any energy be lost?
To put another way, assume I have a wheel with a frictionless axle at rest in a vacuum. If I spin it, it will spin endlessly. The conclusion that it will have perpetual motion doesn’t violate thermodynamics; the assumption that there is no friction does. Likewise, the wire would not violate any physical laws by endlessly transferring heat; those laws were broken by the assumption of a closed system with a perfect conductor/insulator.
I know I’m disputing people far above my pay-grade, so I’m assuming that I’m wrong in this. I’m just curious as to why.
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Trick
Heat flows forever in fig. 2. The reason is a grand master thermal law is broken, the easiest one, the zeroth law. There can be no perfect insulator.
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Correct.
All real heat engines increase entropy. Engines do work. Figure 2 doesn’t.
Robert, thank you for making this excellent point.
Precisely the situation you outline is present in all of the world’s high-speed centrifuges containing uranium hexafluoride (UF6) for isotope separation.
If an adiabatic lapse were present in the centrifuges, between the high-pressure rim and the low-pressure central axis, then solid UF6 would condense at the cold central axis … which needless to say, is not observed.
Elevator Summary: Gas centrifuges prove that gravito-thermal theory is wrong.
kuhnkat says:
January 24, 2012 at 2:32 pm
kuhnkat, you are conflating a constant force with unending work. Gravity is just there all the time, a force pulling in one direction, keeping you on the planet. When you move upwards against gravity, it takes energy to do that. When you move with it you get the energy back.
But when you come back to where you started, it’s a zero sum game (less with friction). No matter how many times you go up and down the hill, you don’t gain any energy at all, despite the constant presence of gravity. Which is another way of saying that in all of those trips up and down the hill, the lazy bum gravity hasn’t done a net lick of work. It did do work, but what gave with one hand, it took with the other by requiring the exact same amount of work in the other direction.
It’s like running a waterwheel by continuously filling the headrace up with buckets of water from below the wheel. Sure, you can get work out of the wheel … but that’s work that you are putting in by continuously lifting the water, not work that’s coming from gravity. Stop lifting the water and see what your friend gravity does for you … nothing.
Hope that helps.
w.