BackgroundAs an extension of the conversation on the Competing Mechanism thread, Chic and I have been swapping e-mails behind the scenes. Over the course of the exchanges, some thought experiments have been proposed which I think warrant an article of their own, and Chic has given me permission to publish whatever portions of our private communications as grist for that mill.
As some of these thought experiments get quite long, this will be a multi-part series. First thought experiment is an actual experiment ...
Centrifuge Tubes Full of Water
Test Tubes Full of Water[Update 3/19/2015: Chic notes in comments that I erred thinking that Graeff's protocol involved spinning his tubes in a centrifuge, thus allaying some of my confusion below about his theoretical derivation.]
Chic brings up a fellow called Roderich W. Graeff who penned a note in 2006 entitled, Measuring the Temperature Distribution in Columns of Liquids. I have not yet read it, so let's take a look.
His main finding appears to be:
Vertical temperature gradients:I'll skip over the derivation and discussion to give the final form:
The most important result is the temperature gradient value 1 of the inner axis of the glass tube 1, filled with water and glass powder, as shown as the lowest blue curve in GRAPH 2. It is quite stable around a value of about -0.034 K/meter, the minus sign indicating a lower temperature at the top than on the bottom. This value is close to the theoretical value of -.04 K/m as discussed below.
TGr = -g x H / (c/n)He doesn't give units, so I assume them:
- g is acceleration due to gravity in m s-2
- H is vertical distance (height) in m
- c is specific heat in m2 s-2 K-1
- n is number of degrees of freedom (unitless), which for water he gives as 18
-0.04 K/m = -g m s-2 / 4186 m2 s-2 K-1 * 18Eh? He's saying the experimental rate under centrifugal acceleration (which he does not specify) is the same as the rate under (roughly) Earth standard gravity? Did I miss something?
g m s-2 = 0.04 K/m * 4186 m2 s-2 K-1 / 18
= 9.3 m s-2
[Update 3/19/2015: yes I did, he did NOT spin his tubes in a centrifuge, so Graeff really is saying -0.04 K/m under 1 gee acceleration. As my next calculation demonstrates, this is a wildly implausible result.]
For some real-world perspective, the Challenger Deep in the Mariana Trench is between 10,898 and 10,916 m deep. I'll average the range as 10,907 m. Thus:
10,907 m * 0.04 K/m = 436.28 KOne of us has goofed somewhere. I'll drill into the note some more, starting with the ...
AbstractSo he confirms that this idea does not conform to how the Second Law is formulated. Clearly, simply appealing to it as presently stated isn't going to work for Chic as Graeff is saying he thinks it needs to be rewritten. Let's see if I can figure out why:
Measurements of the temperature distribution in vertical tubes filled with water under equilibrium conditions are being reported. They show a negative temperature gradient, cold at the top and warm at the bottom within an environment showing a positive gradient. This is explainable by the influence of gravity. The measured effect comes close to a theoretical estimation. The temperature difference so created can be used to produce work out of a heat bath. These surprising results, if confirmed, necessitate a rewording of many statements of the Second Law reflecting the influence of force fields.
INTRODUCTIONThe Wikipedia article on Loschmidt has this to say:
Late in the 19th century J. Loschmidt believed that a vertical column of gas or of solids in an isolated system would show a temperature gradient under the influence of gravity, cold at the top and warm at the bottom. L.Boltzmann and J.C. Maxwell disagreed. Their theories tried to prove an equal temperature over height. The temperature distribution in liquids was not discussed. The historical discussion between J.Loschmidt, L. Boltzmann and J.C. Maxwell is covered in , , and . A. Trupp gives a good summary in . The author reported for the first time in  and  about actual measurements of the temperature gradient in gas columns in isolated systems. They are critically discussed by Sheehan . They seem to strengthen the position of Loschmidt.
Loschmidt and his younger university colleague Ludwig Boltzmann became good friends. His critique of Boltzmann's attempt to derive the second law of thermodynamics from kinetic theory became famous as the "reversibility paradox". It led Boltzmann to his statistical concept of entropy as a logarithmic tally of the number of microscopic states corresponding to a given thermodynamic state.The article does not go on to say whether Loschmidt came to agree with Boltzmann's statistical concept of entropy or not. However, Chic in comments at WUWT quotes Dr. Roy Spencer (my emphasis added):
The most celebrated gravitational second law challenge revolves around an unresolved dispute between Josef Loschmidt and the two thermodynamic giants, Maxwell and Boltzmann. Loschmidt claimed that the equilibrium temperature of a gas column subject to gravity should be lower at the top of the column and higher at its base. Presumably, one could drive a heat engine with this temperature gradient, thus violating the second law. This debate has remained unresolved for over a century.I'm dubious. Whenever a climate contrarian like Spencer says something remains unresolved, fair or not, I translate it as, "I'm not convinced that prevailing wisdom is correct".
Back to Graeff's note. Skipping over the experimental setup and to the results:
Vertical temperature gradients:A good scientist will always try to account for any confounding effects in an experimental apparatus. Graeff thinks of several, and rules them all out:
The most important result is the temperature gradient value 1 of the inner axis of the glass tube 1, filled with water and glass powder, as shown as the lowest blue curve in GRAPH 2. It is quite stable around a value of about -0.034 K/meter, the minus sign indicating a lower temperature at the top than on the bottom. This value is close to the theoretical value of -.04 K/m as discussed below. Going from the inner axis radially to the outside, the value 3 of the enclosing PVC tube – black curve PVC tube 1 - shows a slightly less pronounced gradient, but still being colder at the top than on the bottom.
- Exothermic reactions between the water and glass beads.
- Evaporation of water from the top of the tubes.
- Convection currents creating an adiabatic gradient.
- Measurement error.
- (Local) equilibrium conditions never being met.
[Update 3/19/2015: none of the following reasoning applies due to my error in thinking he used a centrifuge in his experiments.]
- The bottom of a centrifuge tube moves faster under rotation than the top. Nothing in the description of the experimental apparatus indicates that the runs were performed in near-vacuum conditions. Hence it is conceivable that greater airflows near the bottom of the tubes caused some additional heating which did not occur near the slower moving upper portions of the tubes.
- Even though centrifuges are constructed to rotate smoothly and without vibration, there is always a bit of wobble due to the drive, bearings, or masses in the tubes being out of balance. Typically it gets worse as RPM increases, but not always depending on any harmonic resonances. Such vibrations, however slight, might be expected to cause mechanical action (compression and rubbing) in the tubes. It is easy to conceive how such actions would be amplified in the bottoms of the tubes where centripetal acceleration, and therefore pressures, are greater.
- Water is a polar molecule, meaning that it has an electric dipole moment. Move water in a circular motion through a magnetic field (like that of the Earth's), and the motions will set up a slight electrical current. Faster the motion through the magnetic field, the more current generated. This is the theory behind how electromagnetic induction heating works, but instead of moving the mass to be heated through a magnetic field, the field itself is pulsed. The result is that electrical eddy currents set up, excite the molecules of the target object, and it warms up.
Graeff himself doesn't consider this a viable form of "free energy" ...
4. Consequences of the measured temperature gradients for the Second Law.... yet he considers his results significant enough to call for overturning the Second Law. I think he needs to revisit his logic. Very next paragraph:
The brown curve 5 shows the temperature differences at the top of tube 1 and tube 2 with an absolute average value of about .01 K. This temperature difference could be used to create work i.e. by creating electric power through a thermocouple, as it is actually continuously taken place during the test. The amount of energy so produced is, of course extremely small. It does not affect the equilibrium condition of the experiment as this small amount of energy taken out of the system is easily replenished from the heat bath of the environment.
But the fact that heat flows under the influence of gravity from a cold reservoir to one with a higher temperature contradicts today’s understanding and present day’s statement of the Second Law. It has to be restated addressing the influence of force fields like gravity.
5. Theoretical Value for temperature gradient TGrYeeessssss ... however for every molecule moving down is one being displaced upward. Unless the water is always falling in the tube, the net effect of molecules moving around in the gravity well and trading potential energy for kinetic and vice versa is going to be goose eggs.
No published treatise of calculating the vertical temperature gradient TGr in solids or liquids under the influence of gravity is known to the author. But the value of TGr can be calculated by equating the potential energy of the molecules with the increase of their speed on their downward path. Their speed represents their temperature. When bouncing off the bottom wall or from another water molecule, their kinetic energy is zero at the moment of impact. Though their loss of potential energy in their downward movement is totally converted to an increase of their average “temperature”. A heat transfer takes place between water molecule and the upper and lower wall of the tube until the wall temperatures equal the “temperature” of the impinging water molecules and equilibrium has been reached.
ConclusionsIf I've done the math above correctly, and am not grossly misunderstanding Graeff's calculations and other arguments, I'm gonna call this one done.
[Update 3/19/2015: I did grossly misunderstand that this was a 1 gee experiment, not a several hundred gee experiment. If you'll pardon the pun, the gravity of the disconnect between experiment and real world observation far outweighs my key misunderstanding of his protocol. This one is not just sunk, it was dead on arrival.]
Postscript -- Where There's Actually Something To ThisI mentioned earlier that this notion of temperature increasing due to gravitational force works if the gas is, on balance, "constantly falling". Hang around this discussion long enough, and someone is sure to bring up Jupiter:
Although Jupiter would need to be about 75 times as massive to fuse hydrogen and become a star, the smallest red dwarf is only about 30 percent larger in radius than Jupiter. Despite this, Jupiter still radiates more heat than it receives from the Sun; the amount of heat produced inside it is similar to the total solar radiation it receives. This additional heat is generated by the Kelvin–Helmholtz mechanism through contraction. This process causes Jupiter to shrink by about 2 cm each year. When it was first formed, Jupiter was much hotter and was about twice its current diameter.Shrinking by 2 cm/yr takes this out of the realm of a constant volume problem. The constant shrinkage can be seen as Jupiter's atmosphere constantly falling on balance ... in other words, being compressed and leading to heating such that it radiates out more energy than it absorbs from the Sun.
Note however that this does NOT mean that this process is the only thing which accounts for Jupiter radiating more than it absorbs.