Temperature Gradients

Almost by the definition of temperature, an isolated system in a state of equilibrium has a constant uniform temperature. Surely, the processes of conduction and convection allow for fluctuations away from this equilibrium state. While the system isn’t always in the same state of equilibrium, it is entropically driven to enter the state with equal temperature throughout. After all, that would give the most “disorder”, maximizing the entropy.

Now, consider the case where an external force field, such as gravity, is applied to the isolated system. On one hand, it seems logical that a particle with higher kinetic energy than another would prefer to be lower, due to preferring a lower potential energy. If faster moving particles correspond to higher temperature molecules, wouldn’t the background field prefer hotter particles to move to the bottom, while colder ones would be at the top? This seems to contradict the previous notion that isolated systems tend to uniform temperatures, as a temperature gradient is created in this example.

After some research, it is majority opinion that the first scenario is correct. The most common objection is that it would seem a temperature gradient would defy the second law. One argument is here: http://wattsupwiththat.com/2012/01/24/refutation-of-stable-thermal-equilibrium-lapse-rates/. Personally, I find the logic a bit circular, but this does not mean he is incorrect. But perhaps the question is not as trivial as it appears at first glance. There are a few papers which try to argue that this occur, and the first known scientist to think that a spontaneous temperature gradient would be created from gravity is Loschmidt. At the end of the day, history decided to listen to Boltzmann and Maxwell (H theorem).

Interestingly enough, a paper has come out recently which has created Maxwell’s demon by recording information. The thermodynamic entropy in this system decreases; however, the information entropy increases enough to allow for the total entropy to increase. If the memory was then deleted, the thermodynamic entropy would then increase. Would this then give a uniform temperature?

If Maxwell’s demon can occur, a temperature gradient is created spontaneously. From here, a wire connecting the two ends would allow for electricity to be created due to the Seebeck effect (https://en.wikipedia.org/wiki/Thermoelectric_effect). The Seebeck effect creates electricity, at the cost of mixing the hot and cold ends. One could then disconnect the wire and wait for the temperature gradient to be created again. The system would return to the same state, except being at an overall lower temperature. This cyclic process could be repeated, creating more and more electricity from heat. No energy is being put in, and electricity is being created! The first law is not violated, as heat is being converted to electricity.

What other ways can a temperature gradient be created spontaneously? Would an external field, such as gravity do the trick? Most people argue no, but only an experiment would give the correct answer. Roderich Graeff claims to have done this experiment. More to come on this subject!

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