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Q & A: entropy in a closed universe

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Most recent answer: 10/03/2010
Suppose the universe is closed, does not inflate nor deflate and contains absolutely nothing expect a 1kg iron perfect sphere heated at 1,000K degrees in a single instant by some divine entity. The sphere radiates all its possible heat in space in all directions but since the universe is closed and contains nothing else except that sphere, the electromagnetic waves that carried away the sphere's heat will eventually come back at the sphere and reheat it up. A never ending cycle of heating and cooling will occur. Does it violates any thermodynamic laws? Is this the only way for entropy to remain constant (if there is any entropy in such a scenario in the first place)? Thank you!
- Anonymous
This is a profound question, which I will only begin to answer.
For starters, I should say that the universe you propose isn't quite gravitationally stable, but let's ignore that. Let's also ignore that with a finite binding energy, the ball's atoms will gradually evaporate.

Given that the radiation is not all emitted immediately, on each emission/absorption cycle the period will spread out. After enough cycles, the system will approach an equilibrium in which the ball is steadily emitting and absorbing equal amounts of radiation, within the margins of statistical fluctuations. Any standard thermodynamic description of this process would show that the net entropy, the sum of the radiation entropy and the ball entropy, increases until this equilibrium is reached. The laws of thermodynamics would work normally. By the way, since that radiation is spread out over a big universe, the whole thing will be pretty cold.

There are more subtle issues in describing the entropy of a closed system (a hint: quantum Liouville theorem) but I think that the answer above gets at what you were asking. If not, ask more!

Mike W.

(published on 10/03/2010)

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