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TheoryOfSomething t1_j5qmn7j wrote

Reply to comment by KenKaniff- in Why does hot air cool? by AspGuy25

I know you were probably not trying to be completely rigorous in your answer, but I would add an important qualifier to the gist of your answer. All other things being equal (AKA ceterus paribus), heat will always flow from the hot thing to the cold thing.

Heat can and sometimes without (human) intervention does flow from a cold thing to a hot thing, but it requires some other change. That change could be doing work on the system ala refrigeration. The change could be that a chemical potential gradient is causing a certain type of particle to move preferentially from a cold region to a hot one which leaves the cold region even colder (something like this is the principle behind Helium dilution refrigerators). I'm sure there are other example, although I can't think of more off the top of my head.

So to be more general we might say that closed systems tend toward maximum entropy (or equivalently minimum grand thermodynamic potential), which usually means heat flows from hot to cold, and all else being equal guarantees that heat will flow from hot to cold.

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