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Is it possible for heat to flow between two objects with the same internal energy?

The crux of the issue here is "extensive property" vs. and "intensive property". An "extensive property", such as energy, heat capacity is proportional to the amount of matter present. If the amount of material is doubled, the amount of energy, heat capacity also doubles. The "extensive property" is doubled, the amount of matter is also doubled, so the energy per amount of material remains the same.

But that does not determine whether heat flows from one object to another. The flow of heat is determined by the difference in temperature, which is an "intensive property". That is a property that is not dependent upon the amount of material present. Heat will flow from a high temperature object (say 1 gm of water at 80 C.) to a lower temperature object (say 1 kg of water at 20 C.) without regard to the amounts of material present. Temperature difference "drives" the flow of heat, not energy. Again, put another way 1 gm of water at 25 C. has the same temperature as 1 kg of water at the same temperature, 25 C. The amount of material present irrelevant. It makes no sense to say talk about 25 C. per gram of water and doubling the amount of water, all things being equal, doubles the temperature. The "intensive" property is independent of the amount of material present.

This is lucidly explained in a new little book, ~100 pages, entitled "The Four Laws that Govern the Universe" by P.W. Atkins. A short by extraordinary presentation of thermodynamics with less than a couple of dozen equations.

Vince Calder

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