Question

Consider an isolated system in equilibrium. What is the relation between the temperatures of two different parts of this system ?​

Answer 1

Answer:

Ok, so the question is about the concept of increasing entropy. We obtain the result (by utilizing the Clausius inequality theorem) dS=dQrevT≥dQirrTdS=dQrevT≥dQirrT.

Then it's stated that for a closed system, dQirrdQirr is zero and therefore dS≥0dS≥0. Fair enough, the total energy in a closed system is constant and therefore no heat (thermal energy in transit) can flow in or out. The thing that bothers me though, is that I cannot imagine any process where an amount dQrevdQrev can transferred to or from the system if the system is closed. And that leads me to dQrev=0dQrev=0 as well which results in dS=0dS=0 .

Now I know that there is a problem, as entropy is in fact generated when heat flows between subsystems in the isolated system, which one could calculate. The problem originates from the statement that dQirrdQirr is zero. In the isolated system an irreversible amount of heat can (and will be) transferred between subsystems of different temperatures. Even though the net heat transfer is zero, dQirrT1+−dQirrT2dQirrT1+−dQirrT2 should also be zero in an isolated system with two subsystems of temperatures T1T1 and T2(>T1)T2(>T1) for this to work out, which is incorrect. The explanation is much appreciated.

Kind regards!

Explanation:

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