Physics Asked on December 8, 2020
When we put two bodies with different temperatures in contact, there will be a heat transference between them. The variation of the entropy of the system is well known (this is computed in most physics textbooks). However, I was thinking: in the beginning, when we put the bodies in contact, the total system will not be in a thermodynamic equilibrium, so it does not make sense to talk about the entropy of the initial state. After a time, the system will be in equilibrium, so we can define a final entropy, but not an initial one. So, I think we can’t talk about the variation of the entropy of the system. It’s like asking "what is the variation of the temperature of the system?" In the beginning, the system does not have a definite temperature. As we can ask what is the variation of the temperature of each of the bodies, but not of the total system, we can compute the variation of entropy of body 1 and body 2, but not of them together. What’s wrong with this thought?
The initial state is a composite system made by two subsystem each one at equilibrium. Entropy is an additive quantity: the entropy of the composite system is the sum of the entropy of each subsystem. Notice that the situation is different for temperatures: temperature is not an additive quantity and it is meaningless to add temperatures of each subsystem as well as there is not a temperature which can be considered a property of the combined system.
After creating a thermal contact, the system reaches a final equilibrium state. The entropy of that state is a well definite concept, exactly like the entropy of the original composite system.
Correct answer by GiorgioP on December 8, 2020
Immediately before we put the bodies in contact, the system is in a thermodynamic equilibrium, so it has a well-defined entropy. The final state also has a well-defined entropy, as you note. We can use the difference between these values to define $Delta S$. This does not require that we define $S$ at every intermediate time.
Answered by Daniel on December 8, 2020
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