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Entropy is a state function.

Is it true that at the end of a cyclic process, the change in entropy of the of the system and that of its surrounding are both separately zero irrespective of whether the cycle is reversible or not?

I have two particular cycles in mind-the reversible Carnot cycle and the irreversible hysteresis loop.

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No. For a cyclic process, the system returns to its original state at the end of the process, so its entropy change is zero. But for the surroundings, that are typically envisioned as being comprised of ideal reservoirs, the entropy change is not necessarily zero. In the case of a reversible cycle, the change in entropy of the surroundings is zero. But, for an irreversible cycle, any entropy that is generated within the system during the cycle is transferred to the surroundings. So, in this case, the entropy of the surroundings increases, but the entropy change of the system is still zero.

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