Entropy change in a reversible isothermal process

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SUMMARY

In a reversible isothermal process, the change in entropy (∆S) for the system is defined by the equation ∆S(system) = nRln(Vf/Vi), where n represents the number of moles, R is the ideal gas constant, Vf is the final volume, and Vi is the initial volume. The total change in entropy (∆S(total)) for the system and surroundings equals zero, confirming that the entropy change of the surroundings offsets that of the system. This relationship highlights the distinction between the entropy of the system and the total entropy change in reversible processes.

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Why does ∆S = 0 for a reversible process, but for a reversible isothermal process, ∆S is given by nRln(Vf/Vi) (or other variations of that equation)?
 
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You are confusing ΔS for the system with ΔS for the combination of system and surroundings.
 
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Chestermiller is correct.∆S(system) = nRln(Vf/Vi)

∆S(total)= ∆S(surroundings) + ∆S(system) = 0
 

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