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For an irreversible change occurring at constant temperature and pressure, with only pressure–volume work involved, which relation between the entropy change and Gibbs free energy change is correct?

1. (dS) at constant V and E is zero, and (dG) at constant T and P is negative
2. (dS) at constant V and E is positive, and (dG) at constant T and P is negative
3. (dS) at constant V and E is negative, and (dG) at constant T and P is positive
4. (dS) at constant V and E is negative, and (dG) at constant T and P is negative

Correct answer: (dS) at constant V and E is positive, and (dG) at constant T and P is negative

Solution

Criteria for a spontaneous (irreversible) process: entropy of the isolated system increases, so (dS) at constant U,V is positive, while (dG) at constant T,P is negative. dS = 0 corresponds only to reversible/equilibrium conditions.

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