The relation (∂U/∂S)V = T [Eq. (4.37)] is notable because is relates the three fundamental thermodynamic state functions U, S, and T. The reciprocal of this relation, (∂S/∂U)V = 1 /T, shows that entropy always increases when internal energy increases at constant volume. Use the Gibbs equation for dU to show that (∂S/∂V)U = P/T.
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