1. The problem statement, all variables and given/known data How to demonstrate that U is minimized at constant V and S, while H at constant P and S? 2. Relevant equations ΔS universe = ΔS system + ΔS environment ≥ 0 ΔU system = δq reversible + δw reversible = δq irreversible + δw irreversible ΔS environment = −∫(δq reversible / T) dU = TdS − PdV = δq + δw 3. The attempt at a solution ΔS universe = ΔS system + ΔS environment > 0 ΔS universe = ΔS system − ∫ ( δq rev /T ) > 0 ΔS universe = ΔS system − ∫( δq irrev/T + δw irrev − δw rev ) > 0 TΔS system − T∫( δq irrev/T + δw irrev − δw rev ) > 0 T∫( δq irrev/T + δw irrev − δw rev ) − TΔS system < 0 If the process is isoentropic, it follows that it's an adiabatic process with δq irrev = 0 T∫( δw irrev − δw rev ) < 0 * If, furthermore, the volume of the system is constant, it follows that irreversible and reversible works are 0, leading to a senseless expression. * If not the volume but the pressure is constant, we get T∫( δw irrev − δw rev ) < 0 T∫( δq rev − δq irrev ) < 0 and we recover ∫δq irrev = ΔH Now, since reversible −∫PdV is minimum in reversible process, δ rev is maximum. It follows that the T∫(positive quantity) < 0 Which is another senseless expression. I guess the flaw comes from the assumption that an isoentropic process is always adiabatic... but how?