[30 points] Recall thermodynamic potentials discussed in class: enthalpy, Helmholtz free energy, and Gibbs free energy (for a simple PVT system). (a) Obtain the differential form for each potential using the definitions HU+PVFUTSGUTS+PV and using the expression for the internal energy from the combined first and second laws of thermodynamics. (b) Write down equations of state for each potential. (c) Write down Maxwell relations for each potential