Maxwell's Four Thermodynamics Relations

In this lecture you will derive Maxwell's four relations from four thermodynamic potential functions, internal energy, U, enthalpy, H, Helmholtz free energy, F, Gibbs free energy, G, for closed systems. 

Question: Maxwell’s thermodynamic relations are given by,

Derive these relations from four thermodynamic potential functions, U, H, F, G for a closed system, where U is internal energy, H is enthalpy, F is Helmholtz free energy, and G is the Gibbs free energy of the system.

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