DERIVING MAXWELL'S RELATIONS
So far we have derived the differential forms of the four thermodynamic potentials in which we're interested and have identified their natural variables. This is summarised in the following table:
Let's start by again considering the differential form of the internal energy, given by dU=TdS−PdV. Consider now U as a function of entropy, S, and volume, V, such that U=U(S,V). Notice that these are the natural variables of internal energy. We can now write the total differential of U(S,V) as:
