All the four types of energy relations above satisfy the mathematical condition of being continuous variables, as they are themselves functions of state variables. One can thus apply of the criterion of exact differential for these functions.
For a function of the form P = P(X ,Y) one can write the following total differential:
Applying eqn. 5.11 to 5.3, 5.5, 5.6 and 5.7 one may derive the following relationships termed Maxwell relations:
...(5.12 , 5.13)