Pressure and Temperature Derivatives of the Functions

As dG is a criterion for equilibrium and spontaneity at constant P and P, and as P and P are natural variables for G, it is useful to express the total differential when considering G as a function of P and P. That is. 

In addition to determining the dependence of G on pressure for a substance, it is useful to determine the dependence of AG on pressure for a transformation. To do so, let us represent a transformation by the equation 

Subtracting the sum of the pressure coefficients for the reactants from that for the products, we obtain the desired relationship  

If the same operations are carried out using the Helmholtz function, with namral variables T and V, the results are 

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