Fundamental thermodynamic property relations for a fluid of constant composition are as follows:

**Criterion of exactness for a differential expression:**

If , then the total differnential of F is defined as

Otherwise,

where, and

By further differentiation, we obtain

Since the order of differentiation in mixed second derivatives is immaterial, these equations give

Equation VI serves as a *criterion of exactness*, when F is a
function of *x* & *y*