Maxwell Relations

First law of Thermodynamics:

Gibbs Function:

Helmholtz Function:

Subbing 1 into 2 and rearranging:

Differentiation:

Subbing 1 into 3 and rearranging:

Differentiating:

Some Thermodynamic properties cannot be measured directly (e.g. entropy) so we use other properties that can be measured (e.g. pressure or temperature) to calculate them by relating them both.

Using equations 5 and 7, then through partial derivation, the Maxwell relations can be deduced: