Maxwell Relations

Origin

Thermodynamic potentials are state functions. Their mixed second derivatives therefore commute. For the Helmholtz free energy,

$$dF=-S\,dT-p\,dV,$$

so

$$\left(\frac{\partial S}{\partial V}\right)_T = \left(\frac{\partial p}{\partial T}\right)_V.$$

Use

Maxwell relations convert difficult entropy derivatives into measurable pressure, volume, or temperature derivatives.