Maxwell's relations

$\left. \frac{\partial S}{\partial V} \right\vert_T = \left. \frac{\partial p}{\partial T} \right\vert_V$

$\left. \frac{\partial T}{\partial p} \right\vert_S = \left. \frac{\partial V}{\partial S} \right\vert_p$

$\left. \frac{\partial S}{\partial p} \right\vert_T = - \left. \frac{\partial V}{\partial T} \right\vert_p$

$\left. \frac{\partial T}{\partial V} \right\vert_S = - \left. \frac{\partial p}{\partial S} \right\vert_V$

where $S$ is the entropy, $V$ is the volume, $T$ is the temperature, $p$ is the pressure

See also

• Thermodynamic relations
• Bridgman thermodynamic formulas