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