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, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle V} is the volume, Failed to parse (SVG (MathML can be enabled via browser plugin): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle T} is the temperature, $p$ is the pressure

See also

• Thermodynamic relations