Maxwell's relations

${\frac{\partial S}{\partial V}|}_T={\frac{\partial p}{\partial T}|}_V$

${\frac{\partial T}{\partial p}|}_S={\frac{\partial V}{\partial S}|}_p$

${\frac{\partial S}{\partial p}|}_T=-{\frac{\partial V}{\partial T}|}_p$

${\frac{\partial T}{\partial V}|}_S=-{\frac{\partial p}{\partial S}|}_V$

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

See also

• Thermodynamic relations
• Bridgman thermodynamic formulas