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# Maxwell relations

Maxwell's relations are a set of equations in Thermodynamics which are derivable from the definitions of the four thermodynamic potentials. They involve the following quantities:

• V  is volume
• T  is temperature
• P  is pressure
• S  is entropy

Ignoring the chemical potential, they are:

$\left(\frac{\partial T}{\partial V}\right)_S = -\left(\frac{\partial P}{\partial S}\right)_V$
$\left(\frac{\partial T}{\partial P}\right)_S = +\left(\frac{\partial V}{\partial S}\right)_P$
$\left(\frac{\partial S}{\partial V}\right)_T = +\left(\frac{\partial P}{\partial T}\right)_V$
$\left(\frac{\partial S}{\partial P}\right)_T = -\left(\frac{\partial V}{\partial T}\right)_P$