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

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