Chemical Engineering Thermodynamics
The Maxwell relation derived from the differential expression for the Helmholtz free energy (dA) is

(∂T/∂V)S = -(∂P/∂S)V
(∂S/∂V)T = (∂P/∂T)V
(∂S/∂P)T = -(∂V/∂T)P
(∂V/∂S)P = (∂T/∂P)S

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