Maxwell Relations - Thermodynamic and Statistical Physics, CSIR-NET Physical Sciences Physics Notes | EduRev

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Maxwell equations (thermodynamics)

In thermodynamics, the Maxwell equations are a set of equations derived by application of Euler's reciprocity relation to the thermodynamic characteristic functions. The Maxwell relations, first derived by James Clerk Maxwell, are the following expressions between partial differential quotients:

Maxwell Relations - Thermodynamic and Statistical Physics, CSIR-NET Physical Sciences Physics Notes | EduRev
  Maxwell Relations - Thermodynamic and Statistical Physics, CSIR-NET Physical Sciences Physics Notes | EduRev

The characteristic functions are: U (internal energy), A (Helmholtz free energy), H (enthalpy), and G (Gibbs free energy). The thermodynamic parameters are: T (temperature), S (entropy), P (pressure), and V (volume).

As an example of a derivation, consider

Maxwell Relations - Thermodynamic and Statistical Physics, CSIR-NET Physical Sciences Physics Notes | EduRev

Euler's reciprocity relation reads:

Maxwell Relations - Thermodynamic and Statistical Physics, CSIR-NET Physical Sciences Physics Notes | EduRev

which indeed gives

Maxwell Relations - Thermodynamic and Statistical Physics, CSIR-NET Physical Sciences Physics Notes | EduRev

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