Maxwell construction

In thermodynamic equilibrium, a necessary condition for stability is that pressure, , does not increase with volume, or molar volume, ; this is expressed mathematically as , where is the temperature. This basic stability requirement, and similar ones for other conjugate pairs of variables, is violated in analytic models of first order phase transitions. The most famous case is the van der Waals equation, where are dimensional constants. This violation is not a defect, rather it is the origin of the observed discontinuity in properties that distinguish liquid from vapor, and defines a first order phase transition.

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