Transcription of Maxwell relations - USTC
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Maxwell relations - USTC
Maxwell relationsMaxwell's relations are a set ofequations in thermodynamics which arederivable from the symmetry of secondderivatives and from the definitions ofthe thermodynamic potentials. eserelations are named for the nineteenth-century physicist James Clerk four most commonMaxwell relationsDerivationDerivation based on JacobiansGeneral Maxwell relationshipsSee also e structure of Maxwell relations is astatement of equality among the secondderivatives for continuous functions. Itfollows directly from the fact that theorder of differentiation of an analytic function of two variables is irrelevant (Schwarz theorem). In the case of Maxwellrelations the function considered is a thermodynamic potential and xi and xj are two different natural variables for thatpotential:Schwarz' theorem (general)where the partial derivatives are taken with all other natural variables held constant.
volume work are considered or when the number of particles is included as a natural variable, other Maxwell relations become apparent. For example, if we have a single-component gas, then the number of particles N is also a natural
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