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Maxwell relations : ウィキペディア英語版 | Maxwell relations
Maxwell's relations are a set of equations in thermodynamics which are derivable from the symmetry of second derivatives and from the definitions of the thermodynamic potentials. These relations are named for the nineteenth-century physicist James Clerk Maxwell. ==Equation==
The structure of Maxwell relations is a statement of equality among the second derivatives for continuous function. It follows directly from the fact that the order of differentiation of an analytic function of two variables is irrelevant (Schwarz theorem). In the case of Maxwell relations the function considered is a thermodynamic potential and ''xi'' and ''xj'' are two different natural variables for that potential: where the partial derivatives are taken with all other natural variables held constant. It is seen that for every thermodynamic potential there are ''n''(''n'' − 1)/2 possible Maxwell relations where ''n'' is the number of natural variables for that potential.
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