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- W2000005317 abstract "Attention is called to the fact that certain important equations of thermodynamics such as the two Gibbs-Helmholtz equations may be grouped into families, but that a precise definition of such families has hitherto been lacking. For the case of a single phase of k components in equilibrium a method is given for splitting a certain class of equations, the ``f11-equations,'' into families in a precise manner as follows. The f11-class of equations is defined by means of four ``basic'' equations and two ``basic'' assumptions, and involves the 2k+8 variables E, H, F, A, V, S, P, T, μi, ni. For the f11-equations there is in turn defined a number of ``standard forms'' which depend upon the introduction of absolute value signs in a certain way. Then the ``characteristic group,'' a substitution group of the eighth order on the letters E, H, F, A, V, —S, —P, T, μi, ni is generated by a series of geometrical operations on a square. The theorem is stated that the transformation of any f11-equation in standard form by any element of the characteristic group yields an f11-equation in standard form. No formal proof of this theorem is given, but its correctness is sufficiently demonstrated by systematic verification. The theorem leads immediately to the definition of a family of f11-equations as the totality of distinct f11-equations resulting from the transformation of a given f11-equation in standard form by all the elements of the characteristic group. It is found that every f11-equation is a member of one and only one f11-family. The method increases the number of fundamental equations readily available and emphasizes the symmetry of these equations." @default.
- W2000005317 created "2016-06-24" @default.
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- W2000005317 date "1935-01-01" @default.
- W2000005317 modified "2023-09-25" @default.
- W2000005317 title "Families of Thermodynamic Equations. I The Method of Transformations by the Characteristic Group" @default.
- W2000005317 cites W1993977824 @default.
- W2000005317 doi "https://doi.org/10.1063/1.1749549" @default.
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