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The Symmetrical Fundamental Property Relation of Thermodynamics
Author(s) -
Martin J. J.
Publication year - 1972
Publication title -
chemie ingenieur technik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.365
H-Index - 36
eISSN - 1522-2640
pISSN - 0009-286X
DOI - 10.1002/cite.330440502
Subject(s) - thermodynamics , partial differential equation , extension (predicate logic) , property (philosophy) , physics , differential equation , gravitation , relation (database) , ordinary differential equation , mathematics , mathematical analysis , statistical physics , classical mechanics , computer science , philosophy , epistemology , database , programming language
While the relation between thermodynamic properties of any uniform mass of material, first presented by Gibbs in the form d U = T d S – P d V + ∑ μ i d n i is well understood, its attempted extension to effects other than thermal, compression, and change in mass has caused some confusion. The above equation can be presented in a symmetrical form and, on going back to basic principles, it proves possible also to develop the complete symmetrical fundamental property relation including surface, tensile, gravitational, centrifugal, kinetic, electrical, and magnetic effects. Integration of the resulting differential equation yields the primitive or non‐differential form. The complete sets of cross partial derivatives, which can be obtained from a generalized form of the fundamental equation, may be compared with the derivatives obtained by conventional methods. Selection of useful cross partials for practical situations is demonstrated.