The symmetrical fundamental property relation of thermodynamics

Scientific article. — Chemie-Ingenieur-Technik, 1972, Bd. 44, H. 5, S. 249–257.While the relation between thermodynamic properties of any uniform mass of material, first presented by Gibbs in the form dU = TdX – PdV + Σμ_idn_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-merential 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.