7. Mahmoud A. Melehy, Thermal Momentum in Thermodynamics, Part 3: On the Evaluation of Thermodynamic Parameters and Entropy Uniqueness

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Volume 14: Pages 49-58, 2001

Thermal Momentum in Thermodynamics, Part 3: On the Evaluation of Thermodynamic Parameters and Entropy Uniqueness

Mahmoud A. Melehy

University of Connecticut, School of Engineering, Department of Electrical and Systems Engineering, Room 312, U157, 260 Glenbrook Road, Storrs, Connecticut 062692157 U.S.A.

In Part 1, it was shown that the principle of detailed balancing requires the exclusive use in thermodynamics of the internal pressure, which reflects the rate of change of the particle thermal momentum per unit area, rather than the external, measurable pressure. This fundamental result has led to a generalization of Einstein's thermodynamic treatment of the Brownian motion. From the resulting thermodynamic theory, new interfacial theories followed that have been corroborated by numerous experiments and observable phenomena, described in Parts 1 and 2. This paper further confirms the exclusive relevance of the internal pressure to thermodynamics. Specifically, it is shown that, for a constituent, values of the thermodynamic pressure and of other basic parameters are largely predetermined by the first and second laws. The procedure used involves calculating from those two laws the equilibrium value of the entropy per particle by two independent methods, which, to satisfy the second law, must be equal. One method is classical, but the other method requires additional information from quantum mechanics and quantum or classical statistics. Thus, the study of various systems must be undertaken case by case. In this article, three general systems are considered: ideal, monatomic gases, andconduction electrons and holes, which may have unspecified, isotropic energy bands, and any degree of degeneracy. From those exemplary cases, an important conclusion emerges that quantitatively confirms the prediction of the principle of detailed balancing: it is necessary to use exclusively the internal pressure in thermodynamics if the condition of uniqueness of entropy is to be satisfied. Furthermore, to completely fulfill this central requirement of the second law, the calculated values of all other basic parameters must be consistent with that particular pressure.

Keywords: detailed balancing, pressure, internal energy, chemical potential, conditions for entropy uniqueness

Received: May 23, 2000; Published online: December 15, 2008