Gibbs, Helmholtz, and Clausius–Clapeyron

Abstract

Section 10.1 begins with a description of the treatment of energy and entropy extrema. Two phases with a single variety of constituent atoms are studied in Sect. 10.2. Minimum energy in adiabatically isolated phases is considered in Sect. 10.3, while Sect. 10.4 deals with relative size of phases, equality of energy minimum and specific internal energy of the phases. Various aspects of entropy are examined in Sects. 10.5 and 10.6. Legendre transformations and Helmholtz free energy are discussed in Sects. 10.7 and 10.8. Some of Helmholtz’ work relevant to this study is examined in Sects. 10.8.1 and 10.8.4–10.8.6. Clausius’ inequality in differential form is described in Sect. 10.8.2. Validity of the suggestion that maximum possible work that a given system, in thermal contact with a constant temperature reservoir, can possibly perform is equal to the resulting decrease in its Helmholtz free energy is checked in Sect. 10.8.3. That specific Helmholtz free energy is equal for different phases in thermodynamic equilibrium is noted in Sect. 10.8.7.