6 - Phase Transitions

Summary

The stability of a system is discussed in terms of the curvature of entropy as a function of internal energy and volume, then in terms of internal energy as a function of entropy and volume. Global and local conditions are given. The most difficult mathematical developments are differed to worked solutions and exercices. This analysis introduces the notion that phase diagrams may contain regions where distinct phases coexist. The slope of phase coexistence lines are deduced from thermodynamic principles and give the Clausius-Clapeyron formula. Equilibrium between coexisting phases is shown to imply the Gibbs phase rule which gives the number of degrees of freedom of a system in terms of the number of substances and phases present in the system. The van der Waals equation of state is discussed. In the worked solutions, a model is presented for a concrete case of phase coexistence, and observations from every day life are analysed, such as the melting temperature of salt water or the gas pressure of a bottle containing liquid in which gas is dissolved.