Until now, most of what we have discussed has involved general relationships among thermodynamic quantities that can be applied to any system, such as the fundamental equation, reversibility, Legendre transforms, and Maxwell equations. In this and the coming chapters, we begin to investigate properties of specific types of substances. We will mostly consider very simple models in which only the essential physics is included; these give insight into the basic behaviors of solids, liquids, and gases, and actually are sufficient to learn quite a bit about them. Of course, there are also many detailed theoretical and empirical models for specific systems, but very often these theories simply improve upon the accuracy of the approaches rather than introduce major new concepts and qualitative behaviors.

Statistical mechanics provides a systematic route to state- and substance-specific models. If one can postulate a sufficiently simple description of the relevant atomic interaction energetics, the entropy or free energy can be determined in fundamental form. Ultimately our strategy for most of these simple models will be to determine the chemical potential μ(T, P) in single-component systems or μ(T, P, {x}) for multicomponent ones, where {x} gives the mole fractions. In both cases, knowledge of the chemical potentials does indeed give a fundamental perspective, allowing us to extract all of the intensive thermodynamic properties. Moreover, for problems involving phase equilibrium, the chemical potential is the natural starting point, as we will see in Chapter 10.