The purpose of this chapter is to derive expressions for the specific partial quantities ψk = vk, Sk, ek, hk, fk, μk, k = 2, 3 for the condensed phases of water vapor. These quantities are needed to describe the thermodynamics of cloud air. In our treatment we assume that the liquid water and ice occur unmixed and neither liquid water nor ice contain foreign materials. Due to this assumption we cannot describe the formation of a water droplet. Such a droplet forms when water vapor condenses on a suitable aerosol particle so that the resulting droplet cannot be viewed as a pure substance. With this in mind, we may consider the ψk as the pure phase, i.e.. For simplicity we leave out the superscript ∘ denoting the pure phase and also drop the suffix k since confusion is unlikely. In the final section we will add the suffix k for completeness and accuracy.

The material coefficients

First of all, we need to define the coefficients of the isothermal compressibility (K) and the adiabatic compressibility (?S). They are defined by

Similarly, we define the isochoric pressure coefficient β and the isobaric expansion coefficient v* by

The quantities ?, β and v* are not independent. We recognize this by writing the state equation according to the Appendix of Chapter 6 in the form

Expansion of (9.5) gives

This expression is also valid if we choose any of the independent variables T, v and p as constant.