Phase Transitions in Pure Substances

Abstract

In this chapter, we introduce the concept of phase and discuss various phase transitions in pure substances. Modern classification of phase transitions as well as the historical Ehrenfest classification are presented. We discuss mainly first order transitions but examples of continuous (second order) transitions are also given. First, we derive the conditions of twophase coexistence and then discuss also coexistence of three phases. The phase diagrams of a typical substance (e.g. carbon dioxide), water and helium 4He are discussed in more detail. Then the Clapeyron and Clausius–Clapeyron equations are derived to determine the solid–liquid, liquid–gas and solid–gas phase boundaries. Special attention is paid to the liquid–vapour coexistence and the critical point at which the difference between the two phases disappears. Next we discuss the liquid–vapour coexistence using the van der Waals equation of state and describe the Maxwell construction. Finally, the van der Waals equation of state is expressed in terms of the ratios of temperature, pressure and volume to their critical values (reduced variables). This form, independent of any characteristics of the substance, leads to the principle of corresponding states.