Chapter 8 approaches the topics of phase equilibrium and phase transitions from a microscale perspective. Specifically, the roles of fluctuations and system stability in the onset of phase transitions are examined in detail. Using aspects of statistical thermodynamics theory developed in earlier chapters, the van der Waals model is used to demonstrate how fluctuations and system instability give rise to phase transitions in fluid systems. Binary fluid systems are considered, with pure fluid results being recovered when the mass of one species is set to zero. It is shown that critical exponents and the law of corresponding states can be deduced from the van der Waals model for pure fluids. Microscale aspects of solid–liquid transitions are also considered.

Fluctuations and Phase Stability

In the development of thermodynamics presented in the preceding chapters, we have identified different categories of substances according to the density of the substance and the nature of molecular interactions in the substance. Gases have low density and the molecules spend most of the time traveling through space with momentum and energy being exchanged between molecules only through brief collisions. In liquids, the molecules are free to roam about within the system but the density is much higher than in gases, with the mean distance between adjacent molecules being only one to two molecular diameters. Because the molecules are close to their neighbors, they continuously are subject to force interactions with nearby molecules, resulting in continuous exchange of momentum and energy.