Equations of State of a Pure Material, Binodal, Spinodal, Critical Point, and Sample Problem

Abstract

The material presented in this lecture is adapted from Chapters 8 and 7 in T&M. In this lecture, we will continue discussing pure materials (n = 1). First, we will discuss the mathematical relation between P, V, and T, referred to as the volumetric equation of state, or in short, the equation of state (EOS). In particular, we will discuss the ideal gas EOS and the van der Waals EOS, including providing an underlying molecular interpretation for both EOS. Second, we will solve Sample Problem 17.1 to calculate the excluded volume between two spheres of equal radius. Third, we will examine the various forms of the isotherms in a pressure (P)-volume (V) phase diagram at temperatures which are high, equal, or low relative to the critical temperature. Fourth, we will discuss the coexistence curve, the spinodal curve, and the critical point, including providing mathematical criteria to calculate them. Finally, we will discuss stability, metastability, and instability, including providing mathematical criteria to characterize these behaviors, as well as useful mechanical analogies to rationalize what each behavior entails.