Chapter 5 - Equations of State for Simple Fluids – The Basis

Abstract

We begin our discussion of “nonideality” by considering the virial equation of state in which deviations from the ideal gas pressure arise systematically in a Taylor series expansion of the pressure in terms of density n. Due to poor convergence properties of this expansion, we focus on the first two terms and derive the second virial coefficient B2(T). We then proceed to derive the van der Waals (vdW) equation of state in its original form as an ideal gas law corrected for excluded volume and intermolecular binding energy. The presence of nonphysical regions of the P(V,T)-phase plane is shown to indicate phase separation into gas, and liquid and the Maxwell construction is derived. The critical parameters are discussed, and it is noted that they are often used to determine the a,b-parameters of the vdW equation of state so as to give it a semiempirical form. The vdW equation of state with empirical parameters has been used extensively and many variants have been proposed and tried as vehicles for systematization and prediction of equation of state data. We end up with a list of such equations of state mainly of a “cubic” form close to the original equation of van der Waals but also including two inspired by the virial equation of state and including a larger number of parameters.