Equation of State in the Neighborhood of the Critical Point

A specific form is proposed for the equation of state of a fluid near its critical point. A function Φ(x, y) is introduced, with x a measure of the temperature and y of the density. Fluids obeying an equation of state of van der Waals type (``classical'' fluids) are characterized by Φ being a constant. It is suggested that in a real fluid Φ(x, y) is a homogeneous function of x and y, with a positive degree of homogeneity (Sec. 2). This leads to a nonclassical compressibility, the behavior of which is determined by the degree of homogeneity of Φ (Sec. 3). A previously derived relation connecting the degree of the critical isotherm, the degree of the coexistence curve, and the compressibility index, again follows, this time without the restrictive assumption of effective isochore linearity (Sec. 4). The locus in the temperature—density plane of the points of inflection in the pressure—density isotherms, as determined experimentally by Habgood and Schneider, is accounted for (Sec. 5). It is shown that if a certain combination of the compressibility and coexistence curve indices is an integer, then the constant-volume specific heat on the critical isochore has a logarithmic singularity at the critical temperature with, in general, a superimposed finite discontinuity (Sec. 6).