Relation between Isotherms and Coexistence Curve in the Critical Region

Abstract

A general relation has been given relating the slope of the isotherms along the liquid-vapor coexistence curve to the shape of the latter, and has been applied to the case where the coexistence curve is rounded on the top and to the case where it has a flat horizontal portion. If the coexistence curve has the form T—Tc = — a|ρc—ρ|n (where T = temperature, ρ=density, subscript c indicates a value at the critical point, and a and n are constants) it can be shown that the critical isotherm is given by P−Pc=a(∂2P/∂T∂ρ)c(ρ−ρc)|ρ−ρc|n,provided (∂2P/∂T∂ρ)c is finite. This equation should hold over the region where ∂2P/∂T∂ρ is approximately constant. If there is a flat, horizontal portion at the top of the isotherm a similar equation will be approximately true under the same conditions beyond the flat portion. The actual shape of experimental isotherms in the critical region is considered. ∂2P/∂T∂ρ is approximately constant only over a limited range of densities, and beyond this range the slopes of the isotherms become greater than indicated by the equation; however, general orders of magnitude are as expected. It is not possible to decide definitely from the data considered whether the critical isotherm has a horizontal region over a finite range of densities. Finally, a discussion is given of the discontinuities of thermodynamic quantities, particularly Cv, as one passes from the one-phase to the two-phase region. It is shown that Cv must be much larger in the two-phase than in the one-phase region.