On the Critical Region of a Simple Fluid. I. Two Elementary Index Inequalities

Abstract

The continuity of the slopes of isochores (∂P / ∂T)V of a simple fluid at its critical point is shown to imply, and be implied by, the strict index inequality β + γ − > 1 , which is not a consequence of known index inequalities based on thermodynamic stability. Under certain assumptions relating to the index inequality α − + β < 1 , it is shown that C P diverges with index γ − on the phase boundary, and that the saturated specific heat diverges with index (1 − β)