Critical Region Scaled Equation-of-State Calculations and Gravity Effects

The scaled equation of state proposed and extensively applied by Vicentini‐Missoni, Levelt Sengers, and Green is expanded in forms more tractable for manipulation of higher free energy derivatives, such as $C_{\upsilon }$ , at densities away from the critical isochore. Using the xenon liquid–vapor critical region as an example, these methods are applied to the computation of the specific heat for a sample in a gravitational field. Numerical integrations for several sample depths using scaling parameter sets consistent with PVT data are presented, and sample shape effects as well as meniscus position changes with temperature are illustrated. The results are compared with experiment and those of a previous calculation using the “linear model” of the Schofield parametric equation of state. The present results differ from that computation in some respects significant for interpretation of experiments.