A switch function applied to the thermodynamic properties of steam near and not near the critical point

摘要

A study is presented of the still-unsolved problem of estimating thermodynamic property values in a region intermediate between the critical region in which the scaling laws apply, and regions further from critical, where classical behavior prevails. A procedure has been developed in which a varying weighting function is used in obtaining a weighted “average” of the scaled and the classical Helmholtz free energy. Other properties are then obtained by differentiation. It is first demonstrated that it is fundamentally impossible for the “averaged” Helmholtz free energy and its first two derivatives to all be intermediate between the corresponding values from the scaled and the classical formulations. The procedure has been developed and tested for steam. The scaled function is the simple linear model of Murphy et al., the classical equation that of Pollak. The properties of power-weighted switch functions, particularly with respect to the behavior of higher-order derivatives, and the choice of the boundaries of the switching region, were examined in detail and optimized by proper choice of parameters. It is shown that a reasonably smooth transfer from the scaled to the classical region can be achieved as far as free energy, energy, and specific heatCVare concerned. For satisfactory behavior of all second derivative properties, the two formulations need to be more compatible in the switching region than they are in the prese