Cubic thermodynamic PVT equations and a modified corresponding states principle

Several fundamental issues related to the development of generalized equations describing thermodynamic pressure-volume-temperature (PVT) behavior of pure substances are investigated. An invariance rule for PVT equations is presented along with supporting evidence. This rule can be used as a mathematical tool for generating a family of PVT equations having the same relation between reduced saturation pressure and the reduced saturation temperature but different values of the critical compressibility factor.Accurate substance specific cubic PVT equations for 21 substances have been developed. Tables of the predicted thermodynamic properties in the metastable and unstable regions, based on these equations, are presented. A generalized PVT equation, based on the new form of the corresponding states principle, is developed. By successfully including both polar and nonpolar substances into the generalized PVT equation, it has been shown that additional molecular parameters (like the Stiel polar factor) are not necessary for developing generalized equations.The van der Waals theory for the temperature variation of surface tension has been reviewed. The critical exponent for variation of surface tension near the critical point has been estimated as 1.26 using a novel estimation technique and data from the literature. It has been shown that van der Waals surface tension theory yields excellent results when used with accurate PVT equations that have the correct behavior in the metastable and unstable regions.Most of the popular generalized PVT equations in the literature are based on a modified form of the corresponding states principle originally proposed by van der Waals. These equations use the Pitzer acentric factor as an additional parameter and assume the existence of a strong correlation between the Pitzer acentric factor and the critical compressibility factor. It has been shown that such a correlation does not exist. Based on dimensional arguments and the invariance rule, a new form of the corresponding states principle is presented which does not require the assumption of the existence of such a correlation. The new form uses five substance specific parameters, namely, the three critical constants, the ideal gas constant, and the Pitzer acentric factor.