Simple modifications of the van der Waals and Dieterici equations of state: vapour–liquid equilibrium properties

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Recent studies have considered simple (i.e., no adjustable parameters) modifications to the van der Waals and Dieterici equations of state. It is still unclear, however, at least for the calculation of vapour–liquid equilibrium properties, whether the appropriate repulsive term is that of the classical van der Waals equation or that given by the Carnahan–Starling equation for hard spheres. Moreover, the studies on the Carnahan–Starling–Dieterici equation of state have raised the interesting question of the comparison between the van der Waals (summed terms) and Dieterici (multiplied terms) approaches. We study here the suitability of six families of equations of state in obtaining the main vapour–liquid properties of simple fluids. These families include, together with the aforementioned equations, a variable exponent in the power-law temperature dependence. The main aims are to identify the best choice of a simple predictive equation of state, and to determine whether the Carnahan–Starling repulsive equation is a clearly acceptable alternative to the traditional van der Waals repulsive term, and whether the Dieterici-type equations can give better results than those based on the van der Waals equation.