Excluded Volume: A Historical Enigma of the van der Waals Equation of State

The value of excluded volume taken by van der Waals as the quadruple molecular volume was a subject of discussion for a long time. The enigma of the van der Waals equation of state consists in the fact that it yields a correct result only with an incorrect excluded volume. The paradox has been recently resolved in the author’s general theory of an equation of state based on the excluded volume. A short outline of the theory is given with the derivation of the van der Waals equation as corresponding to a linear dependence of the exclusion factor on the packing fraction. The generation of other equations of state is exhibited by example of a system of hard spheres. The novel theory is shown to be potentially important for mixtures with large molecular size ratios.