On the internal consistency of the hyper-chain approximation in the theory of classical fluids

Abstract

The hyper-chain approximation in the theory of classical fluids, and a second approximation in which some account is taken of the first elementary diagram, are examined for internal consistency by calculating virial expansions of the pressure both directly and from the compressibility equation. Both theories are internally inconsistent at the fourth virial coefficient. Numerical results are presented for both fourth and fifth virial coefficients for a gas of hard spheres, and compared with those given by earlier treatments. A brief comment is made on the consistency of the equations for fluid mixtures.