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The distribution of zeros of the grand partition function is calculated in the thermodynamic limit for a class of one-dimensional gas models in two ways: (1) from the equation of state and (2) directly from the partition function. In this way one obtains (for these cases) a verification of the assumptions we had to make in order to associate a unique distribution of zeros with a given equation of state. In the Appendix we present some numerical evidence for the validity of these assumptions also in the case of the van der Waals gas.

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We consider a classical system of particles interacting via a pair potential consisting of a strong short-range repulsion us(r) and a weak long-range potential of the form ul(r)=γ3 F(γr), where the range γ−1 is long compared with the range of us. The systematic expansion of the thermodynamic quantities in the ratio of the two ranges has been developed previously and is briefly reviewed. The expansion breaks down when the inverse compressibility of the fluid vanishes. Explicit calculations of the equation of state for special choices of the two parts of the intermolecular potential are presented and compared with the corresponding experimental results for argon. It is also shown that to first order in the expansion parameter the specific heat cv has a maximum near the critical isochore.

Part of the fourth virial coefficient, D2(T,λ), is calculated with square-well potential in the region 1≤λ≤2. The location of the singularities in ring integrals as functions of λ is discussed.