Point of Condensation and the Volume Dependency of the Cluster Integrals

In the theory of imperfect gas, the cluster integrals bl depend on V (total volume of the system). The double limit process V →∞ and l →∞ defines two different functions χ(z) and χ∞(z) (or, ζ(z) and ζ∞(z)). The real behaviour of partition function is not given by χ(z), but by χ∞(z), ζ∞(z). Instead of the singularity of χ(z), the upper limit of the regular interval of χ∞(z) is important. Inadequateness of the method of generating function is discussed.