### Abstract:

In this paper we revisit the problem of explaining phase transition by a study of a form of
the Boltzmann equation, where inter-molecular attraction is included by means of a Vlasov
term in the evolution equation for the one particle distribution function.We are able to show
that for typical gas densities, a uniform state is unstable if the inter-molecular attraction is
large enough. Our analysis relies strongly on the assumption, essential to the derivation of
the Boltzmann equation, that ν ≪ 1, where ν = d/l is the ratio of the molecular diameter
to the mean inter-particle distance; in this case, for fluctuations on the scale of the molecular
spacing, the collision term is small, and an explicit approximate solution is possible. We
give reasons why we think the resulting approximation is valid, and in conclusion offer some
possibilities for extension of the results to finite amplitude.