The equation of state describing the Coulomb liquids and the vapour-liquid
phase transition in dusty plasmas is derived by making a virial expansion i
n terms of g(-1) = n(d)lambda(D)(3) < 1, where n(d) and lambda(D) are the d
ust number density and the Dusty plasma Debye length, respectively. The exp
ressions for the latent heat of transition, the Joule cooling of the dust g
rains and the Boyles temperatures are obtained. Furthermore, a simple model
for the one-dimensional dust crystal is constructed and the process of the
sublimation of the linear dust chain, melting of the two-dimensional latti
ces, etc, are briefly discussed. (C) 1999 Elsevier Science B.V. All rights
reserved.