Abstract The grand potential, the density and the molecular distribution functions are obtained in the form of virial expansions for systems of arbitrary size and inhomogeneity by using an external field to replace the conventional fixed geometric boundaries of a system. The equations are applied first to the calculation of the density and of different representations of the pressure tensor for a system of gaussian (repulsive) molecules in a simple harmonic potential, and, secondly, to obtaining an expression for the isosteric heat of absorption of interacting molecules in the pores of a zeolite.