On the Theory of Condensation

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Abstract
In an attempt to understand why approximations of the van der Waals type can yield semiquantitative results in spite of being qualitatively wrong, we have assumed that the partition function for submacroscopic volumes, as a function of the number of particles, is of the van der Waals type. We have considered, as a model of a real fluid, a cubic array of submacroscopic cells with variable numbers of particles and have assumed an interaction energy between adjacent cells only. Since the van der Waals equation predicts two sharp peaks in the probability function for the occupation numbers, one has then essentially a three-dimensional Ising model. Using some of the known properties of the Ising model (and some which can be safely anticipated), we find that with plausible assumptions about the interaction energy between cells this model exhibits condensation, and that its condensation pressure, its isotherm in the stable states, and its critical temperature, are still essentially determined by those of the individual cell.