Study of the critical line and its double point in the intermediate model

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Abstract I show that it is possible to generalise the van Laar calculation for the critical double point for the intermediate model, i.e. a model intermediate between the lattice gas and the van der Waals equation for binary mixtures. The calculation was done to investigate whether the double point is also a tricritical point, as is found both in the case of the lattice gas and in the case of the van der Waals case. Although the double point coordinates and their corresponding potential parameters can be determined, one cannot prove, by analytical means, that the point is also tricritical. Most likely the geometric-mean condition is too stringent in this case.