We propose a novel approach to the construction of multi-parameter generalisations of the van der Waals model constructed in such a way that the equation of state is a solution to an integrable nonlinear conservation law linearisable by a Cole–Hopf transformation. We show that our extended van der Waals equation of state is compatible with notable empirical models for a suitable choice of the free parameters and can be viewed as a master interpolating equation. The present approach also suggests that further generalisations can be obtained by including the class of dispersive and viscous-dispersive nonlinear conservation laws and could lead to a new type of thermodynamic phase transitions associated to nonclassical and dispersive shock waves.
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