On Failures of van der Waals’ Equation at the Gas–Liquid Critical Point

Abstract

This comment is in response to a recent “new comment” by Umirzakov on the article “Gibbs density surface of fluid argon: revised critical parameters.” It was incorrectly asserted that van der Waals equation “proves” the existence of a scaling singularity with a divergent isochoric heat capacity (Cv). Van der Waals’ equation, however, is inconsistent with the universal scaling singularity concept; it erroneously predicts, for instance, that Cv is a constant for all fluid states. Van der Waals hypothetical singular critical point is based upon a common misconception that van der Waals equation represents physical reality of fluids. A comparison with experimental properties of argon shows that state functions of van der Waals’ equation fail to describe the thermodynamic properties of low-temperature gases, liquids and of gas–liquid coexistence. The conclusion that there is no “critical point” singularity on Gibbs density surface remains scientifically sound.