Analytical Equation for Rigid Spheres: Application to the Model of Longuet-Higgins and Widom for the Melting of Argon

Recent developments in the theory of fluids have produced an analytical expression for the $\mathrm{PVT}$ behavior of rigid-sphere fluids. The equation ${\left(\frac{\mathrm{PV}}{\mathrm{NkT}}\right)}^0=\frac{(1+y+y^2-y^3)}{{\mathrm{}(1-y)\mathrm{}}^3}$, where $y=\frac{b}{4V}=\frac{\sqrt{2}\pi N{\sigma }^3}{6V}$, has been shown to be the best analytical equation for rigid-sphere fluids presently known. Incorporation of the expression into the model of Longuet-Higgins and Widom for argon near its triple point, in a manner used by Guggenheim, demonstrates the sensitivity of predicted liquid behavior to the mathematical expression for rigid-sphere $\mathrm{PVT}$ behavior.