5) The van der Waals Equation of State (EOS) is as given below: \left(\mathbf{P}+\frac{\mathbf{a}}{\mathbf{v}^{2}}\right)(\mathbf{v}-\mathbf{b})=\mathbf{R T} where, the constants a, b account for the inter molecular forces and the volume occupied

by the gas molecules themselves in the case of high density (real) gases. On noting that the critical isotherm on the P-v diagram has a horizontal inflection point at the that the Van derWaals constant a and b are given as: \mathbf{a}=\frac{27 \mathbf{R}^{2} \mathrm{~T}_{\mathbf{C r}}^{2}}{\mathbf{6 4 P}_{\mathbf{\alpha}}} ; \quad \mathbf{b}=\frac{\mathbf{R T}_{\mathbf{\alpha}}}{\mathbf{8 P}_{\mathbf{C}}} where Pa and Tr are the critical pressure and critical temperature of the gas respectively.