Linear isothermal regularity

The linear isothermal regularity was discovered by Parsafar in 1991. It suggests that $(Z-1)v^{2}$ vs $\rho ^{2}$ is linear. This led to a new Van der Waals like equation of state (Ref. 2 Eq. 8):

$(Z-1)v^{2}={\frac {1}{\rho }}\left({\frac {\alpha }{1-\lambda b\rho }}-{\frac {\alpha -B_{2}}{1+\delta b\rho }}\right)$

References

1. Gholam Abbas Parsafar "Deriving the Equation of State for Liquids and Extension of the Principle of Corresponding States", Journal of Sciences, Islamic Republic of Iran 2 pp. 111-123 (1991)
2. Gholam Abbas Parsafar and E. A. Mason "Linear isotherms for dense fluids: a new regularity", Journal of Physical Chemistry 97 pp. 9048-9053 (1993)
3. Mohammad Shokouhi and Gholam Abbas Parsafar "A new equation of state derived by the statistical mechanical perturbation theory", Fluid Phase Equilibria 264 pp. 1-11 (2008)