Phenomenological models for the generic van der waals equation of state and critical parameters

In this paper, phenomenological models for the generic van der Waals equation of state are proposed for the subcritical regime of a simple fluid by assuming empirical forms for the generic van der Waals parameters A and B. The models that are assumed are tested against the critical parameters. It is shown that quadratic and cubic models for A and B are shown to give good critical parameters. The quadratic and cubic models are then employed to calculate critical isotherms of argon and methane to determine which model is superior. It is found that the quadratic model yields excellent critical isotherms in comparison with experimental data and is much superior to the cubic model in the experimental range of density. The model equation of state is also used to determine the spinodal curve, which is shown to be closely related to the nonanalytic behavior of A and B with respect to temperature.