Can cubic equations of state be recast in the virial form?

In this paper, we propose a mathematical study of the virial expansion of cubic equations of state. We attempt to provide an answer to the following questions:-Is the virial equation only appropriate for the description of gases at low to moderate densities?-What is the impact of the order of truncation on the representation of P−vP−v isotherms?-What is the difference between a truncation at an even order and a truncation at an odd order?-What is the theoretical volume range of validity of a virial expansion?To illustrate and apply these concepts, we considered four classical cubic equations of state, namely: Van der Waals, Redlich–Kwong–Soave, Peng–Robinson and Schmidt–Wenzel. For all of these equations, we detail the limitations and the capabilities of the virial expansions.Finally, we propose a new general relation between the coefficients of the virial equation in pressure and those of the virial equation in density.