On the range of applicability of the Carnahan–Starling–Patel–Teja equation of state

The Carnahan–Starling–Patel–Teja equation of state is analysed in terms of their range of applicability. We show that there is a physical limit in the lowest value that the pseudo-critical compressibility factor can take, and that this value is 0.299256. This limit was not considered in the two versions of this equation presently available, with the consequence that they give physically impossible infinite and negative values for the pressure at temperatures near the critical point and for some particular values of the volume. The location of the singularity is given here, and correlated with a simple Padé approximant. The singularities are also present for supercritical conditions, so that the two equations studied cannot be used at any supercritical temperature because negative pressures will always be found for volumes larger than certain particular value. It is also shown that these limitations are not in the original Patel–Teja equation.