An intensified analytic solution for finding the roots of a cubic equation of state in low temperature region

Because of the effect of the enlarging process of errors in low temperature region, the analytical solutions of a cubic equation of state (CES) lead to illogical results. To overcome this problem, we recommend an enhanced analytic method, in this paper. Up to now, there is not any analytical method for this problem. In the present study, the general cubic equation x3 + Bx2 + Cx + D = 0 is transformed into simple equation γ3 − βγ + β = 0. For β ≥ 27/4, then the three roots are real. To compare, as an example, for 1-butene at T = 112.3 (K) and P = 3.79 × 10− 9(Pa), the empirical value of the molar volume is 72.00 (m3mol− 1). By using Patel-Teja (PT) CES, the molar volume value is obtained as − 342.3 from traditional analytic method and 73.88 from both the new intensified analytic method and the iterative Newton-Raphson method.