Calculation of the second virial coefficients of alkali metals by modified Peng–Robinson equation

Abstract

In this work, the Peng–Robinson (P–R) equation of state has been modified by proposing a new α function for calculating the second virial coefficients of alkali metals. The relationship between α0.5 and (1 − T 0.5 ) is a nonlinear function. The correlation between the second virial coefficient and P–R equation was presented by expanding the P–R equation into its Taylor series form. For P–R equation, the linear correlation between parameters C1 and C2 of α function and acentric factors $$ \omega $$ of alkali metals was proposed. The new α function and its first, second and third derivatives are continuous. The average standard deviations of compressibility factor which calculated by modified P–R equation are less than 4.3%. The second virial coefficients of alkali metals were calculated over the temperature range 600–3000 K by using the modified P–R equation. Comparison with literature data, the new equation provides more reliable and accurate second virial coefficient predictions for alkali metals than the original P–R equation. It is useful to guide and improve calculation of the second virial coefficients of other metal vapors for design and operation of separation processes in vacuum metallurgy.