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Reference of this paragraph: Introduction to Chemical Engineering Thermodynamics Eighth Edition by J. M. Smith, H. C. Van Ness, M. M. Abbott and M. T. Swihart (Pg no 105-107)

Pitzer Correlations for the Second Virial Coefficient The tabular nature of the generalized compressibility-factor correlation is a disadvantage, but the complexity of the functions Z0 and Z1 precludes their accurate representation by simple equations. Nonetheless, we can give approximate analytical expression to these functions for a limited range of pressures. The basis for this is Eq. (3.36), the simplest form of the virial equation: Z = 1 +BP/RT The simplest form of the virial equation has validity only at low to moderate pressures where Z is linear in pressure. The generalized virial-coefficient correlation is therefore useful only where Z0 and Z1 are at least approximately linear functions of reduced pressure. Figure 3.13 compares the linear relation of Z0 to Pr as given by Eqs. (3.60) and (3.61) with values of Z0 from the Lee/Kesler compressibility-factor correlation, Tables D.1 and D.3 of App. D. The two correlations differ by less than 2% in the region above the dashed line of the figure. For reduced temperatures greater than Tr ≈ 3, there appears to be no limitation on the pressure. For lower values of Tr the allowable pressure range decreases with decreasing temperature. A point is reached, however, at Tr ≈ 0.7 where the pressure range is limited by the saturation pressure.20 This is indicated by the left-most segment of the dashed line. The minor contributions of Z1 to the correlations are here neglected. In view of the uncertainty associated with any generalized correlation, deviations of no more than 2% in Z0 are not significant. The relative simplicity of the generalized second-virial-coefficient correlation does much to recommend it. Moreover, temperatures and pressures of many chemical-processing operations lie within the region appropriate to the compressibility-factor correlation. Like the parent correlation, it is most accurate for nonpolar species and least accurate for highly polar and associating molecules.