This exercise illustrates one approach commonly used in developing thermodynamic models: a reliable functional form for a property of one substance is extended to a class of substances by...

This exercise illustrates one approach commonly used in developing thermodynamic models: a reliable functional form for a property of one substance is extended to a class of substances by parameterizing in terms of critical properties, and perhaps improved somewhat by curve fitting. Use the Redlich-Kwong equation of state to obtain an expression for the temperature dependence of the second virial coefficient. Then use the relations a(Tc, Pc ) and b(Tc , Pc ) from Table 4.4 to replace the equation of state parameters a and b with critical properties. Show that your result can be expressed in reduced form as

We then obtain values of the parameters α, β, and γ by a least squares fit to B(T) data for gases composed of small rigid nonpolar molecules. Using the numerical values in (P4.31.1) as initial guesses in the fit, the result is the expression for Bo given by the Pitzer correlation in Problem 4.22.

Problem 4.22.~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~