Mixing rules for cubic EOSs

This formidable-looking integral is quite easy, because the two derivatives in the integrand are not functions of V, so we may integrate, finding 

Here we have dropped the lower integration limit, because all of terms on the right in Eq. F.29 are zero at V = oo. Equation F.29 is correct for the vdW EOS for any set of mixing rules for determining the mixture values of a and b.  

This form is correct only for the arbitrary mixing rules shown in Eqs. F.30 and F.31 (which are the most widely used mles for the vdW EOS).  

Please review Sections 7.12 and 9.7, which present the idea of mixing rules, and show a simple example. To use any cubic EOS for mixtures, we must use some set of mixing rules. The study of mixing rules for such EOSs is an active area of research [3] formulating a set of rules that are simpler and more accurate than those in common use will bring the author (temporary) fame  

Example F.4 Show the form of Eq. F.29 for the following commonly used mixing rules for the vdW EOS (similar to those in Section 9.7)  

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