Yesterday in class I worked an example for how to calculate residual properties using the van der Waals equation of state. The first step of performing such calculations was to convert the integrals for the residual properties to a form that allowed easy substitution of an equation of state in the form P(T,rho). This meant we had to convert the integrals in P to integrals in rho.
I know we went through this very quickly, due to time constraints, but just keep in mind that this is just a mathematical manipulation of the equations to swap rho for P. It is just like any other variable substitution you have done in integral calculus. The book has a detailed derivation on pages 216 and 217 that shows exactly how to do this manipulation.
The final equations for the residual properties are given in 6.58, 6.59, and 6.60. These equations are fundamentally no different than those we discussed earlier (shown in the book in 6.46, 6.48, and 6.49); they simply involve integrals using rho rather than P.
This should be helpful in your working with problem 44 on the homework.
MSS
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