Chapter 3, Problem 3.43P

Interpretation Introduction

Interpretation:

Show that the second and third virial coefficients implied by the generic cubic equation of state are $B=b-\frac{a\left(T\right)}{RT}$ and $C=b^2+\frac{\left(\epsilon +\sigma \right)ba\left(T\right)}{RT}$ . And compare the results for $B$ using Redlich/Kwong equation of state with generalized correlation for $B$ of simple fluids.

Concept Introduction:

Write down the general cubic equation in terms of compressibility factor and for simplicity in terms of density and compare the results with standard expression of compressibility factor in terms of virial coefficients to find relations for both second and third virial coefficients.

Redlich/Kwong equation of state is used to find the values of second and third virial coefficients by formulating the positive constants use in generic cubic equations. So, here we first find the value of $B$ using Redlich/Kwong equation of state and then compare the results with generalized correlation for $B$ of simple fluids.

The general cubic equation of state is:

$P=\frac{RT}{V-b}-\frac{a(T)}{(V+\epsilon b)(V+\sigma b)}$......(1)

For Redlich/Kwong equation of state,

$\epsilon =0,\sigma =1,\psi =0.42748,\Omega =0.08664\text{and}\alpha {\text{(T}}_r)=T_r{}^{-1/2}$