Chapter 6, Problem 6.12P

Interpretation Introduction

Interpretation:

Derive expressions for $G^R$, $H^R$ and $S^R$ implied by the van der Waals equation of state.

Concept Introduction:

The van der Waals equation of state is given as:

  $P=\frac{RT}{V-b}-\frac{a}{V^2}$............(a)

The expressions used for residual properties in terms of density are:

  $P=\rho ZRT$

  $\frac{G^R}{RT}={\displaystyle \underset{0}{\overset{\rho }{\int }}(Z-1)}\frac{d\rho }{\rho }+Z-1-\ln Z$............(1)

  $\frac{H^R}{RT}=-T{\displaystyle \underset{0}{\overset{\rho }{\int }}{\left(\frac{\partial Z}{\partial T}\right)}_{\rho }}\frac{d\rho }{\rho }+Z-1$............(2)

  $\frac{S^R}{RT}=\ln Z-T{\displaystyle \underset{0}{\overset{\rho }{\int }}{\left(\frac{\partial Z}{\partial T}\right)}_{\rho }}\frac{d\rho }{\rho }-{\displaystyle \underset{0}{\overset{\rho }{\int }}(Z-1)}\frac{d\rho }{\rho }$............(3)