Chapter 6, Problem 6.13P

Interpretation Introduction

Interpretation:

Derive expressions for $G^R$, $H^R$ and $S^R$ implied by the Dieterici equation.

$P=\frac{RT}{V-b}\exp \left(-\frac{a}{VRT}\right)$............(a)

Where $a$ and $b$ are the functions of compositions only

Concept Introduction:

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)