Chapter 10, Problem 10.20P

Interpretation Introduction

Interpretation:

To justify the following equations.

  ${(\frac{\partial \ln \widehat{\Phi }i}{\partial P})}_{T,x}=\frac{{\overline{V}}_i^R}{RT}$

  ${(\frac{\partial \ln \widehat{\Phi }i}{\partial T})}_{P,x}=-\frac{{\overline{H}}_i^R}{R{T}^2}$

  $\frac{G^R}{RT}={\displaystyle \sum _i{x}_i}\ln \widehat{\Phi }i$

  ${\displaystyle \sum _i{x}_i}d\ln \widehat{\Phi }i=0$(const T,P)

Concept introduction:

The Fundamental residual property relation is written as follows:

  $d(\frac{G^R}{RT})=\frac{V^R}{RT}dP-\frac{H^R}{R{T}^2}dT+{\displaystyle \sum _i\frac{{\overline{G}}_i^R}{RT}}d{x}_i$ ......eq 1