Chapter 6, Problem 6.5P

Interpretation Introduction

Interpretation:

Derive the expressions of $V$, $S$, $H$, $U$, $C_P$ and $C_V$ for the pure fluid which is described by canonical equation of state: $G=\Gamma (T)+RT\ln P$ such that these results are consistent with the important model of gas phase behavior. Give the description about model also.

Concept Introduction:

Since canonical equation contains Gibbs free energy term, so we will use the standard forms of Gibbs free energy initially and then use standard forms of internal energy, enthalpy, heat capacity at constant pressure and volume to find other required relations. The standard forms use in this problem is:

  $dG=VdP-SdT$............(1)

  $U=H-PV$

  $H=G+TS$

  ${\frac{\partial H}{\partial T}}_P=C_P$

and

  ${\frac{\partial U}{\partial T}}_V=C_V$