Chapter 7, Problem 7.13NP

Interpretation Introduction

Interpretation : It should be shown that in the limit of low density, the van der Waals and Redlich-Kwong equations of state can be reduced to the ideal gas equation of state.

Concept Introduction :

Van der Waals equation of state:

  $P=\frac{RT}{V_m-b}-\frac{a}{V_m^2}=\frac{nRT}{V-nb}-\frac{n^{2}a}{V^2}$

P − pressure

R − universal gas constant

V_m − molar volume

n − number of moles

a − correction for volume

b − correction for attractive force

Redlich-Kwong equation of state:

  $P=\frac{RT}{V_m-b}-\frac{a}{\sqrt{T}}\frac{1}{V_m\left(V_m+b\right)}=\frac{nRT}{V-nb}-\frac{n^{2}a}{\sqrt{T}}\frac{1}{V(V+nb)}$