Chapter 1, Problem 1.8CP

Interpretation Introduction

Interpretation:The form of Vander Waal equation at sufficiently high temperature is represented as follows:

  $\text{P}\approx \frac{\text{RT}}{{\text{V}}_{\text{m}}\text{- b}}$

The above equation has no influence of the attractive part, this behavior needs to be justified using the potential energy diagram.

Concept Introduction: The ideal gas equation is the equation which gives the relations between P,V, n and T of gases. It can be written as:

  $PV=nRT$

Here, P is pressure, V is volume, n is number of moles, R is Universal gas constant and T is temperature of the gas.

Usually gases do not follow ideal behavior under all conditions of pressure, temperature and volumes. The relation of P, V, n and T of real gases can be given by Vander Waals equation:

  $\left(\text{P + }\frac{{\text{n}}^{\text{2}}\text{a}}{{\text{V}}^{\text{2}}}\right)\left(\text{V- n b}\right)\text{ = nRT}$

Hence $\text{P = }\frac{\text{nRT}}{\text{ V-nb}}\text{ - }\frac{{\text{n}}^{\text{2}}\text{a}}{{\text{V}}^{\text{2}}}$