Chapter 13, Problem 13.62P

Interpretation Introduction

Interpretation:

Limit when the volume of a gas is large relative to the number of gaseous particles that leads to van der Waals equation almost identical to the corresponding ideal-gas equation has to be shown.

Concept Introduction:

For most of the gaseous molecules, the size is not almost negligibly small and this is accounted for finite-size factor denoted by constant $b$. Thus the usual ideal gas equation is transformed as follows:

  $P\left(V-nb\right)=nRT$

Here the reduced volume is accounted for by the term $V-nb$, here $b$ is dependent upon nature of the gas.

The attractive forces that result in less actual pressure than the pressure in an ideal gas, a constant $a$ is employed and transformed ideal gas equation is as follows:

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

Here, the terms $a{n}^2\text{/}{V}^2$ account for attraction among molecules.