Chapter 3, Problem 3.78P

(a)

Interpretation Introduction

Interpretation:

The second virial coefficient B is zero at the Boyle temperature should be proved.

Concept Introduction:

By differentiating the virial equation with respect to pressure P and applying the limit pressure to zero virial coefficient B can become zero.

The virial equation has the following form:

  $Z=1+B\text{'}P+C\text{'}{P}^2+D\text{'}{P}^3+\mathrm{....}$

The differentiation form of viral equation is as follows:

  ${\left(\frac{\partial Z}{\partial P}\right)}_r=B\text{'}+2C\text{'}P+3D\text{'}{P}^2+\mathrm{....}$

Here, Z is compressibility factor, P is pressure and B’, C’ and D’ are constants.

(b)

Interpretation Introduction

Interpretation:

The reduced Boyle temperature for simple fluids should be estimated.

Concept Introduction:

Use the generalised correlation for $B$ and Eq (3.58)-(3.62), to estimate the reduced Boyles temperature for simple fluids.