Chapter 3, Problem 3.42P

(a)

Interpretation Introduction

Interpretation:

The work of mechanically reversible, isothermal compression of $1\text{mol}$ of methyl chloride from $1\text{bar to 55 bar}$ at ${100}^{\circ }\text{C}$ for the given virial equation should be calculated.

Concept Introduction:

Since virial equation is given hence gas must be a non-ideal gas. For non-ideal gas work is find by following formula:

  $W=-{\displaystyle \underset{V_1}{\overset{V_2}{\int }}PdV}$

           ..(1)

And for non-ideal gases $Z=\frac{{\left(V_m\right)}_{observed}}{{\left(V_m\right)}_{ideal}}$ and hence $PV=ZnRT$ is applicable.

Where $P$ can put from given virial equation and volumes are find out by different state pressures in virial equation. The work is positive for compression process and work is done on system.

(b)

Interpretation Introduction

Interpretation:

The work of mechanically reversible, isothermal compression of $1\text{mol}$ of methyl chloride from $1\text{bar to 55 bar}$ at ${100}^{\circ }\text{C}$ for the given virial equation should be calculated.

The reason behind the different results of the same process for the different virial equations should be determined.

Concept Introduction:

Since virial equation is given hence gas must be a non-ideal gas. For non-ideal gas work is find by following formula:

  $W=-{\displaystyle \underset{P_2}{\overset{P_1}{\int }}VdP}$

           ..(1)

And for non-ideal gases $Z=\frac{{\left(V_m\right)}_{observed}}{{\left(V_m\right)}_{ideal}}$ and hence $PV=ZnRT$ is applicable.

Where $V$ can put from given virial equation. The work is positive for compression process and work is done on system.