Chapter 5, Problem 5.24NP

Interpretation Introduction

Interpretation: In the cycle, the volume at c and d needs to be determined to get the given result which is as follows:

  $w_{cycle}=-nR\left(T_{hot}-T_{cold}\right)\ln \frac{V_b}{V_a}$

Concept introduction:

The work done for cycle is as follows:

  $w_{cycle}=nR\left(T_{hot}-T_{cold}\right)\ln \frac{V_b}{V_a}$

Here, work done is of cycle, n is number of moles, T is temperature for hot and cold reservoir, R is Universal gas constant.

The work done can be calculated using the two equations depending on the conditions.

  $w=-nRT\ln \frac{V_f}{V_i}$

Here, n is number of moles, R is Universal gas constant, T is temperature, $V_f$ is final volume and $V_i$ is initial volume.

Also,

  $w=n{C}_{V,m}\left(T_f-T_i\right)$

Here, $C_{V,m}$ is molar heat capacity at constant volume.