Chapter 5, Problem 5.16P

Interpretation Introduction

Interpretation:

Find the value of total work in J.mol-1 of the Carnot engine and the heat discarded to the heat reservoir at $T_{\sigma }$, the entropy change of the heat reservoir and the total entropy change $\Delta S_{\text{total}}$ .

Concept Introduction:

If a Carnot engine operating between hot and cold reservoirs at temperature $T$ and $T_{\sigma }$, Hence from the Carnot’s equation

$\eta =\frac{dW}{dQ}=1-\frac{T_{\sigma }}{T}$   .....(1)

Where $dQ$ is the heat absorbs from the hot reservoir and $dW$ is the net amount of work.

And

from first law of thermodynamics

  $\left|W\right|=\left|Q\right|-\left|Q_{\sigma }\right|$   .....(a)

And for an ideal gas and for constant heat capacity, heat transfer is given by:

  $Q=C_P\left(T_2-T_1\right)$

The entropy change in an ideal gas with constant heat capacity is defined as:

  $\Delta S=C_P\ln \frac{T_2}{T_1}$