Chapter 5, Problem 5.17P

Interpretation Introduction

Interpretation:

Determine the ratio of heat extracted by refrigerator (Cooling load) to heat delivered to the engine (Heating load).

Concept Introduction:

The ratio is calculated from thermal efficiency of Carnot engine and Carnot refrigerator. The thermal efficiency of Carnot engine is the ratio of the net work output to heat delivered to the engine $Q_H$ and the thermal efficiency of Carnot refrigerator is the ratio of the net work output to heat extracted by the refrigerator $Q_L$ .

  ${\eta }_{HE}=\frac{W_{cycle}}{Q_H}=1-\frac{T_{L1}}{T_{H1}}$

Here ${\eta }_{HE}$ is thermal efficiency of Carnot engine, $T_{H1}$ is the hot reservoir temperature and $T_{L1}$ is low reservoir temperature in between where Carnot engine is working.

  ${\eta }_{\text{Refri}}=\frac{W_{cycle}}{Q_L}=\frac{T_{H2}}{T_{L2}}-1$

Here ${\eta }_{\text{Refri}}$ is thermal efficiency of Carnot refrigerator, $T_{H2}$ is the hot reservoir temperature and $T_{L2}$ is low reservoir temperature in between where Carnot refrigerator is working.