Question

A heat engine operates between a hot reservoir at a temperature of 500°C and a cold reservoir at a temperature of -100°C. The engine produces 1000 J of work per cycle and releases 500 J of waste heat to the cold reservoir per cycle. Determine the efficiency of the heat engine.

Solution

The efficiency of a heat engine is given by the equation:

Given: Hot reservoir temperature $\left( T_H \right) = 500°C = 500 + 273 = 773 \, \text{K}$ Cold reservoir temperature $\left( T_C \right) = -100°C = -100 + 273 = 173 \, \text{K}$ Work done per cycle $\left( W \right) = 1000 \, \text{J}$ Waste heat released per cycle $\left( Q_C \right) = 500 \, \text{J}$

First, we need to calculate the input heat energy ($Q_H$) using the equation:

Substituting the given values:

Now, we can calculate the efficiency:

Substituting the given values:

Therefore, the efficiency of the heat engine is $\frac{{2}}{{3}}$ or approximately 0.67.