Question

The heat input to a heat engine is 40 kJ while the heat output from the heat engine is 20 kJ. Determine the efficiency of the heat engine.
1. 0.3
2. 0.45
3. 0.35
4. 0.5

Answer 1

Correct Answer - Option 4 : 0.5

Concept:

The efficiency of the heat engine (η):

η = \(\rm \dfrac{net\: work\: done}{heat\: absorbed} = \dfrac{W}{Q_1} = \dfrac{Q_1 - Q_2}{Q_1} = 1 - \dfrac{Q_2}{Q_1}\)  

Calculation:

Given:

Q₁ = 40 kJ, Q₂ = 20 kJ

η = \(\rm \dfrac{net\: work\: done}{heat\: absorbed} = \dfrac{W}{Q_1} = \dfrac{Q_1 - Q_2}{Q_1} = 1 - \dfrac{Q_2}{Q_1}\)

η = \(1 - \dfrac{Q_2}{Q_1}\) = \(1 - \dfrac{20}{40}\)

η = 0.5

∴ The efficiency of the heat engine is 50%