Question

In a Carnot engine, if the work done during isothermal expansion is 25% more than the work done during isothermal compression, then the efficiency of the engine is:

• A. \( 10% \)
• B. \( 15% \)
• C. \( 20% \)
• D. \( 25% \)

Hint:

For Carnot efficiency calculations, use: \[ \eta = 1 - \frac{T_C}{T_H} = \frac{W_H - W_C}{W_H} \] to express efficiency in terms of work done.

Answer 1

The Correct Option is C

Step 1: Efficiency of a Carnot Engine The efficiency of a Carnot engine is given by: \[ \eta = 1 - \frac{T_C}{T_H} \] where: - \( T_H \) is the temperature of the hot reservoir, - \( T_C \) is the temperature of the cold reservoir. Step 2: Relating Work to Heat Input In isothermal expansion, the heat absorbed \( Q_H \) is proportional to the work done \( W_H \): \[ Q_H = W_H \] Similarly, in isothermal compression: \[ Q_C = W_C \] Given: \[ W_H = 1.25 W_C \] Using efficiency definition: \[ \eta = \frac{W_H - W_C}{W_H} \] \[ \eta = \frac{1.25 W_C - W_C}{1.25 W_C} \] \[ \eta = \frac{0.25 W_C}{1.25 W_C} = \frac{0.25}{1.25} = 0.2 \] \[ \eta = 20% \] Conclusion Thus, the correct answer is: \[ 20% \]