Question

The work done by a Carnot engine operating between $ 300\, \text{K} $ and $ 400\, \text{K} $ is $ 400\, \text{J} $. The energy exhausted by the engine is:

• A. 800 J
• B. 1200 J
• C. 400 J
• D. 1600 J

Hint:

Use \( \eta = 1 - \frac{T_C}{T_H} = \frac{W}{Q_H} \) and find \( Q_C = Q_H - W \) for energy rejected.

Answer 1

The Correct Option is B

Efficiency of a Carnot engine: \[ \eta = 1 - \frac{T_C}{T_H} = 1 - \frac{300}{400} = \frac{1}{4} \] \[ \text{Efficiency} = \frac{W}{Q_H} \Rightarrow \frac{1}{4} = \frac{400}{Q_H} \Rightarrow Q_H = 1600\, \text{J} \] Energy exhausted (heat rejected): \[ Q_C = Q_H - W = 1600 - 400 = 1200\, \text{J} \]