Question

If a Carnot engine working between the temperatures \(300 \, \text{K}\) and \(600 \, \text{K}\) has work output of \(800 \, \text{J}\) per cycle, then the heat supplied to the engine from source per cycle is

• A. \(1800 \, \text{J}\)
• B. \(1000 \, \text{J}\)
• C. \(2000 \, \text{J}\)
• D. \(1600 \, \text{J}\)

Hint:

Use Carnot efficiency formula \( \eta = 1 - \frac{T_C}{T_H} \) and relate work to heat using \( \eta = \frac{W}{Q_H} \).

Answer 1

The Correct Option is D

Efficiency of Carnot engine: \[ \eta = 1 - \frac{T_C}{T_H} = 1 - \frac{300}{600} = 0.5 \] \[ \text{Efficiency} = \frac{W}{Q_H} \Rightarrow 0.5 = \frac{800}{Q_H} \Rightarrow Q_H = \frac{800}{0.5} = 1600 \, \text{J} \]