Question

A Carnot engine is working between 400K and 500K. If the output work is 1 kJ, what is the heat absorbed?

• A. 2 kJ
• B. 3 kJ
• C. 4 kJ
• D. 5 kJ

Hint:

For a Carnot engine, use the efficiency formula \( \eta = 1 - \frac{T_C}{T_H} \) to find the efficiency, and then use \( \eta = \frac{W}{Q_H} \) to calculate the heat absorbed.

Answer 1

The Correct Option is B

Step 1: Use the Carnot efficiency formula.
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 (500K),
- \( T_C \) is the temperature of the cold reservoir (400K).
Substitute the given values: \[ \eta = 1 - \frac{400}{500} = 1 - 0.8 = 0.2 \]
Step 2: Relate the output work and heat absorbed.
The output work \( W \) is related to the heat absorbed \( Q_H \) by the efficiency equation: \[ \eta = \frac{W}{Q_H} \] We are given that \( W = 1 \, \text{kJ} \), so: \[ 0.2 = \frac{1}{Q_H} \] Solving for \( Q_H \): \[ Q_H = \frac{1}{0.2} = 5 \, \text{kJ} \]
Step 3: Conclusion.
Thus, the heat absorbed is 5 kJ.
Final Answer: 5 kJ.