Question

For which of the following combinations of working temperatures, the efficiency of Carnot's engine is maximum?

• A. 40 K and 20 K
• B. 50 K and 30 K
• C. 70 K and 50 K
• D. 90 K and 60 K

Hint:

- Efficiency increases when $\frac{T_C}{T_H}$ is minimum - Larger temperature difference $\Rightarrow$ higher efficiency

Answer 1

The Correct Option is A

Concept:
Efficiency of Carnot engine: \[ \eta = 1 - \frac{T_C}{T_H} \]

Step 1: Calculate efficiency for each option.
(A) \[ \eta = 1 - \frac{20}{40} = 1 - 0.5 = 0.5 \] (B) \[ \eta = 1 - \frac{30}{50} = 1 - 0.6 = 0.4 \] (C) \[ \eta = 1 - \frac{50}{70} \approx 1 - 0.714 = 0.286 \] (D) \[ \eta = 1 - \frac{60}{90} = 1 - 0.667 = 0.333 \]

Step 2: Compare values.
Maximum efficiency is $0.5$.