A Carnot engine works between 600K and 300K. The efficiency of the engine is

Options

A. (a) 50%
B. (b) 70%
C. (c) 20%
D. (d) 80%

Explanation

To find the efficiency of a Carnot engine operating between two temperatures, we can use the formula for the efficiency (η) of a Carnot engine:

\[ \eta = 1 - \frac{T_2}{T_1} \]

Where:
- \( T_1 \) is the absolute temperature of the hot reservoir (in Kelvin).
- \( T_2 \) is the absolute temperature of the cold reservoir (in Kelvin).

### Step-by-step Solution:

1. **Identify the temperatures**:
- The hot reservoir temperature \( T_1 = 600 \, K \)
- The cold reservoir temperature \( T_2 = 300 \, K \)

2. **Substitute the values into the efficiency formula**:
\[ \eta = 1 - \frac{T_2}{T_1} = 1 - \frac{300}{600} \]

3. **Calculate \( \frac{T_2}{T_1} \)**:
\[ \frac{T_2}{T_1} = \frac{300}{600} = \frac{1}{2} \]

4. **Substitute back into the efficiency formula**:
\[ \eta = 1 - \frac{1}{2} = \frac{1}{2} \]

5. **Convert to percentage**:
\[ \eta = 0.5 \times 100\% = 50\% \]

6. **Conclusion**: The efficiency of the Carnot engine is 50%.

### Final Answer:
The efficiency of the engine is **50%**.

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