For a carnot engine, the source is at 500 K and the sink at 300 K. What is efficiency of this engine

Options

A. 0.2
B. 0.4
C. 0.6
D. 0.3

Explanation

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

\[ \eta = \frac{T_H - T_L}{T_H} \]

Where:
- \( T_H \) is the temperature of the hot reservoir (source).
- \( T_L \) is the temperature of the cold reservoir (sink).

### Step-by-Step Solution:

1. **Identify the temperatures:**
- The temperature of the hot source \( T_H = 500 \, K \)
- The temperature of the cold sink \( T_L = 300 \, K \)

2. **Substitute the values into the efficiency formula:**
\[ \eta = \frac{T_H - T_L}{T_H} = \frac{500 \, K - 300 \, K}{500 \, K} \]

3. **Calculate the difference in temperatures:**
\[ T_H - T_L = 500 \, K - 300 \, K = 200 \, K \]

4. **Substitute the difference back into the efficiency formula:**
\[ \eta = \frac{200 \, K}{500 \, K} \]

5. **Perform the division:**
\[ \eta = 0.4 \]

6. **Convert to percentage (if needed):**
\[ \eta = 0.4 \times 100 = 40\% \]

### Final Answer:
The efficiency of the Carnot engine is \( 0.4 \) or \( 40\% \).