Efficiency of carnot engine working between ice point and steam point is

Options

A. 0.249
B. 0.257
C. 0.268
D. 0.288

Explanation

To find the efficiency of a Carnot engine working between the ice point and the steam point, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the temperatures**:
- The ice point (0°C) and steam point (100°C) are given.
- Convert these temperatures from Celsius to Kelvin because the Carnot efficiency formula requires temperatures in Kelvin.

2. **Convert temperatures to Kelvin**:
- Ice point:
\[ T_1 = 0°C + 273 = 273 \, K \]
- Steam point:
\[ T_2 = 100°C + 273 = 373 \, K \]

3. **Use the Carnot efficiency formula**:
- The efficiency (\( \eta \)) of a Carnot engine is given by:
\[ \eta = 1 - \frac{T_2}{T_1} \]
- Here, \( T_1 \) is the temperature of the hot reservoir (steam point) and \( T_2 \) is the temperature of the cold reservoir (ice point).

4. **Substitute the values into the formula**:
- Substitute \( T_1 = 373 \, K \) and \( T_2 = 273 \, K \):
\[ \eta = 1 - \frac{273}{373} \]

5. **Calculate the fraction**:
- Calculate \( \frac{273}{373} \):
\[ \frac{273}{373} \approx 0.731 \]

6. **Calculate the efficiency**:
- Now, substitute this back into the efficiency formula:
\[ \eta = 1 - 0.731 = 0.269 \]

7. **Final result**:
- Therefore, the efficiency of the Carnot engine working between the ice point and steam point is approximately:
\[ \eta \approx 0.268 \]

### Conclusion:
The efficiency of the Carnot engine working between the ice point and steam point is approximately **0.268**.

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