A Carnot engine works between temperature `0^(@)C` and `100^(@)C`. Calculate its efficiency.

Answer

To calculate the efficiency of a Carnot engine working between two temperatures, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the temperatures**: The Carnot engine operates between two temperatures: the lower temperature \( T_1 \) and the higher temperature \( T_2 \). In this case, we have:
- \( T_1 = 0^\circ C \)
- \( T_2 = 100^\circ C \)

2. **Convert temperatures to Kelvin**: The efficiency formula requires temperatures to be in Kelvin. We convert Celsius to Kelvin using the formula:
\[ T(K) = T(°C) + 273.15 \]
- For \( T_1 \):
\[ T_1 = 0 + 273.15 = 273.15 \, K \]
- For \( T_2 \):
\[ T_2 = 100 + 273.15 = 373.15 \, K \]

3. **Use the efficiency formula**: The efficiency \( \eta \) of a Carnot engine is given by the formula:
\[ \eta = 1 - \frac{T_1}{T_2} \]

4. **Substitute the values**: Now, we can substitute the values of \( T_1 \) and \( T_2 \) into the efficiency formula:
\[ \eta = 1 - \frac{273.15}{373.15} \]

5. **Calculate the fraction**: First, calculate the fraction:
\[ \frac{273.15}{373.15} \approx 0.731 \]

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

7. **Final result**: Therefore, the efficiency of the Carnot engine is approximately:
\[ \eta \approx 0.269 \text{ or } 26.9\% \]