If a carnot engine works between `127^(@)C` and `527^(@)C` then its efficiency is

Options

A. 0.25
B. 0.375
C. 0.5
D. 0.75

Answer

To find the efficiency of a Carnot engine working between two temperatures, we can use the formula for the efficiency of a Carnot engine:

\[ \text{Efficiency} (\eta) = 1 - \frac{T_L}{T_S} \]

where:
- \( T_S \) is the absolute temperature of the heat source (in Kelvin),
- \( T_L \) is the absolute temperature of the heat sink (in Kelvin).

### Step-by-Step Solution:

1. **Convert the temperatures from Celsius to Kelvin**:
- The temperature of the heat source \( T_S = 527^\circ C \).
- To convert to Kelvin, use the formula:
\[ T(K) = T(°C) + 273 \]
- Therefore:
\[ T_S = 527 + 273 = 800 \, K \]

- The temperature of the heat sink \( T_L = 127^\circ C \).
- Similarly, convert to Kelvin:
\[ T_L = 127 + 273 = 400 \, K \]

2. **Substitute the values into the efficiency formula**:
- Now we can substitute \( T_S \) and \( T_L \) into the efficiency formula:
\[ \eta = 1 - \frac{T_L}{T_S} = 1 - \frac{400}{800} \]

3. **Calculate the fraction**:
- Simplifying the fraction:
\[ \frac{400}{800} = 0.5 \]

4. **Calculate the efficiency**:
- Now substituting back into the efficiency formula:
\[ \eta = 1 - 0.5 = 0.5 \]

5. **Convert the efficiency to percentage (if required)**:
- To express efficiency as a percentage:
\[ \eta \times 100 = 0.5 \times 100 = 50\% \]

### Final Answer:
The efficiency of the Carnot engine is \( 0.5 \) or \( 50\% \).

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