A carnot's engine works between a source at a temperature of `27^(@)C` and a sink at `-123 ^(@)C`. Its efficiency is

Options

A. 0.5
B. 0.25
C. 0.75
D. 0.4

Explanation

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

### Step-by-Step Solution:

1. **Identify the temperatures**:
- The temperature of the source (T1) is given as \(27^\circ C\).
- The temperature of the sink (T2) is given as \(-123^\circ C\).

2. **Convert temperatures to Kelvin**:
- To convert Celsius to Kelvin, use the formula:
\[ T(K) = T(°C) + 273.15 \]
- For the source:
\[ T1 = 27 + 273.15 = 300.15 \, K \]
- For the sink:
\[ T2 = -123 + 273.15 = 150.15 \, K \]

3. **Use the formula for Carnot efficiency**:
- The efficiency (\(\eta\)) of a Carnot engine is given by:
\[ \eta = 1 - \frac{T2}{T1} \]

4. **Substitute the values into the efficiency formula**:
- Now plug in the values of T1 and T2:
\[ \eta = 1 - \frac{150.15}{300.15} \]

5. **Calculate the fraction**:
- Calculate \(\frac{150.15}{300.15}\):
\[ \frac{150.15}{300.15} \approx 0.500 \]

6. **Calculate the efficiency**:
- Now substitute this back into the efficiency formula:
\[ \eta = 1 - 0.500 = 0.500 \]

7. **Final Result**:
- The efficiency of the Carnot engine is:
\[ \eta = 0.5 \text{ or } 50\% \]

### Summary:
The efficiency of the Carnot engine working between a source at \(27^\circ C\) and a sink at \(-123^\circ C\) is \(0.5\) or \(50\%\).

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