Efficiency of a heat engine working between a given source and sink is 0.5 . Coefficient of performance of the refrigerator working between the same source and the sink will be

Options

A. 1
B. `0.5`
C. `1.5`
D. 2

Answer

To find the coefficient of performance (COP) of a refrigerator working between the same source and sink as a heat engine with a given efficiency, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Given Information**:
- The efficiency of the heat engine (η) is given as 0.5.

2. **Recall the Relationship**:
- There is a relationship between the efficiency of a heat engine (η) and the coefficient of performance (COP) of a refrigerator (β):
\[ \beta = \frac{1 - \eta}{\eta} \]

3. **Substitute the Given Efficiency**:
- Substitute the value of η into the equation:
\[ \beta = \frac{1 - 0.5}{0.5} \]

4. **Calculate the Numerator**:
- Calculate \(1 - 0.5\):
\[ 1 - 0.5 = 0.5 \]

5. **Divide by Efficiency**:
- Now, divide the result by η:
\[ \beta = \frac{0.5}{0.5} \]

6. **Final Calculation**:
- Calculate the final value:
\[ \beta = 1 \]

### Conclusion:
The coefficient of performance of the refrigerator working between the same source and sink is **1**.