A Carnot heat engine has an efficiency of `10%`. If the same engine is worked backward to obtain a refrigerator, then find its coefficient of performance.

Options

A. 3
B. 5
C. 7
D. 9

Explanation

To solve the problem, we need to find the coefficient of performance (COP) of a refrigerator that is based on a Carnot heat engine with an efficiency of 10%.

### Step-by-Step Solution:

1. **Understanding Efficiency and COP**:
- The efficiency (η) of a Carnot engine is given as 10%, which can be expressed as a decimal:
\[ \eta = \frac{10}{100} = 0.1 \]

2. **Using the Relation Between Efficiency and COP**:
- The coefficient of performance (β) for a refrigerator can be calculated using the formula:
\[ \beta = \frac{1 - \eta}{\eta} \]

3. **Substituting the Efficiency into the Formula**:
- Now, substituting the value of η into the COP formula:
\[ \beta = \frac{1 - 0.1}{0.1} \]
- Simplifying the numerator:
\[ \beta = \frac{0.9}{0.1} \]

4. **Calculating the Coefficient of Performance**:
- Performing the division:
\[ \beta = 9 \]

5. **Conclusion**:
- Therefore, the coefficient of performance of the refrigerator is:
\[ \beta = 9 \]

### Final Answer:
The coefficient of performance of the refrigerator is **9**.