The values of coefficient of performance `(alpha)` and efficiency `(eta)` of refrigerator are

Options

A. `alpha lt 1, eta=2`
B. `alpha gt 1, eta lt 1`
C. `alpha gt 1, eta =1.5`
D. `alpha lt 1, eta gt 1`

Answer

To solve the problem regarding the values of the coefficient of performance (α) and efficiency (η) of a refrigerator, we will analyze the definitions and properties of these terms.

### Step-by-Step Solution:

1. **Understanding Coefficient of Performance (α)**:
- The coefficient of performance (α) of a refrigerator is defined as the ratio of the heat removed from the cold reservoir (Q2) to the work input (W) required to remove that heat.
- Mathematically, it is expressed as:
\[ \alpha = \frac{Q_2}{W} \]
- Since work (W) is the difference between the heat rejected to the hot reservoir (Q1) and the heat absorbed from the cold reservoir (Q2), we can express it as:
\[ W = Q_1 - Q_2 \]
- Thus, the coefficient of performance can also be expressed as:
\[ \alpha = \frac{Q_2}{Q_1 - Q_2} \]

2. **Analyzing the Value of α**:
- Since Q2 is the heat extracted from the cold reservoir and W (the work done) is always positive, it follows that:
\[ \alpha > 1 \]
- This indicates that the coefficient of performance of a refrigerator is always greater than 1.

3. **Understanding Efficiency (η)**:
- The efficiency (η) of a refrigerator is defined differently than that of a heat engine. For refrigerators, efficiency is often considered in terms of the work done relative to the heat rejected.
- The efficiency can be expressed as:
\[ \eta = \frac{W}{Q_1} \]
- Since W is always less than Q1 (because some heat is absorbed from the cold reservoir), the efficiency will be less than 1.

4. **Conclusion**:
- From the analysis:
- The coefficient of performance (α) of a refrigerator is greater than 1.
- The efficiency (η) of a refrigerator is less than 1.

### Final Answer:
- Coefficient of Performance (α) > 1
- Efficiency (η) < 1