Which of the following can be coefficient of perfomace refrigerator?

Options

A. 1
B. 0.5
C. 9
D. All of these

Answer

To determine which of the given options can be the coefficient of performance (COP) for a refrigerator, we can follow these steps:

### Step 1: Understand the Definition of Coefficient of Performance (COP)
The coefficient of performance for a refrigerator is defined as the ratio of the heat extracted from the cold reservoir (Q) to the work input (W) required to extract that heat. Mathematically, it is expressed as:

\[ COP = \frac{Q}{W} \]

### Step 2: Analyze the Options
We are given four options for the coefficient of performance:
1. 1
2. 0.5
3. 9
4. All of these

### Step 3: Evaluate Each Option
- **Option 1: COP = 1**
- This means that the heat extracted is equal to the work done. This is theoretically possible, but not efficient for a refrigerator.

- **Option 2: COP = 0.5**
- This implies that the work done is greater than the heat extracted, which is not feasible for a refrigerator. A COP less than 1 indicates that the refrigerator is not performing effectively.

- **Option 3: COP = 9**
- This indicates that the heat extracted is nine times the work done. This is a highly efficient refrigerator and is possible in practical scenarios.

- **Option 4: All of these**
- This option suggests that all previous values can be coefficients of performance for a refrigerator. However, since COP must be greater than 1 for practical refrigerators, this option is not valid.

### Step 4: Conclusion
From the analysis, we find that:
- COP = 1 is possible but not efficient.
- COP = 0.5 is not feasible for a refrigerator.
- COP = 9 is a valid and efficient option.

Thus, the only valid coefficient of performance for a refrigerator from the options given is **9**.

### Final Answer
The coefficient of performance for a refrigerator can be **9**.

---