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 (COP) for a refrigerator is defined as the ratio of the heat extracted from the cold reservoir (Q_c) to the work input (W) required to extract that heat. Mathematically, it is expressed as:
\[ \text{COP} = \frac{Q_c}{W} \]

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

### Step 3: Determine the Range of COP
For a refrigerator, the COP can theoretically take any positive value. However, it is important to note that the efficiency of a refrigerator is always less than 1. The relationship between efficiency (η) and COP can be expressed as:
\[ \text{COP} = \frac{1}{1 - \eta} \]
Since η is always less than 1, this means that COP can be greater than 1.

### Step 4: Evaluate Each Option
- **Option 1 (1)**: This is a possible value for COP, as it is greater than 0.
- **Option 2 (0.5)**: This value is less than 1, which is not possible for COP, as it must be greater than or equal to 1.
- **Option 3 (9)**: This is a possible value for COP, as it is much greater than 1.
- **Option 4 (All of these)**: This cannot be true since option 2 (0.5) is not a valid COP.

### Step 5: Conclusion
Based on the analysis, the only valid value for the coefficient of performance of a refrigerator from the given options is **9** (Option 3).

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

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