The coefficient of performance of a Carnot refrigerator working between `30^(@)C & 0^(@)C` is

Options

A. `10`
B. `1`
C. `9`
D. `0`

Answer

To find the coefficient of performance (COP) of a Carnot refrigerator working between temperatures of \(30^\circ C\) and \(0^\circ C\), we will follow these steps:

### Step 1: Convert Temperatures to Kelvin
The temperatures need to be converted from Celsius to Kelvin using the formula:
\[ T(K) = T(°C) + 273.15 \]
- For the lower temperature \(T_L = 0^\circ C\):
\[ T_L = 0 + 273.15 = 273.15 \, K \]
- For the higher temperature \(T_H = 30^\circ C\):
\[ T_H = 30 + 273.15 = 303.15 \, K \]

### Step 2: Use the Formula for COP of a Carnot Refrigerator
The coefficient of performance (COP) for a Carnot refrigerator is given by the formula:
\[ COP = \frac{T_L}{T_H - T_L} \]

### Step 3: Substitute the Values into the COP Formula
Substituting the values of \(T_L\) and \(T_H\) into the formula:
\[ COP = \frac{273.15}{303.15 - 273.15} \]

### Step 4: Simplify the Expression
Calculating the denominator:
\[ 303.15 - 273.15 = 30 \]
Now substituting this back into the COP formula:
\[ COP = \frac{273.15}{30} \]

### Step 5: Calculate the COP
Now, performing the division:
\[ COP \approx 9.105 \]
We can round this to:
\[ COP \approx 9.1 \]

### Final Answer
Thus, the coefficient of performance of the Carnot refrigerator is approximately \(9.1\).

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