The coeffcient of performance of a refrigerator working between `10^(@)C` and `20^(@)C` is

Options

A. 28.3
B. 29.3
C. 2
D. 0.5

Answer

To find the coefficient of performance (COP) of a refrigerator working between two temperatures, we can use the formula for the coefficient of performance of a refrigerator, which is given by:

\[ COP = \frac{T_L}{T_H - T_L} \]

where:
- \( T_L \) is the absolute temperature of the cold reservoir (in Kelvin),
- \( T_H \) is the absolute temperature of the hot reservoir (in Kelvin).

### Step 1: Convert temperatures from Celsius to Kelvin
We need to convert the given temperatures from degrees Celsius to Kelvin.

- For the cold reservoir (lower temperature):
\[ T_L = 10^\circ C = 10 + 273 = 283 \, K \]

- For the hot reservoir (higher temperature):
\[ T_H = 20^\circ C = 20 + 273 = 293 \, K \]

### Step 2: Calculate the temperature difference
Now, we calculate the temperature difference \( T_H - T_L \):
\[ T_H - T_L = 293 \, K - 283 \, K = 10 \, K \]

### Step 3: Substitute values into the COP formula
Now we can substitute the values into the COP formula:
\[ COP = \frac{T_L}{T_H - T_L} = \frac{283 \, K}{10 \, K} = 28.3 \]

### Final Answer
The coefficient of performance of the refrigerator is:
\[ COP = 28.3 \]