Question:
The coefficient of performance of a refrigerator is 5. If it is placed in a room at a temperature of 39°C, the temperature inside the refrigerator is:
The coefficient of performance of a refrigerator is 5. If it is placed in a room at a temperature of 39°C, the temperature inside the refrigerator is:
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The coefficient of performance for refrigerators and heat pumps can be used to determine the temperature inside the appliance, given the room temperature.
Updated On: May 5, 2026
- 13°C
- 32.5°C
- -13°C
- -32.5°C
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The Correct Option is C
Solution and Explanation
- For a refrigerator, the coefficient of performance is defined as: \[ COP = \frac{Q_c}{W} \] and for an ideal refrigerator: \[ COP = \frac{T_2}{T_1 - T_2} \]
- Given: \[ COP = 5,\quad T_1 = 312\,K \]
- Substitute in the formula: \[ 5 = \frac{T_2}{312 - T_2} \]
- Multiply both sides: \[ 5(312 - T_2) = T_2 \]
- Expanding: \[ 1560 - 5T_2 = T_2 \]
- Rearranging: \[ 1560 = 6T_2 \]
- So: \[ T_2 = 260\,K \]
- Converting to Celsius: \[ T_2 = 260 - 273 = -13^\circ C \]
- Hence, the temperature inside the refrigerator is: \[ -13^\circ C \]
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