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The COP of an ideal refrigerator is N. If the machine is operated as a heat pump between the same temperature limits, its COP will be
- a)N – 1
- b)N
- c)N + 1
- d)2N
Correct answer is option 'C'. Can you explain this answer?
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The COP of an ideal refrigerator is N. If the machine is operated as a...
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The COP of an ideal refrigerator is N. If the machine is operated as a...
The COP of an ideal refrigerator is defined as the ratio of the heat extracted from the refrigerated space to the work done on the refrigerator. Mathematically, it is given by:
COP_refrigerator = Q_cooling / W_work
Where Q_cooling is the heat extracted from the refrigerated space and W_work is the work done on the refrigerator.
If the machine is operated as a heat pump between the same temperature limits, the COP as a heat pump is defined as the ratio of the heat delivered to the heated space to the work done on the heat pump. Mathematically, it is given by:
COP_heat pump = Q_heating / W_work
Where Q_heating is the heat delivered to the heated space and W_work is the work done on the heat pump.
Since the temperature limits are the same for both the refrigerator and the heat pump, the heat extracted from the refrigerated space in the refrigerator is equal to the heat delivered to the heated space in the heat pump. Therefore, Q_cooling = Q_heating.
As a result, the COP as a heat pump will be equal to the COP of the refrigerator, which is N.
Therefore, the answer is: a) N
COP_refrigerator = Q_cooling / W_work
Where Q_cooling is the heat extracted from the refrigerated space and W_work is the work done on the refrigerator.
If the machine is operated as a heat pump between the same temperature limits, the COP as a heat pump is defined as the ratio of the heat delivered to the heated space to the work done on the heat pump. Mathematically, it is given by:
COP_heat pump = Q_heating / W_work
Where Q_heating is the heat delivered to the heated space and W_work is the work done on the heat pump.
Since the temperature limits are the same for both the refrigerator and the heat pump, the heat extracted from the refrigerated space in the refrigerator is equal to the heat delivered to the heated space in the heat pump. Therefore, Q_cooling = Q_heating.
As a result, the COP as a heat pump will be equal to the COP of the refrigerator, which is N.
Therefore, the answer is: a) N
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The COP of an ideal refrigerator is N. If the machine is operated as a heat pump between the same temperature limits, its COP will bea)N – 1b)Nc)N + 1d)2NCorrect answer is option 'C'. Can you explain this answer?
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