# If the source and sink temperature for a refrigerator and a heat pump is same, then the COP of the refrigerator will be:

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If the source and sink temperature for a refrigerator and a heat pump is same, then the COP of the refrigerator will be:
1. More than the heat pump
2. Less than the heat pump
3. Equal to the heat pump
4. None of these

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Correct Answer - Option 2 : Less than the heat pump

CONCEPT:

 S.No. Refrigerator Heat pump 1. A refrigerator is a device that maintains a system or a body at a temperature lower than the surrounding temperature. A heat pump is a device that maintains a system or a body at a temperature higher than the surrounding temperature. 2. In the refrigerator, the heat is removed from the low-temperature body and is rejected to the high-temperature body. In the heat pump, the heat is removed from the low-temperature body and is added to the high-temperature body. 3. Generally, the surrounding atmosphere acts as the high-temperature body for a refrigerator. Generally, the surrounding atmosphere acts as the low-temperature body for a heat pump. 4. The coefficient of performance of a refrigerator is given as, $⇒ COP_{R}=\frac{Q_{L}}{W}=\frac{Q_{L}}{Q_{H}-Q_{L}}=\frac{T_{L}}{T_{H}-T_{L}}$ Where QL = heat removed from the system (refrigerator), QH = heat given to the surrounding (refrigerator), W = work input, TL = temperature of the system (refrigerator), and TH = temperature of the surrounding (refrigerator) The coefficient of performance of a heat pump is given as, $⇒ COP_{HP}=\frac{Q_{H}}{W}=\frac{Q_{H}}{Q_{H}-Q_{L}}=\frac{T_{H}}{T_{H}-T_{L}}$ Where QL = heat removed from the surrounding (heat pump), QH = heat given to the system (heat pump), W = work input, TH = temperature of the system (heat pump), and TL = temperature of the surrounding (heat pump)

EXPLANATION:

• We know that when a refrigerator and a heat pump are working between the same low and high temperature, the relation between the coefficient of performance of the refrigerator and the heat pump is given as,

⇒ COPHP = COPR + 1     -----(1)

• By equation 1 it is clear that when a refrigerator and a heat pump are working between the same low and high temperature, the COP of the heat pump will be more than the refrigerator. Hence, option 2 is correct.