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

Question

Question

Answer 1

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.