# Relation between COP of heat pump & COP of refrigerator - Thermodynamics

Q.  Which among the following is correct relation between COP of heat pump and COP of refrigerator?
- Published on 19 Aug 15

a. [COP]H.P. = 1 + [COP]ref
b. [COP]H.P. = 1 – [COP]ref
c. [COP]H.P. = [COP]ref
d. none of the above

ANSWER: [COP]H.P. = 1 + [COP]ref

The COP of a device, operating in a cycle is given by,
[COP] = Desired effect / Work input
In refrigerator,

the desired effect is to maintain temperature of the body A lower than the surrounding temperature.
Therefore, A refrigerator is a device, which operates in a cycle and maintains the temperature a particular body lower than the surrounding temperature.
[COP]ref = Desired effect / Work input
[COP]ref = Q2 / W

[COP]H.P
And in heat pump,

the desired effect is to maintain temperature of the body B more than the surrounding temperature.
Therefore,
[COP]H.P. = Desired effect / Work input
[COP]H.P = Q1 / W

and the work input is given by,
W = Q1 – Q2

From the equations of [COP]ref and [COP]H.P ,
[COP]H.P. = 1 + [COP]ref

#### Discussion

• Mukul Das   -Posted on 04 Dec 21
Show that the COP of a heat pump is greater than the COP of a refrigerator by unity.
• Sahil   -Posted on 03 Dec 18
I want to learn thermodynamics
• Sahil   -Posted on 03 Dec 18
I want to learn thermodynamics
• Md shakib al hasan   -Posted on 25 Jan 18
Write your comment here...I went to learn RAC

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