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**Mumbai university > Mechanical Engineering > Sem 3 > Thermodynamics**

**Marks: 5M**

**Year:** May 2016

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Define COP for refrigerator and heat pump. Derive relation between them.

written 7.2 years ago by | • modified 7.2 years ago |

**Mumbai university > Mechanical Engineering > Sem 3 > Thermodynamics**

**Marks: 5M**

**Year:** May 2016

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written 7.2 years ago by |

The efficiencyof a refrigerator is expressed in terms of the coefficient of performance (COP), denoted by COPR. The objective of a refrigerator is to remove heat (QL) from the refrigerated space. To accomplish this objective, it requires a work input of Wnet,in. Then the COP of a refrigerator can be expressed as

$COP_R=\frac{(desired output)}{(required input)}=\frac{Q_L}{W_(net,in)} ………(1)$

This relation can also be expressed in rate form by replacing QL by QL andWnet,in by Wnet,in.

The conservation of energy principle for a cyclic device requires that

$W_(net,in)=Q_H-Q_L (KJ)………(2)$

Then the COP relation becomes

$COP_R=\frac{Q_L}{(Q_H-Q_L )}=\frac{1}{Q_H/Q_L-1}………(3)$

Notice that the value of COPR can be greater than unity.

Another device that transfers heat from a low-temperature medium to a high temperature one is the heat pump. Refrigerators and heat pumps operate on the same cycle but differ in their objectives. The objective of a heat pump, however, is to maintain a heated space at a high temperature. This is accomplished by absorbing heat from a low temperature source, such as well water or cold outside air in winter, and supplying this heat to the high-temperature medium such as a house.

The measure of performance of a heat pump is also expressed in terms of the coefficient of performanceCOP_HP, defined as

$COP_HP=\frac{(Desired output)}{(Required input)}=\frac{Q_H}{W_(net,in)} ……..(4)$

This can also be expressed as,

$COP_HP=\frac{Q_H}{(Q_H-Q_L )}=\frac{1}{(1-Q_L⁄Q_H )}………(5)$

Comparing equation 3 and 5 reveals that,

$COP_HP=COP_R+1$

for fixed values of QLand QH. This relation implies that the coefficient of performance of a heat pump is always greater than unity since COPR is a positive quantity.

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