Refrigerator or Heat Pump

A refrigerator or heat pump is basically a heat engine run in reverse direction.

It essentially consists of three parts

Source : At higher temperature T₁.

Working substance : It is called refrigerant liquid ammonia and freon works as a working substance.

Sink : At lower temperature T₂.

The working substance takes heat Q₂ from a sink (contents of refrigerator) at lower temperature, has a net amount of work done W on it by an external agent (usually compressor of refrigerator) and gives out a larger amount of heat Q₁ to a hot body at temperature T₁ (usually atmosphere). Thus, it transfers heat from a cold to a hot body at the expense of mechanical energy supplied to it by an external agent. The cold body is thus cooled more and more.

The performance of a refrigerator is expressed by means of “coefficient of performance” b which is defined as the ratio of the heat extracted from the cold body to the work needed to transfer it to the hot body.

i.e.    

Therefore 

A perfect refrigerator is one which transfers heat from cold to hot body without doing work

i.e. W = 0 so that Q₁ = Q₂ and hence β=∞

(1) Carnot refrigerator

For Carnot refrigerator Therefore or

So coefficient of performance

where T₁ = temperature of surrounding, T₂ = temperature of cold body

It is clear that b = 0 when T₂ = 0

i.e. the coefficient of performance will be zero if the cold body is at the temperature equal to absolute zero.

(2) Relation between coefficient of performance and efficiency of refrigerator

We know or ….. (i)

But the efficiency or ......(ii)

From (i) and (ii) we get