Question 12:What do you mean by a refrigerator? How does it function? Derive an expression for the coefficient of performance of a refrigerator.

### Refrigerator

A refrigerator is a heat engine that operates in reverse; takes heat from a cold reservoir or sink and transfers it to a hot reservoir with the help of some external work. The working substance, a gas, used in a refrigerator is called ‘refrigerant’.

### Functioning of refrigerator

The working principle of a refrigerator is that the refrigerant (working substance) undergoes a cyclic process in such a way that it takes some amount of heat from the low temperature reservoir (LTR) and transfers it to the high temperature reservoir (HTR), making use of external work (energy).

Consider the figure. An amount of heat Q2 is transferred from the cold reservoir at temperature T2to a hot reservoir at temperature T1. As it is not possible to make the flow of heat in this direction without expenditure of energy, so this external energy (work, W) is provided by the compressor of the machine. Let the quantity of heat rejected to the hot reservoir is Q1. So, the work W converts into heat energy which combines with heat Q2 and flow in the form of heat Q1 which is given out to the surrounding.

Q1 = W + Q2 —— (1)

### Coefficient of performance

It is defined as the ratio of the amount of heat energy removed from the sink to the work required to do so.

Therefore,

Dividing the nominator and denominator by Q2 and simplifying,

This equation gives the coefficient of performance for cooling.

When the refrigerator is used for heating, the coefficient of performance for heating is

In terms of temperature

No cyclic device has ever been built that extracts heat from the sink and rejects all of it to the hot reservoir without the expenditure of energy. This is Clauses statement of the Second Law of Thermodynamics.