# Refrigerator (Or) Heat Pump

## Refrigerator (Or) Heat Pump

A refrigerator of heat pump is basically a heat engine run in reverse direction. It essentially consists of three parts:

1) Source: At higher temperature $${{T}_{1}}$$.

2) Working Substance: It is called refrigerant liquid ammonia and freon works as working substance.

3) Sink: At lower temperature $${{T}_{2}}$$.

The working substance takes heat $${{Q}_{2}}$$ from a sink at lower temperature, as a net amount of work done W on it by an external agent and gives out a larger amount of heat $${{Q}_{1}}$$ to a hot body at temperature $${{T}_{1}}$$. 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 $$\beta$$ which is defined as the ratio of the extracted from the cold body to the work needed to transfer it to the hot body.

$$\beta =\frac{Heat\,\,Extracted}{Work\,\,Done}=\frac{{{Q}_{2}}}{W}=\frac{{{Q}_{2}}}{{{Q}_{1}}-{{Q}_{2}}}$$

A perfect refrigerator is one which transfer heat from cold to hot body without doing work i.e. W = 0, so that $${{Q}_{1}}={{Q}_{2}}$$ and hence $$\beta =\infty$$.

Carnot Refrigerator:

For Carnot refrigerator, $$\frac{{{Q}_{1}}}{{{Q}_{2}}}=\frac{{{T}_{1}}}{{{T}_{2}}}$$ $$\Rightarrow \frac{{{Q}_{1}}-{{Q}_{2}}}{{{Q}_{2}}}=\frac{{{T}_{1}}-{{T}_{2}}}{{{T}_{2}}}$$ (or) $$\Rightarrow \frac{{{Q}_{2}}}{{{Q}_{1}}-{{Q}_{2}}}=\frac{{{T}_{2}}}{{{T}_{1}}-{{T}_{2}}}$$ . So, coefficient of performance, $$\beta =\frac{{{T}_{2}}}{{{T}_{1}}-{{T}_{2}}}$$. Where, $${{T}_{1}}=$$ Temperature of surrounding, $${{T}_{2}}=$$ Temperature of cold body. It is clear that $$\beta =0$$ when $${{T}_{2}}=0$$. i.e. the coefficient of performance will be zero if the cold body is at the temperature equal to absolute zero.