Refrigerator Or Heat Pump - Practice Questions & MCQ

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

It consists of three parts
1. Source: At higher temperature T₁
2. Working substance: It is called refrigerant. I.e liquid ammonia and freon works as a working substance.
3. Sink: At lower temperature T₂.

• Working of refrigerator

As shown in the above figure, The working substance takes heat Q₂ from a sink (contents of refrigerator) at lower temperature T₂, 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).

• Use of refrigerator-

  The cold body is cooled more and more with the help of a refrigerator. Because the refrigerator transfers heat from a cold to a hot body at the expense of mechanical energy supplied to it by an external agent.

• - Coefficient of performance $\left(\beta^\beta\right.$ -

  The coefficient of performance is defined as the ratio of the heat extracted from the cold body to the work needed to transfer it to the hot body.

  $
  \beta=\frac{\text { Heat extracted }}{\text { work done }}=\frac{Q_2}{W}=\frac{Q_2}{Q_1-Q_2}
  $

  
  A perfect refrigerator is one which transfers heat from cold to a hot body without doing work.
  i.e. $W=0$ so that $Q_1=Q_2$ and hence $\beta=\infty$
  - Carnot refrigerator-

  For Carnot refrigerator $\frac{Q_1}{Q_2}=\frac{T_1}{T_2}$

  $
  \therefore \frac{Q_1-Q_2}{Q_2}=\frac{T_1-T_2}{T_2} \text { or } \frac{Q_2}{Q_1-Q_2}=\frac{T_2}{T_1-T_2}
  $

  
  So using

  $
  \beta=\frac{Q_2}{Q_1-Q_2}
  $

  we get

  $
  \beta=\frac{T_2}{T_1-T_2}
  $

  where $\mathrm{T}_1=$ temperature of surrounding, $\mathrm{T}_2=$ temperature of cold body and $T_1>T_2$
  when $\mathrm{T}_2=0$ then $\beta=0$
  I.e if the cold body is at the temperature equal to absolute zero, then the coefficient of performance will be zero
  - The relation between $\beta$ and $\eta$ of the refrigerator

  $
  \beta=\frac{1-\eta}{\eta}
  $