# Difference between Heat Engine Heat Pump and Refrigerator

## Refrigerator

In this article we are going to have detailed study of difference between Heat Engine Heat Pump and Refrigerator.

#### Heat Engine:

Heat engine is a device which converts heat energy into mechanical work. In heat engine how much work is extracted from a given amount of heat is an important quantity.

Q1=W+Q2    ⇒     W=Q1-Q2

Efficiency $\displaystyle (\eta )=\frac{W}{{{Q}_{1}}}=\frac{{{Q}_{1}}-{{Q}_{2}}}{{{Q}_{1}}}$

or              $\displaystyle \eta =\frac{{{T}_{H}}-{{T}_{L}}}{{{T}_{H}}}=1-\frac{{{T}_{L}}}{{{T}_{H}}}$

For Heat Engine,  W < Q1  ⇒  η < 1

#### Heat PUmp:

Heat pump is a device that transfers heat from a colder area to a hotter area by using mechanical/electrical energy, as in a refrigerator. Heat pumps may be used either to heat or cool. In heat pump how much heat is rejected at higher temperature is an important quantity.

Example: Room Heater

Q1=W+Q2    ⇒     W=Q1-Q2

Efficiency(Coefficient of Performance) $\displaystyle (\eta )=\frac{{{Q}_{1}}}{W}=\frac{{{Q}_{1}}}{{{Q}_{1}}-{{Q}_{2}}}$

or     $\displaystyle \eta =\frac{{{T}_{H}}}{{{T}_{H}}-{{T}_{L}}}$

For Heat Pump,  Q1 > W ⇒  η > 1

#### Refrigerator:

refrigerator is a device which is designed to remove heat from a space that is at lower temperature than its surroundings. In refrigerator heat extracted from lower temperature is an important quantity.

Q1=W+Q2    ⇒     W=Q1-Q2

Efficiency(Coefficient of Performance) $\displaystyle (\beta )=\frac{{{Q}_{2}}}{W}=\frac{{{Q}_{2}}}{{{Q}_{1}}-{{Q}_{2}}}$

or  $\displaystyle \beta =\frac{{{T}_{L}}}{{{T}_{H}}-{{T}_{L}}}$

Important: For refrigerator  TH > TL

⇒ β >1 , if T≤  2TL

for TH>2TL , let TL=5°C=278K, So 2TL = 556K=283°C  , which is not possible.

Generally TH and TL difference is less than TL, so β is always greater than 1 for refrigerator.]

[Example:-  let TL=5°C=278K and TH=25°C=300K , So TH-TL=300-278=22K<TL(278K) ]