# Basic Thermodynamics of Refrigerators and Heat Pumps

The ideal body having large thermal energy capacity which either continuously supplies or absorbs the infinite amount of heat without changing its temperature is called thermal energy reservoir or heat reservoir.

If the reservoir continuously supplies heat energy to the system, it is called a source. The source is always at higher temperature. If the reservoir continuously absorbs heat energy from the system, it is called a sink.

#### Refrigerator

Refrigerator is a device which is used to remove heat from a cold system. In other words, it is used to maintain the temperature of the body lower than that of surroundings.

Example: Air conditioners, Freezers etc.

The efficiency of a refrigerator is expressed in terms of the ‘Coefficient of performance‘ (COP). It is the ratio of heat extracted to the work input.

COP of a refrigerator is given by

$(\mathrm{COP})_{r e f}=\frac{\text { Desired heat output }}{\text { Required work input }}$

$=\frac{Q_{R}}{W}=\frac{Q_{R}}{Q_{S}-Q_{L}}=\frac{T_{L}}{T_{H}-T_{L}}$

where TH and TL are high and low temperature of reservoirs respectively.

Note that the value of COP can be greater than unity. This is in contrast to the thermal efficiency, which can be greater than 1.

#### Heat Pump

Heat pump is a device which is used to supply heat to a hotter system. In other words, it is used to maintain the temperature of the body higher than the surroundings.

Example: Room heater used during winter season.

COP of a heat pump is given by

\begin{aligned} \text { (C.O.P) }_{H P} &=\frac{\text { Desired work output }}{\text { Required heat input }} \\ &=\frac{Q_{S}}{W}=\frac{Q_{S}}{Q_{S}-Q_{L}}=\frac{T_{H}}{T_{H}-T_{L}} \end{aligned}

Where TH and TL are high and low temperature of reservoirs respectively.   