Question

What is refrigeration ? Explain the working of refrigerator and find an expression for its coefficient of performance.​

Answer 1

★ Concept

Let's proceed with the concept of refrigeration

The phenomenon by which heat is removed from bodies colder than their surroundings is called refrigeration and the device which works on this principle is called a refrigerator.

The working of Refrigerator

In refrigerator, heat is absorbed at low temperature and rejected at higher temperature with the help of external mechanical work. Thus, refrigerator is a heat engine working backward and hence it is also called heat pump. The working substance used in a refrigerator is called refrigerant. The commonly used refrigerants are ammonia and freon.

Derivation of the expression for its coefficient of performance.

Let heat Q₂ from a cold body at temperature T₂ is transferred to a hot body at temperature T₁ with the help of external mechanical work W

Let Q₁ be the heat rejected to the hot body

According to the law of conservation of energy,

☞ Q₁ = Q₂ + W

Instead of efficiency, we use the quantity of performance (E) in the refrigerator, which is defined as

☞ E = Desired output/Required Input

E = Heat extracted from the cold body / Work done on the refrigerant

In short,

$\sf \red{E = \dfrac{Q_2}{W}}$

Using eqn. ⑴, we have

$\sf {E = \dfrac{Q_2}{Q_1 -Q_2 }}$

Since, Q₂/Q₁ = T₂/T₁

The above equation can be written as

$\sf {E = \dfrac{T_2}{ T_1-T_2}}$

Conclusion

The coefficient of performance is large for small temperature difference (T₁ - T₂) between hot body and cold body. When temperature of two bodies becomes equal i.e T₂ = T₁ , then coefficient of performance becomes infinite.

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More to know

1. To have large coefficient of performance, the object to be cooled must have temperature close to the temperature of the surroundings (i.e the room temperature) before placing it in the refrigerator.
2. The room can be warmed by keeping the door of a refrigerator open.

☞ Reason for part (2)

A refrigerator is a heat pump. It extracts heat from low temperature reservoir and transfer it to a high temperature reservoir. Thus, it exhausts more heat into the room than it extracts from it. Hence, the room will become warm.