Efficiency and Coefficient of Performance (COP)

Efficiency of a Heat Engine

A heat engine is a device which is used to convert heat into work. Efficiency of a heat engine is defined as the ratio of its work output and heat input.

Efficiency of a Heat Engine = Work output/ Heat input

η = (Q₁-Q₂)/Q₁ = 1 – (Q₂/Q₁)

For a reversible heat engine:

Q₂/Q₁ = T₂/T₁

For understanding above relation refer: Absolute thermodynamic scale of temperature

Hence for a reversible heat engine

η_REV = 1- (T₂/T₁)

Coefficient of Performance (COP) of Heat pump and Refrigerator

Heat pump and refrigerator are two names of the same device.

When we use this device to remove heat then it is called a refrigerator and when we use this device to obtain heat then it is called a heat pump.

Coefficient of Performance (COP) is defined as the ratio of desired effect to work input.

COP = Desired effect/ Work input

In case of heat pump this desired effect is heating and in case of refrigerator this desired effect is cooling.

1. COP of a Heat Pump

COP_HP = Q₁/Q₁-Q₂

COP for a reversible Heat Pump

COP_{HP REV} = T₁/T₁-T₂

2. COP of a Refrigerator

COP_REF = Q₂/Q₁-Q₂

COP for a reversible Refrigerator

COP_{REF REV} = T₂/T₁-T₂

By comparing COPs of Heat pump and Refrigerator we can easily observe that

COP_HP = 1 + COP_REF

Also read:

What is Carnot’s theorem?

What is first law of thermodynamics?

What is a thermodynamic process?

What is thermodynamic equilibrium?