Heat Engine Efficiency

What is Heat Engine?

A heat engine is a device that converts heat to work. It takes heat from a reservoir then does some work like moving a piston, lifting weight etc, and finally discharging some of the heat energy into the sink. Schematically it can be represented as:

Heat Engine - Engine Efficiency

Heat Engine Efficiency

Let us derive an expression for the efficiency of a heat engine. We can define heat engine efficiency as:

\(η\) =\({W}{Q_1}\)


\(W \)= Work done by the engine

\(Q_1\) = Heat taken from the source

After each cycle, the engine returns to its initial state so,

\(∆U\) =\( 0\).

So from the figure it is clear that,

\(W\) = \(Q_1- Q_2\)

Hence the heat engine efficiency is:

\(η\) =\(\frac{Q_1- Q_2}{Q_1}\)

\(η \) = \(1- \frac{Q_2}{Q_1}\)

So for \(Q_2\) = \(0\), efficiency will be 100% but in actual this is not possible because there will be some loss of energy in the system. Hence for every engine there is a limit for its efficiency. It has been found that efficiency is maximum for a reversible engine like Carnot heat engine.

Heat Pump:

So now that we have seen the above system we will now see what a refrigerator is. Before getting into the working of refrigerator we will define Heat pump. It is a device used to pump heat into the system. So it is similar to a refrigerator but works exactly opposite to it. A refrigerator takes out heat from a lower temperature \(T_2\) and releases it to a higher temperature \(T_1\). For this process to happen some work is done on the system. It can be schematically represented as follows:

Heat Engine

In this case, we define the coefficient of performance. It is defined as:

\(α\) = \(\frac{Q_2}{W}\)

Where, \(Q_2 \)= Heat taken from the system

W = Work done on the refrigerator

Similar to heat engine after a cycle the refrigerator returns to its original state hence ∆U = 0. So from the figure,

\(W\) = \(Q_1 – Q_2\)


\(α \)=\(\frac{Q_2}{Q_1 – Q_2}\)

A refrigerator will not be able to function without external work so its coefficient of performance can never be infinite.

Below video will help you visualize and understand the concept of transition of heat.

Going further we will see what second law of thermodynamics is and how Carnot heat engine is the most efficient engine. To explore more on heat engines, download BYJU’S – The Learning App.

Practise This Question

The height of a mercury barometer is 75 cm at sea level and 50 cm at the top of a hill. Ratio of density of mercury to that of air is 104. The height of the hill is