**Heat Engine**

Heat engine is a machine which converts ** thermal energy into work**. The discovery of heat engine played a crucial role in many technological developments that include, among others, automobile engines and steam turbines to run generators to produce electricity. A heat engine typically uses energy provided in the form of heat to do work and then exhausts the heat which cannot be used to do work. A schematic diagram of a heat engine is shown in Figure.

In a heat engine heat energy q_{2} is absorbed from a hot reservoir at temperature T_{2}. The engine does work w (w is negative as work is done by the engine or the system) and discards the remaining heat q_{1} (q_{1} is negative as heat is given out) to the cold reservoir at temperature T_{1}. In thermodynamic terms, the hot reservoir is called a ‘Source’ and the cold reservoir is called a ‘Sink’.

**Figure: schematic diatom of a heat engine**

To repeat the process, the engine must be returned to the initial temperature T_{2} and the steps followed in sequence and we say that it completes a ‘cycle’. However, in order to evaluate the usefulness of a heat engine a quantity, known as ‘Efficiency (E) of the engine, is defined. The efficiency is defined as,

*“The ratio of work done to the quantity of energy supplied”.*

Mathematically,

E = (Energy out/Energy in) = (Work done/ Energy Supplied)

= (Heat input – Heat discharged) / Heat Supplied

so, E = (q_{T2} – q_{T1}) / q_{T2} … … … (1)

From detailed analysis of the reversible Carnot cycle, Lord Kelvin later concluded that the quantities of heat for a reversible Carnot engine are proportional to absolute temperature. Thus, equation (1) can be written as,

E = (T_{2} – T_{1}) / T_{2} … … … (2)

It may, therefore, be concluded that the efficiency of a reversible heat engine is dependent on the temperatures of the source and the sink. High efficiency is obtained when T_{2} >> T_{1} and 100% efficiency is predicted when T_{1} = 0. But in practice 100% efficiency can never be obtained, since there is always some unavailable energy.

Example: What is the efficiency of a reversible cyclic engine operating between temperatures 20°C and 500^{0}C?

**Solution**: T_{2} = 273 + 500= 773

and T_{1} = 273 + 20 = 293

Using equation (2) we get, E = (T_{2} – T_{1}) / T_{2}

= (773 – 293) / 773 = 0.620