What is heat engine? Obtain a general expression for its efficiency.

A machine that converts heat energy into mechanical energy is called heat engine. 
Heat engine consists of three essential parts: 
(i) Source: It is a hot body at high temperature having infinite heat capacity. 
(ii) Working substance: It is an ideal gas. 
(iii) Sink: It is cold body at low temperature having infinite heat capacity. 
The block diagram for the engine is as shown: 
 
The working substance is carried through a series of cyclic process, in which it absorbs some heat from source. 
A part of the heat is converted into mechanical work and rest of heat is rejected to sink. 
In a cyclic process, the working substance absorbs heat from source and rejects Q₂ heat to the sink. 
The change in internal energy of gas is zero.
Therefore, using first law of thermodynamics, the net amount of work done by an ideal engine is, 
                 
                 
The efficiency of heat engine is defined as the ratio of work obtained to the heat taken up from the source. Efficiency is denoted by .  
i.e.