Give the basic features of heat engine based on cyclic process and obtain the formula of its efficiency

Explanation

The basic features of a heat engine are those that the engine takes heat `Q_1` from a hot reservoir at temperature `T_1`, releases heat `Q_2`, to a cold reservoir at temperature `T_2`, and delivers work W to the surroundings. The basic features of this engine are represented in figure.

Hence, the net amount of heat absorbed by the working substance is Q=W
`therefore W=Q_1 ~ Q_2`
The ratio of net work done per cycle by the engine to the total amount of heat absorbed percycle by the working substance from the source is known as efficiency `eta` of engine.
`therefore` Efficiency = `"Net work done / cycle"/"Heat absorbed / cycle"`
`therefore eta =W/Q_1 =(Q_1-Q_2)/Q_1`
`therefore eta=1-Q_2/Q_1`
Above equation suggests that efficiency of a engine is `eta` = 1 if `Q_2 = 0`, means efficiency of the engine becomes 100%.
The first law of thermodynamics does not rule out such an engine but an ideal engine with `eta` = 1 (100 % efficiency) is never possible even if we can eliminate various kinds of losses associated with actual heat engine.
The second law of thermodynamics gives fundamental limitation to the efficiency of a heat engine.