Efficiency of a heat engine:
The fraction of the heat absorbed by an engine which can be converted into work is known as efficiency of the heat engine.
Mathematically,
Efficiency, η = w / q2 = (T2 – T1) / T2 ……………. (1)
As (T2 – T1) / T2 is infinitesimally small i.e. less than 1, the efficiency of a heat engine is always less than 1.
No heat engine can have efficiency equal to one.
From above equation we can conclude that greater the difference between the temperature T2 – and T1 i.e. the difference between the temperature of the source and the sink, greater will be the efficiency.
The work delivered from the system during the cycle is represented by the enclosed area of the cycle. According to the first law of thermodynamics, the work obtained is equal to the difference between the heat supplied by the source (q2) and the heat rejected to the sink (q1 i.e. the net work done by the system.
Hence,
w = q2 – q1
Combining this with equation (1), we will get
(q2 – q1)/ q2 = (T2 – T1) /T2
Thus, efficiency,
η = (q2 – q1)/q2 = (T2 – T1)/T2
