Clausius inequality - thermodynamics:

Whenever closed system undergoes cyclic process, cyclic integralis less than zero (that is negative) for an irreversible cyclic process and equal to zero for a reversible cyclic process. 

The efficiency of reversible H.E. operating within temperature T₁ & T₂ can be given by:

or for a reversible engine.                                                                                                  .......(i)

Now efficiency of irreversible H.E. operating within same temperature limit T1 and T2 can be given by

Combining equation (i) and (ii); we get
  d ≤ 0
The equation for irreversible cyclic process can be written as:
  + 1 = 0
I = Amount of irreversibility of cyclic process.