Clausius inequality and the change of entropy for nonequilibrium processes

5 Clausius inequality and the change of entropy for nonequilibrium processes 

Remember that the thermal efficiency of the thermal Carnot heat engine is given by equations 

As noted earlier, the work of any heat engine is always accompanied by a thermal loss. Therefore, the thermodynamic cycles of real engines are irreversible and their thermal efficiency is less than that of ideal and reversible Carnot cycles 

However, the mathematical equations e=(Qi - 0a)/0i (real, irreversible) and t= T -T. T (ideal, reversible) are still valid. That is, or 1 Q2lQi -T2lTy. 

The sign of equality relates to reversible processes whereas the sign of non-equality relates to irreversible processes. 

---