What is the Clausius inequality?
The Clausius Inequality is applicable to the operation of all real engines. The ideal heat cycle does not result in a net change in entropy as the increase in entropy during part of the cycle is compensated by an equal decrease during the rest of the cycle.
In case of a real engine on the other hand, there is a negative change in entropy over the entire heat cycle. This is due to the fact that the temperature of the engine when heat is being added to it from the source is less than the temperature of the source. As a result of this, the addition of heat is an irreversible process and there is entropy created which here has to be passed on to the cold reservoir.
Unlike an ideal engine, a real engine cannot convert all the heat from the source into work and its efficiency is less than one.