Second Law For A Cycle

Kelvin Planck Let a substance undergoes heat and work interactions and completes a cycle. Say It takes is Q from a hotter object and it does work. It cannot go back to initial state until it rejects some heat Q1 to an object colder than itself, even if it does work W. So W has to be less than Q by Q1 or that W/Q the efficiency can never be 1.

Reversible Engine Efficiency can never be 100%. In reality Efficiency is much lower, like the best engines have efficiencies around 60% only. There exists a higher limit on all efficiencies. This limit is defined for a Reversible Engine and all other engines corresponding lower efficiencies. If all the processes associated with a cycle are reversible, then its efficiency is the maximum for that process. Engines which execute the same processes under real conditions show an efficiency below the limit. The limit is called Carnot efficiency.

Clausius Statement A substance takes heat Q from colder object, it cannot come back to its initial state by rejecting Q to a hotter object without some work being done on it. So it will reject Q plus W to the hotter object and W can never be zero, or COP can never be infinite.