System: Working Fluid of the Heat Engine
The change in the entropy of the working fluid during the adiabatic expansion and compression (2 –> 3 and 4 –> 1) must equal zero for a reversible process. The change in entropy takes place isothermally for the two processes when heat is absorbed and exhausted (1 –> 2 and 3 –> 4).

Second Law:
If the heat engine is reversible then the DS_sys = 0. This implies

Thus the thermal efficiency of a Carnot heat engine is given by