Bekele, Mulugeta (PhD)Alemye, Mekuannent2018-06-292023-11-092018-06-292023-11-092011-11http://10.90.10.223:4000/handle/123456789/4763In this work we consider spin-half particle with two energy levels in contact with two heat reservoirs and we apply magnetic eld on it whose task is to convert the input energy from the hot reservoir and from the magnetic eld to useful work. We analytically study the optimized quantum thermodynamic e ciency, which lies between Carnot e ciency and e ciency at maximum power. We also nd the time taken to accomplish one complete cycle at the maximum power and at optimized e cienciesenHeat Engine WorkingThesis