  We study a quantum thermal engine model for which the heat transfer law is
determined by Einstein's theory of radiation. The working substance of the
quantum engine is assumed to be a two-level quantum systems of which the
constituent particles obey Maxwell-Boltzmann(M.B.), Fermi-Dirac(F.D.) or
Bose-einstein(B.E.) distributions respectively at equilibrium. The thermal
efficiency and its bounds at maximum power of these models are derived and
discussed in the long and short thermal contact time limits. The similarity and
difference between these models are discussed. We also compare the efficiency
bounds of this quantum thermal engine to those of its classical counterpart.
