A single driven spin is investigated as the working substance of a six-stroke irreversible quantum Carnot cycle. The role of inner friction associated with the finite-time adiabatic transformations on the cycle efficiency and the harvested work are investigated in detail. The inner friction is found to significantly reduce the work output and the cycle efficiency which can make the engine incapable to produce positive work for the too fast adiabatic transformations. The ideal Carnot efficiency is found to be reached only for the quasi-static transformations. A deviation of the cycle efficiency from the classical Carnot efficiency has been given by an efficiency lag which is directly related to the total entropy production due to the inner friction. The released heat in the relaxation processes of the cycle are associated with the entropy production and the inner friction. The extension of the results for a scale invariant quantum working substance and the possible experimental implementation of the irreversible quantum Carnot cycle in a liquid state nuclear magnetic resonance setup are also discussed.

8 pages, 4 Figures, Comments are welcome