Abstract: Based on the low-dissipation Carnot heat engine model, the influence of heat leak on the efficiency at maximum power and its bounds of low-dissipation Carnot heat engine are further discussed. Under the condition of Carnot-like heat engine cycle, the expressions for the efficiency at maximum power of the quantum dot engine are derived in the presence of heat leak between hot reservoir and cold reservoir of the isothermal expansion and the isothermal compression process, and compared with the classical CA efficiency in the symmetric case. It is found that, when there is no heat leak, the efficiency at maximum power of the low-dissipation Carnot heat engine is equal to the CA efficiency. In the presence of heat leak, the efficiency at maximum power of the low-dissipation Carnot heat engine is lower than the CA efficiency, and decreases with the increases of heat leak. In the case of asymmetric, the upper bound and lower bound of efficiency at maximum power are obtained, and compared with different kinds of actual engine efficiency. The results show that the efficiency at maximum power and its bounds in correspondence with the observed performance of real heat engines in the presence of heat leak.

Key words: Carnot heat engine, efficiency, finite-time thermodynamics, heat leak, low-dissipation