Attainability of Maximum Work and the Reversible Efficiency of Minimally Nonlinear Irreversible Heat Engines

摘要

We use the general formulation of irreversible thermodynamics and study theminimally nonlinear irreversible model for heat engines operating between atime varying hot heat source of finite size and a cold heat reservoir ofinfinite size. We explicitly calculate the condition for obtaining optimizedwork output for this model once the system reaches the final thermalequilibrium state with that of the cold heat reservoir. We find that ourcondition resembles with the generalized condition to achieve an optimized workoutput for generalized irreversible heat engines in the nonlinear regime [Y.Wang, Phys. Rev. E {f 93}, 012120 (2016)]. We also find that the optimizedefficiency obtained by this minimally nonlinear irreversible heat engine canreach the reversible efficiency under the tight coupling condition in whichthere is no heat leakage between the system and the reservoirs. Under thiscondition, we find that the reversible efficiency is obtain for any finite timeinterval with arbitrary power. We also calculate the efficiency at maximumpower from the minimally nonlinear irreversible heat engine under the non-tightcoupling condition. We find that the efficiency at maximum power is equal tothe half of the reversible efficiency and the corresponding maximum work ishalf of the exergy for a specific choice of the heat leakage term. Our resultmatches exactly with the efficiency and the work at maximum power obtained inRef. [Y. Izumida and K. Okuda, Phys. Rev. Lett. {f 112}, 180603 (2014)] forthe exergy study of linear irreversible heat engines under the tight couplingcondition.