An irreversible combined Carnot cycle model using ideal quantum gases as a working medium was studied by using finite-time thermodynamics. The combined cycle consisted of two Carnot sub-cycles in a cascade mode. Considering thermal resistance, internal irreversibility, and heat leakage losses, the power output and thermal efficiency of the irreversible combined Carnot cycle were derived by utilizing the quantum gas state equation. The temperature effect of the working medium on power output and thermal efficiency is analyzed by numerical method, the optimal relationship between power output and thermal efficiency is solved by the Euler-Lagrange equation, and the effects of different working mediums on the optimal power and thermal efficiency performance are also focused. The results show that there is a set of working medium temperatures that makes the power output of the combined cycle be maximum. When there is no heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are parabolic-like ones, and the internal irreversibility makes both power output and efficiency decrease. When there is heat leakage loss in the combined cycle, all the characteristic curves of optimal power versus thermal efficiency are loop-shaped ones, and the heat leakage loss only affects the thermal efficiency of the combined Carnot cycle. Comparing the power output of combined heat engines with four types of working mediums, the two-stage combined Carnot cycle using ideal Fermi-Bose gas as working medium obtains the highest power output.

中文翻译：

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具有理想量子气体的不可逆组合卡诺热机性能分析与优化

利用有限时间热力学研究了以理想量子气体为工作介质的不可逆组合卡诺循环模型。组合循环由两个卡诺级联的子循环组成。考虑到热阻，内部不可逆性和热损失，利用量子气体状态方程推导了不可逆联合卡诺循环的功率输出和热效率。通过数值方法分析了工作介质对输出功率和热效率的温度影响，通过欧拉-拉格朗日方程求解了输出功率与热效率的最佳关系，以及不同工作介质对最优功率和热效率的影响。效率绩效也是重点。结果表明，存在一组工作介质温度，使组合循环的功率输出最大。当组合循环中没有热损失时，最佳功率与热效率的所有特性曲线都是抛物线状的，并且内部不可逆性使功率输出和效率均下降。当联合循环中存在热损失时，最佳功率与热效率的所有特性曲线均为环形，并且热损失仅影响联合卡诺循环的热效率。将组合式热机的功率输出与四种类型的工作介质进行比较，使用理想的费米-玻色气体作为工作介质的两阶段组合卡诺循环获得了最高的功率输出。