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 投稿e-mail： jbnuns_sub@bnu.edu.cn 主编e-mail： jbnuns_eic@bnu.edu.cn 办公地点：北京师范大学 科技楼A区216，218，220室 电话：（010）58807851，58802050，58807872，58807713 通信处：北京市海淀区新街口外大街19号北京师范大学理科学报编辑部 邮政编码：100875 办公室e-mail： jbnuns@bnu.edu.cn

 标题 非同型热机的非线性响应关系及其最大功率对应的效率 作者 赵凌飞 涂展春 机构 北京师范大学物理学系 摘要 现有的典型热机模型均表现出同型性:对于循环热机而言,热机的工质与高温热库和低温热库之间的热交换规律具有相同的函数形式;对于自治热机来说,正向速率流和逆向速率流遵从相同的函数形式[Sheng S Q, Tu Z C. New J Phys, 2015, 17(4): 045013].本文提出非同型热机的概念,着重研究非同型循环热机,即热机的工质与高温热库和低温热库之间的热交换规律具有不同的函数形式,并导出这类热机的非线性响应关系以及最大功率对应的效率,发现非同型循环热机不满足现有文献中热机最大功率对应效率存在普适性的充分条件[Esposito M, Lindenberg K, Van den Brock C. Phys Rev Lett, 2009, 102(13): 130602; Sheng S Q, Tu Z C. Phys Rev E, 2015, 91(2): 022136]. 关键词 非同型热机; 非线性响应; 功率; 效率 引用 赵凌飞 涂展春. 非同型热机的非线性响应关系及其最大功率对应的效率.[J]. 北京师范大学学报(自然科学版),2016,52(5)550-555. 基金 中央高校基本科研业务费专项资金资助项目( 2015KJJCB01) 分类号 N414 DOI 10.16360/j.cnki.jbnuns.2016.05.003 Title Nonlinear constitutive relation and efficiency at maximum power for nonhomotypic heat engine Author ZHAO Lingfei; TU Zhanchun Affiliations Department of Physics, Beijing Normal University Abstract Typical heat engine exhibits a kind of homotypy: heat exchanges between the cyclic heat engine and the two reservoirs abide by the same function type. The forward and backward flows for an autonomous heat engine also conform to the same function type [Sheng S Q, Tu Z C. New J Phys, 2015, 17(4): 045013]. These heat engines are named homotypic heat engines. Nonhomotypic cyclic heat engine, with heat exchange between the engine and the two reservoirs not conforming to the same function type, is considered in the present paper. Nonlinear constitutive relation for nonhomotypic cyclic heat engine is derived: $J_m=LA[1+\lambda A-\frac{\delta(1+{\lambda}^2)}{2}A]+O(A^3)$ where Jm and A are flux related to mechanical movement and affinity of the heat engine, respectively. L and Λ are related to the first and the second order Onsager coefficients, respectively. λ and δ represent asymmetric parameter and nonhomotypic degree of the heat engine, respectively. A model of nonhomotypic endoreversible heat engine is constructed to confirm the above nonlinear constitutive relation. Efficiency at maximum power for nonhomotypic cyclic heat engine is: $\eta_{max P}=\frac{\eta_c}{2}+\frac{{\eta_c}^2}{8}+\frac{2\lambda (1-\land \beta \xi)+\delta(1+{\lambda}^2 \beta \xi)}{16}+{\eta_c}^2+O({\eta_c}^3)$ where represents Carnot efficiency. Factorβ is weighted reciprocal of temperature of the heat engine. Factorξ is energy scale of the heat flowing through the heat engine in each cycle. From the above equation, it is found that sufficient condition to achieve universal efficiency at maximum power is: . For nonhomotypic cyclic heat engine, this condition challenges symmetric coupling and energy-matching condition found in the literature [Esposito M, Lindenberg K, Van den Brock C. Phys Rev Lett, 2009, 102(13): 130602; Sheng S Q, Tu Z C. Phys Rev E, 2015, 91(2): 022136]. Key words nonhomotypic heat engine; nonlinear constitutive relation; efficiency; power cite ZHAO Lingfei; TU Zhanchun. Nonlinear constitutive relation and efficiency at maximum power for nonhomotypic heat engine [J]. Journal of Beijing Normal University (Natural Science), 2016,52(5):550-555. DOI 10.16360/j.cnki.jbnuns.2016.05.003
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