非同型热机的非线性响应关系及其最大功率对应的效率

发布时间：2018-05-13 06:32

本文选题：非同型热机 + 非线性响应　；参考：《北京师范大学学报(自然科学版)》2016年05期

【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满足这类条件的热机被称为同型热机.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:J_m=LA[1+ΛλA-δ(1+λ~2)/2A]+O(A~3),其中J_m和A分别是热机的机械流和亲合力,L和Λ与一阶和二阶昂萨格系数相关,λ和δ分别代表热机的非对称度和非同型度.本文导出非同型循环热机最大功率对应的效率为ηmaxP=ηC/2+η~2/8+2λ(1-Λβξ)+δ(1+λ~2)βξ/16η_C~2+O(η_C~3),其中ηC代表卡诺效率,β是加权逆温度,ξ是流过热机的热流的特征能量.由此可见,最大功率时热机取普适效率(ηC/2+η_C~2/8)的充要条件为2λ(1-Λβξ)+δ(1+λ~2)βξ=0.这表明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.
[Abstract]:The existing typical heat engine models all show the same type: for the circulating heat engine, the working fluid of the heat engine has the same function form as the heat exchange law between the high temperature heat reservoir and the low temperature heat reservoir, and for the autonomous heat engine, The heat engines with the same function form for the forward rate flow and the reverse rate flow are called the same type heat engine. In this paper, the concept of non-identical heat engine is put forward, and the heat exchange law between the working fluid of the heat engine and the heat storage at high temperature and low temperature has different function forms. The nonlinear response relation of this kind of heat engine is derived. The nonlinear response relation of this kind of heat engine is: [1 A 位 A-未 1 位 2 / 2 A] O + A 3, where JM and A are the mechanical flow and affinity L and A of the heat engine, respectively, which are related to the first and second order Onzag coefficients, and 位 and 未 represent the asymmetrical degree and the non-homogeneity degree of the engine, respectively. In this paper, the efficiency corresponding to the maximum power of non-homogeneous circulating heat engine is 畏 maxP = 畏 C / 2 畏 2 / 8 2 位 1- 尾尉) 未 1 位 2) 尾尉 / 16 畏 C 2 O (畏 C 3 O, where 畏 C represents Carnot efficiency, 尾 is weighted inverse temperature, 尉 is the characteristic energy of heat flux of the superheat engine. It can be seen that the necessary and sufficient condition for the heat engine to take the universal efficiency (畏 C / 2 畏 C / 2 / 8) at the maximum power is 2 位 (1- 位尾尉) 未 1 位 2) 尾尉 0. This indicates that the non-identical circulating heat engine does not satisfy the sufficient conditions for the existence of universality of the corresponding efficiency of the maximum power of the heat engine in the existing literature.
【作者单位】：北京师范大学物理学系;
【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】：TK05

【相似文献】