非对称有限热源之间热机循环的基本热力学约束  

Thermodynamic constraints on heat engine cycles betweenasymmetrical finite-sized reservoirs

作　　者：赵秀花 涂展春[1] 马宇翰 ZHAO Xiuhua;TU Zhanchun;MA Yuhan(Department of Physics,Beijing Normal University,100875,Beijing,China)

机构地区：[1]北京师范大学物理学系,北京100875

出　　处：《北京师范大学学报（自然科学版）》2023年第6期969-978,共10页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(11975050,12305037);中央高校基本科研业务费专项基金资助项目(2023NTST017)。

摘　　要：为讨论更一般情形中有限热源之间的热力学约束,探讨了在2个具有非对称热容有限热源之间工作的热机循环问题.假定热源热容C满足德拜定律C∝T^(n),高低温热源不对称体现在它们关于温度(T)的幂指数(n)不同.对于通常的固体材料,n由材料的空间维度和所处温度区间决定;在低温热源与高温热源初始热容比很大或很小的2个极限区域,证明了热机最大功率效率关于最大功效率的函数具有不依赖于热源维度的普适形式.在数值上探讨了2热源初始热容大小对称而热容(关于温度变化)行为不对称的特殊情况,结果显示,最大功效率和最大功率效率随高温热源维度的增大而升高,而关于低温热源维度变化的单调性则与低高温热源的初始温度比T_(L)/T_(H)有关.这一结果表明,若将有限热源的热容性质纳入其间热机循环的优化考量,则循环在低温端的优化方向(n在给定区间内的大小选择)要由热源初始温度所确定的卡诺效率η_(C)≡1-T_(L)/T_(H)决定.To study thermodynamic constraints associated with finite-sized reservoirs in more general cases,a thermodynamic cycle between two reservoirs with finite and non-symmetrical heat capacities is proposed,assuming that heat capacities satisfy Debye law C∝T^(n).Here,asymmetry of reservoirs is reflected in different power exponents n of heat capacity C with respect to temperature T of different reservoirs.For common solid materials,n is determined by spatial dimensionality of the material and temperature range it is in.In two limit regimes ofξ(defined as initial heat capacity ratio of low-temperature reservoir to high-temperature reservoir),i.e.,ξ→0 andξ→∞,it is proved that efficiency at maximum power(EMP)as a function of efficiency at maximum work(EMW)has a universality that is independent of dimension of the reservoir.In addition,a special case where initial heat capacities of two heat reservoirs are symmetric in numerical value but their heat capacity behaviors(with respect to temperature)are not symmetric is numerically studied.EMW and EMP are found to increase with increased dimension of hightemperature reservoir,and their monotonic behavior with changed dimension of low-temperature reservoir depends on initial temperature ratio T_(L)/T_(H) of low-and high-temperature reservoirs.This finding suggests that if heat capacity properties of finite-sized reservoirs are incorporated into cycle optimization,optimization direction at low-temperature end(the choice of n in a given interval)should be determined by the initial Carnot efficiencyη_(C)≡1-T_(L)/T_(H).

关 键 词：热力学 有限热源 非对称热容 有限时间热机 最大功效率 最大功率效率 

分 类 号：O414.1[理学—理论物理]