周期性双势垒锯齿势中温差驱动的布朗热机

研究了周期性双势垒锯齿势中, 布朗粒子在外力作用下沿空间坐标方向交替地和高、低温热库接触构成的布朗热机的热力学性能. 考虑布朗粒子动能的变化以及高、 低温库之间热漏的存在, 通过数值计算分析势垒高度、势比、外力等参数对布朗热机效率的影响. 研究表明：当考虑热漏时, 布朗热机始终是不可逆的, 效率小于卡诺效率; 并且当热漏很小时, 势比的增大在一定程度上可提高布朗热机的效率; 其功率与效率之间的关系曲线为闭合线. 当不考虑热漏时, 其功率与效率之间的关系曲线为开型线, 但由于布朗粒子动能的变化引起的不可逆热流, 热机的效率依然小于卡诺效率. 关键词： 布朗热机 双势垒锯齿势 热漏 热力学性能     

Performance characteristics of an irreversible thermally driven Brownian microscopic heat engine

Brownian particles moving in a spatially asymmetric but periodic potential (ratchet), with an external load force and connected to an alternating hot and cold reservoir, are modeled as a microscopic heat engine, referred to as the Brownian heat engine. The heat flow via both the potential energy and the kinetic energy of the particles are considered simultaneously. The forward and backward particle currents are determined using an Arrhenius' factor. Expressions for the power output and efficiency are derived analytically. The maximum power output and efficiency are calculated. It is expounded that the Brownian heat engine is always irreversible and its efficiency cannot approach the efficiency η_C of the Carnot heat engine even in quasistatic limit. The influence of the main parameters such as the load, the barrier height of the potential, the asymmetry of the potential and the temperature ratio of the heat reservoirs on the performance of the Brownian heat engine is discussed in detail. It is found that the Brownian heat engines may be controlled to operate in different regions through variation of some parameters.     

温库边界对布朗热机性能的影响

研究了单势垒锯齿势中,布朗粒子在外力和空间周期温度场作用下构成的布朗热机的热力学性能.考虑布朗粒子动能变化以及高、低温库之间热漏引起的热流.用Smoluchowski方程描述粒子在黏性介质中的动力学特性,推导出高、低温库的热流以及热机功率和效率的解析表达式.通过数值计算分析势垒高度、外力和温库边界对热机性能的影响.研究表明:由于动能变化和热漏引起的不可逆热流的存在,布朗热机为不可逆热机,热机的功率效率特性为一闭合的关系曲线;势垒边界与温库边界重合时,热机的功率达到最大值;通过改变温库边界的位置,可以在一定范围内提高热机的效率,但同时减小了热机的输出功率.     

Performance Analysis and Optimization for Irreversible Combined Carnot Heat Engine Working with Ideal Quantum Gases

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.     

一维晶格中费曼棘齿-棘爪热机

研究了一维晶格中费曼棘齿-棘爪热机模型. 用粒子的概率主方程来描述粒子在晶格中的动力学特性, 推导出热流、 功率和效率的表达式. 通过数值计算分析势垒高度、 外力和温比对热流以及热机功率和效率的影响. 研究表明: 在粒子稳态概率流为零时, 存在非零的热流从高温库流入低温库, 类似于经典不可逆卡诺模型中的热漏; 热漏的存在使得热机的效率远远小于卡诺效率, 功率与效率之间为闭合的关系曲线, 热机为不可逆热机; 对热机性能参数进行优化, 可以使热机工作在最优性能状态下.     

Current,maximum power and optimized efficiency of a Brownian heat engine

A microscopic heat engine is modeled as a Brownian particle in a sawtooth potential (with load) moving through a highly viscous medium driven by the thermal kick it gets from alternately placed hot and cold heat reservoirs. We found closed form expression for the current as a function of the parameters characterizing the model. Depending on the values these model parameters take, the engine is also found to function as a refrigerator. Expressions for the efficiency as well as for the refrigerator performance are also reported. Study of how these quantities depend on the model parameters enabled us in identifying the points in the parameter space where the engine performs with maximum power and with optimized efficiency. The corresponding efficiencies of the engine are then compared with those of the endoreversible and Carnot engines.Received: 28 December 2003, Published online: 28 May 2004PACS: 05.40.Jc Brownian motion - 05.60.-k Transport processes - 05.70.-a ThermodynamicsMesfin Asfaw: Present address: Max Planck Institute of Colloids and Interfaces, 14424 Potsdam, Germany     

Thermodynamic Performance Characteristics of a Brownian MicroscopicHeat Engine Driven by Discrete and Periodic Temperature Field

A Brownian microscopic heat engine with a particle hopping on a one-dimensional lattice driven by a discrete and periodic temperature field in a periodic sawtooth potential is investigated. In order to clarify the underlying physical pictures of the heat engine, the heat flow via the potential energy and the kinetic energy of the particles are considered simultaneously. Based on describing the jumps among the three states, the expressions of theefficiency and power output of the heat engine are derived analytically. The general performance characteristic curves are plotted by numerical calculation. It is found that the power output-efficiency curve is a loop-shaped one, which is similar to one for a real irreversible heat engine. The influence of the ratioof the temperature of the hot and cold reservoirs and the sawtooth potential on the maximum efficiency and power output is analyzed forsome given parameters. When the heat flows via the kinetic energy isneglected, the power output-efficiency curve is an open-shaped one,which is similar to one for an endroeversible heat engine.     

Thermodynamic characteristics of a Brownian heat pump in a spatially periodic temperature field

This paper has studied the thermodynamic performance of a thermal Brownian heat pump,which consists of Brownian particles moving at a periodic sawtooth potential with external forces and contacting with the alternating hot and cold reservoirs along the space coordinate.The heat flows driven by both potential and kinetic energies are taken into account.The analytical expressions for the heating load,coefficient of performance(COP) and power input of the Brownian heat pump are derived and the performance char...     

Quantum point contacts as heat engines

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is a small probability that a mesoscopic heat engine exceeds Carnot's maximum value during a short measurement time. We illustrate this effect using a quantum point contact as a heat engine. When a temperature difference is applied to a quantum point contact, the system may be utilized as a source of electrical power under steady state conditions. We first discuss the optimal working point of such a heat engine that maximizes the generated electrical power and subsequently calculate the statistics for deviations of the efficiency from its most likely value. We find that deviations surpassing the Carnot limit are possible, but unlikely.     

Performance characteristics of low-dissipative generalized Carnot cycles with external leakage losses

Under the assumption of low-dissipation, a unified model of generalized Carnot cycles with external leakage losses is established. Analytical expressions for the power output and efficiency are derived. The general performance characteristics between the power output and the efficiency are revealed. The maximum power output and efficiency are calculated. The lower and upper bounds of the efficiency at the maximum power output are determined. The results obtained here are universal and can be directly used to reveal the performance characteristics of different Carnot cycles, such as Carnot heat engines, Carnot-like heat engines, flux flow engines, gravitational engines, chemical engines, two-level quantum engines,etc.     

斯特林热机的基本优化关系及功率和效率界限

1前言近年来,有些学者应用有限时间热力学研究斯特林热机的优化性能,获得一些比经典热力学界限更有意义的新性能界限。但至今为数还较少,应继续开展研究。特别是有人提出“21世纪是斯特林热机的世纪’巾一］。本文将进一步研究受热阻、热漏和回热损失三种主要不可逆因素影响的斯特林热机的优化性能,导出热机的基本优化关系及功率和效率界限。结果表明,热漏的存在使斯特林热机的优化性能与无热漏时的有质的差异,而在热阻和回热损失的基础上再考虑热漏的影响,其结果将可反映出实际热机观测性能的主要特征【’,‘］,从而对实际更有指…     

Reprint of : Quantum point contacts as heat engines

The efficiency of macroscopic heat engines is restricted by the second law of thermodynamics. They can reach at most the efficiency of a Carnot engine. In contrast, heat currents in mesoscopic heat engines show fluctuations. Thus, there is a small probability that a mesoscopic heat engine exceeds Carnot's maximum value during a short measurement time. We illustrate this effect using a quantum point contact as a heat engine. When a temperature difference is applied to a quantum point contact, the system may be utilized as a source of electrical power under steady state conditions. We first discuss the optimal working point of such a heat engine that maximizes the generated electrical power and subsequently calculate the statistics for deviations of the efficiency from its most likely value. We find that deviations surpassing the Carnot limit are possible, but unlikely.     

Heat flow and efficiency in a microscopic engine

We study the energetics of a thermal motor driven by temperature differences, which consists of a Brownian particle moving in a sawtooth potential with an external load where the viscous medium is periodically in contact with hot and cold heat reservoir along space coordinate. The motor can work as a heat engine or a refrigerator under different conditions. The heat flow via both potential and kinetic energy is considered. The former is reversible when the engine works quasistatically and the latter is always irreversible. The efficiency of the heat engine can never approach Carnot efficiency.     

Efficiency of Brownian heat engines

We study the efficiency of one-dimensional thermally driven Brownian ratchets or heat engines. We identify and compare the three basic setups characterized by the type of the connection between the Brownian particle and the two heat reservoirs: (i) simultaneous, (ii) alternating in time, and (iii) position dependent. We make a clear distinction between the heat flow via the kinetic and the potential energy of the particle, and show that the former is always irreversible and it is only the third setup where the latter is reversible when the engine works quasistatically. We also show that in the third setup the heat flow via the kinetic energy can be reduced arbitrarily, proving that even for microscopic heat engines there is no fundamental limit of the efficiency lower than that of a Carnot cycle.     

Maximum power output of a class of irreversible non-regeneration heat engines with a non-uniform working fluid and linear phenomenological heat transfer law

Maximum power output of a class of irreversible non-regeneration heat engines with non-uniform working fluid, in which heat transfers between the working fluid and the heat reservoirs obey the linear phenomenological heat transfer law [q ∝ Δ(T ⁻¹)], are studied in this paper. Optimal control theory is used to determine the upper bounds of power of the heat engine for the lumped-parameter model and the distributed-parameter model, respectively. The results show that the maximum power output of the heat engine in the distributed-parameter model is less than or equal to that in the lumped-parameter model, which could provide more realistic guidelines for real heat engines. Analytical solutions of the maximum power output are obtained for the irreversible heat engines working between constant temperature reservoirs. For the irreversible heat engine operating between variable temperature reservoirs, a numerical example for the lumped-parameter model is provided by numerical calculation. The effects of changes of reservoir’s temperature on the maximum power of the heat engine are analyzed. The obtained results are, in addition, compared with those obtained with Newtonian heat transfer law [q ∝ Δ(T)].     

The performance analysis of a micro-/nanoscaled quantum heat engine

A new model of micro-/nanoscaled heat engines consisting of two thin long tubes with the same length but different sizes of cross section, which are filled up with ideal quantum gases and operated between two heat reservoirs, is put forward. The working fluid of the heat engine cycle goes through four processes, which include two isothermal processes and two isobaric processes with constant longitudinal pressure. General expressions for the power output and efficiency of the cycle are derived, based on the thermodynamic properties of confined ideal quantum gases. The influence of the size effect on the power output and efficiency is discussed. The differences between the heat engines working with the ideal Bose gas and Fermi gas are revealed. The performance of the heat engines operating at weak gas degeneracy and high temperatures is further analyzed. The results obtained are more general and significant than those in the current literature.     

Irreversible Brownian Heat Engine

We model a Brownian heat engine as a Brownian particle that hops in a periodic ratchet potential where the ratchet potential is coupled with a linearly decreasing background temperature. We show that the efficiency of such Brownian heat engine approaches the efficiency of endoreversible engine \(\eta =1-\sqrt{{T_{c}/T_{h}}}\) [23]. On the other hand, the maximum power efficiency of the engine approaches \(\eta ^{MAX}=1-({T_{c}/T_{h}})^{1\over 4}\). It is shown that the optimized efficiency always lies between the efficiency at quasistatic limit and the efficiency at maximum power while the efficiency at maximum power is always less than the optimized efficiency since the fast motion of the particle comes at the expense of the energy cost. If the heat exchange at the boundary of the heat baths is included, we show that such a Brownian heat engine has a higher performance when acting as a refrigerator than when operating as a device subjected to a piecewise constant temperature. The role of time on the performance of the motor is also explored via numerical simulations. Our numerical results depict that the time t and the external load dictate the direction of the particle velocity. Moreover, the performance of the heat engine improves with time. At large t (steady state), the velocity, the efficiency and the coefficient of performance of the refrigerator attain their maximum value. Furthermore, we study the effect of temperature by considering a viscous friction that decreases exponentially as the background temperature increases. Our result depicts that the Brownian particle exhibits a fast unidirectional motion when the viscous friction is temperature dependent than that of constant viscous friction. Moreover, the efficiency of this motor is considerably enhanced when the viscous friction is temperature dependent. On the hand, the motor exhibits a higher performance of the refrigerator when the viscous friction is taken to be constant.     

非线性二极管系统构成的不可逆热机性能特征分析

研究了一个非线性二极管系统构成的不可逆热机的性能,它是由分别处于两个温度不同的热库中,完全相同的两个非线性二极管反向连接后并联上一个电容器组成的.运用非线性系统涨落理论计算出从两个热库中吸收的热流,考虑热漏损失后得出热机的功率和效率.通过数值模拟可以绘出热机的性能特征曲线以及优化性能参数随两热库温度比等主要参量的特征曲线.分析了二极管的非线性强度、热漏损失和温度比对热机性能特性的影响.最后,讨论了理想二极管热机的性能特征.     

Performance of a two-state quantum engine improved by the superposition effect

The performance of a two-state quantum engine under different conditions is analyzed.It is shown that the efficiency of the quantum engine can be enhanced by superposing the eigenstates at the beginning of the cycle.By employing the finite-time movement of the potential wall,the power output of the quantum engine as well as the efficiency at the maximum power output(EMP) can be obtained.A generalized potential is adopted to describe a class of two-level quantum engines in a unified way.The results obtained show clearly that the performances of these engines depend on the external potential,the geometric configuration of the quantum engines,and the superposition effect.Moreover,it is found that the superposition effect will enlarge the optimally operating region of quantum engines.     

Recent advance on the efficiency at maximum power of heat engines

This review reports several key advances on the theoretical investigations of efficiency at maximum power of heat engines in the past five years. The analytical results of efficiency at maximum power for the Curzon-Ahlborn heat engine, the stochastic heat engine constructed from a Brownian particle, and Feynman's ratchet as a heat engine are presented. It is found that: the efficiency at maximum power exhibits universal behavior at small relative temperature differences; the lower and the upper bounds might exist under quite general conditions; and the problem of efficiency at maximum power comes down to seeking for the minimum irreversible entropy production in each finite-time isothermal process for a given time.