以广义Redlich-Kwong气体为工质的不可逆回热式斯特林热机循环输出功率和效率

研究了热阻、回热损失和热漏等多种不可逆因素对以广义Redlich-Kwong气体为工质的斯特林热机性能的影响,给出了斯特林热机输出功率和效率的具体表达式并分析非理想回热特性及循环主要性能参数(如循环体积比及工质高低温比等)对循环输出功率和效率的影响.同时指出,只有在理想回热及无热漏的情况下,气体斯特林热机的效率才能达到卡诺效率.     

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.     

On the maximum efficiency of the ideal regenerative stirling cycle

It is shown that the efficiency of a regenerative Stirling cycle can principally not reach that of a Carnot cycle operating in the same temperature range. A relation is obtained between the degree of regeneration and the characteristics of regenerator. The maximum efficiency of an ideal regenerative Stirling engine is obtained.     

带有Dzyaloshinski-Mariya相互作用的两比特纠缠量子Otto热机和量子Stirling热机

研究了以带有Dzyaloshinski-Mariya(DM)相互作用的两比特自旋体系为工质的量子纠缠Otto热机和量子Stirling热机.两种不同热机在各自的循环过程中,通过保持其他参量不变,只有DM相互作用发生改变,从而分析热机循环中DM相互作用与热传递、做功以及效率等热力学量之间的关系.研究结果表明:DM相互作用对两种热机的基本量子热力学量都具有重要的影响,但量子Stirling热机由于回热器的使用,其循环效率会大于量子Otto纠缠热机的效率,甚至会超过Carnot效率;得到了量子Otto纠缠热机和量子Stirling热机做正功的条件.因此,在这两个纠缠体系中,热力学第二定律都依然成立.     

量子简并性对气体斯特林制冷循环性能的影响

基于理想量子气体的状态方程，分析了量子气体斯特林制冷循环中的回热特征，推导出循环的制冷系数一般表达式.获得了在强简并和弱简并条件下循环的制冷系数，对全面理解气体斯特林制冷机的性能有所帮助. 关键词： 量子简并性 斯特林制冷循环     

Quantum Heat Engines with Complex Working Media,Complete Otto Cycles and Heuristics

Quantum thermal machines make use of non-classical thermodynamic resources, one of which include interactions between elements of the quantum working medium. In this paper, we examine the performance of a quasi-static quantum Otto engine based on two spins of arbitrary magnitudes subject to an external magnetic field and coupled via an isotropic Heisenberg exchange interaction. It has been shown earlier that the said interaction provides an enhancement of cycle efficiency, with an upper bound that is tighter than the Carnot efficiency. However, the necessary conditions governing engine performance and the relevant upper bound for efficiency are unknown for the general case of arbitrary spin magnitudes. By analyzing extreme case scenarios, we formulate heuristics to infer the necessary conditions for an engine with uncoupled as well as coupled spin model. These conditions lead us to a connection between performance of quantum heat engines and the notion of majorization. Furthermore, the study of complete Otto cycles inherent in the average cycle also yields interesting insights into the average performance.     

谐振电机耦合型双效斯特林燃气热泵系统研究

针对当前国家大力推行清洁能源技术和煤改气政策的供暖现状,本文探索了一种双效斯特林燃气热泵系统。全文基于热声学观点对系统进行了理论研究,并采用SAGE程序对其进行数值模拟和优化设计。计算表明,当加热、供热和冷端温度分别为923 K、333 K和273 K时,系统可获得的泵热量为7000 W,COPh为1.79,系统(火用)效率可达到45.67%;但谐振活塞位移对温度、压力以及谐振电机机械阻尼等参数变化具有敏感性,该特点将会严重制约系统的高效运行。为了降低系统的敏感性,本文采用谐振电机耦合斯特林发动机和斯特林热泵,通过对谐振电机电功输入和输出的调控来保持电机活塞工作状态的稳定。结果表明,谐振电机对于实现斯特林发动机和斯特林热泵的高效耦合以及降低系统敏感性具有可行性。     

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.     

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.     

Efficiency bounds for nonequilibrium heat engines

We analyze the efficiency of thermal engines (either quantum or classical) working with a single heat reservoir like an atmosphere. The engine first gets an energy intake, which can be done in an arbitrary nonequilibrium way e.g. combustion of fuel. Then the engine performs the work and returns to the initial state. We distinguish two general classes of engines where the working body first equilibrates within itself and then performs the work (ergodic engine) or when it performs the work before equilibrating (non-ergodic engine). We show that in both cases the second law of thermodynamics limits their efficiency. For ergodic engines we find a rigorous upper bound for the efficiency, which is strictly smaller than the equivalent Carnot efficiency. I.e. the Carnot efficiency can be never achieved in single reservoir heat engines. For non-ergodic engines the efficiency can be higher and can exceed the equilibrium Carnot bound. By extending the fundamental thermodynamic relation to nonequilibrium processes, we find a rigorous thermodynamic bound for the efficiency of both ergodic and non-ergodic engines and show that it is given by the relative entropy of the nonequilibrium and initial equilibrium distributions. These results suggest a new general strategy for designing more efficient engines. We illustrate our ideas by using simple examples.     

Reversible Carnot cycle outside a black hole

A Carnot cycle outside a Schwarzschild black hole is investigated in detail. We propose a reversible Carnot cycle with a black hole being the cold reservoir. In our model, a Carnot engine operates between a hot reservoir with temperature T₁ and a black hole with Hawking temperature T_H. By naturally extending the ordinary Carnot cycle to the black hole system, we show that the thermal efficiency for a reversible process can reach the maximal efficiency 1-T_H/T₁. Consequently, black holes can be used to determine the thermodynamic temperature by means of the Carnot cycle. The role of the atmosphere around the black hole is discussed. We show that the thermal atmosphere provides a necessary mechanism to make the process reversible.     

The Second Law of Thermodynamics in a Quantum Heat Engine Model

The second law of thermodynamics has been proven by many facts in classical world. Is there any new property of it in quantum world? In this paper, we calculate the change of entropy in T.D. Kieu's model for quantum heat engine (QHE) and prove the broad validity of the second law of thermodynamics. It is shown that the entropy of the quantum heat engine neither decreases in a whole cycle, nor decreases in either stage of the cycle. The second law of thermodynamics still holds in this QHE model. Moreover, although the modified quantum heat engine is capable of extracting more work, its efficiency does not improve at all. It is neither beyond the efficiency of T.D. Kieu's initial model, nor greater than the reversible Carnot efficiency.     

Efficiency of reverse cycles

It is demonstrated that the generally accepted treatment of the second law of thermodynamics is incorrect when the statement of the maximum limiting efficiency of the forward Carnot cycle is applied to the reverse cycles. An analysis of reversible cycles compared with the Carnot cycle shows that the reverse Carnot cycle has the lowest efficiency of all reverse cycles. A new characteristic is proposed — the thermal efficiency of reverse cycles, and a generalized theorem is put forward for the additivity of the thermal efficiencies of the forward and reverse cycles. A formulation of the second law of thermodynamics is suggested from the point of view of the efficiency of reverse cycles. Zh. Tekh. Fiz. 69, 11–14 (June 1999)     

以一维谐振子势阱中的单粒子为工质的量子热机性能分析

建立了以一维谐振子势阱中的单粒子为工质的量子热机模型.当势阱壁宽度和粒子的量子态缓慢改变时, 该热机类似于经典卡诺热机对外做功.假设势阱壁移动速度非常缓慢并且考虑热漏, 推导出量子热机循环的输出功率和效率等重要性能参数的一般表达式.通过优化分析, 获得了热机循环中各主要性能参数的最佳优化值和优化区间.     

Performance characteristic of a Stirling refrigeration cycle in micro/nano scale

The aim of the paper is to present the performance characteristics of a Stirling refrigeration cycle in micro/nano scale, in which the working substance of cycle is an ideal Maxwellian gas. Due to the quantum boundary effect on the gas particles confined in the finite domain, the cycle no longer possesses the condition of perfect regeneration. The inherent regenerative losses, the refrigeration heat and coefficient of performance (COP) of the cycle are derived. It is found that, for the micro/nano scaled Stirling refrigeration cycle devices, the refrigeration heat and COP of cycle all depend on the surface area of the system (boundary of cycle) besides the temperature of the heat reservoirs, the volume of system and other parameters, while for the macro scaled refrigeration cycle devices, the refrigeration heat and COP of cycle are independent of the surface area of the system. Variations of the refrigeration heat ratio r_R and the COP ratio r_ε with the temperature ratio τ and volume ratio r_V for the different surface area ratio r_A are examined, which reveals the influence of the boundary of cycle on the performance of a micro/nano scaled Stirling refrigeration cycle. The results are useful for designing of a micro/nano scaled Stirling cycle device and may conduce to confirming experimentally the quantum boundary effect in the micro/nano scaled devices.     

Ecological optimization of an irreversible harmonic oscillators Carnot heat engine

A model of an irreversible quantum Carnot heat engine with heat resistance, internal irreversibility and heat leakage and many non-interacting harmonic oscillators is established in this paper. Based on the quantum master equation and semi-group approach, equations of some important performance parameters, such as power output, efficiency, exergy loss rate and ecological function for the irreversible quantum Carnot heat engine are derived. The optimal ecological performance of the heat engine in the classical limit is analyzed with numerical examples. Effects of internal irreversibility and heat leakage on the ecological performance are discussed. A performance comparison of the quantum heat engine under maximum ecological function and maximum power conditions is also performed.     

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.     

关于吸收式碳捕集热力学机制的探索

热再生吸收式碳捕集的传统认识难以揭示其热力学机制,一种新的认识是"热-化学能"转换中存在中间能量形式。本文从热力学碳泵概念出发,对吸收式碳捕集理想系统进行了解耦,其可视为"热机-碳泵"的热力学组合,探索了极限效率的表达,并采用第二定律效率作为评价参数对已有中试试验系统进行了性能水平探索。结果表明,理想循环性能系数仅取决于热源汇温度、碳源汇浓度;中试系统第二定律效率普遍低于20%。本文探索了热驱动的吸收式碳捕集热力学机制,为新型吸收剂设计提供了新思路。     

引入熵分析热力学循环的效率

本文从熵的定义和基本性质入手,首先引入T—S图计算卡诺循环的效率,其次利用dS/dV分析经历p=aVb m过程的理想气体的吸热或放热情况,最后运用上述结果求解了一个特殊热力学循环的效率.     

Investigation of oscillation regimes for a modified Carnot engine: II. The Carnot engine is a parametric generator of self-sustained oscillations

The periodic regime of a stable limit cycle for a modified Carnot engine is realized through an algorithmic slide valve. The power, piston oscillation frequency, and efficiency of the engine have been determined in a quasi-harmonic approximation. The modified engine can operate in the regime of a triangular limit cycle (cycles with any number of angles larger than three are realizable). The developed approach to analyzing the dynamic regimes of a Carnot engine allows one to dispense with the concept of entropy.