热功转换循环规律的另一半:逆循环的定理、定律和核心物理量
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摘要
在回顾卡诺定理、热力学第二定律(正循环等价定律)以及核心物理量熵时,发现它们主要讨论的都是热量通过可逆循环转换为功量的规律.即使对于热泵或制冷逆循环,仍然应用正循环的概念和分析方法讨论它们的性能.然后以逆卡诺循环为例,分析和证明了两温限下逆卡诺循环的性能系数不是最大而是最小.随之提出了一个新的逆循环,它是由两个等压和两个等容过程组成,可称之为逆压容(p-V)循环.在净功量给定和两温限条件下,逆压容(p-V)循环的性能系数远大于逆卡诺循环的性能系数.此结果表明,逆循环中功量是有品位的,压力就是功量的品位.最后建立了逆循环的等价定律和逆循环等式,并引入了功熵的概念.基于逆循环的原理、定理、定律、核心物理量和循环性能等,可望形成热功转换循环规律的另一半.
Engineering thermodynamics mainly focuses on the principles and methods for the heat-work conversion and to improve heat-work conversion efficiency. In current literatures, discussions are mainly focused on the heat-work cycles, which converts heat to work. Besides, the core physical quantity of heat-work cycles is entropy, which presents the heat-work conversion ability of the system. As for reversed cycles, the discussions are not quite detailed, and most of them applied the theory for heat-work cycles directly on reversed cycles. However, it's well known that heat cannot be fully converted to work in a reversible thermodynamic cycle, which leads an efficiency less than 1. For reversed cycles, the heat output from the cycle can be much more than the net work the cycle costs, which derives a coefficient of performance(COP) more than 1. This phenomenon implies the principles of heat-work conversion in ordinary heat-work cycles and reversed cycles are somehow different, and some problems are naturally drawn as follows:(1) Is the COP of the reversed Carnot cycle the maximum possible COP for all reversed cycles within two temperature limits?(2) Heat can be judged from its quality, i.e. its temperature, and does the mechanical work have its quality? To answer these questions, this work analyzed and discussed the theorem, principle, and core physical quantity of reversed thermodynamic cycles. First, the principle for ordinary thermodynamic cycles are briefly reviewed, including the Carnot theorem and its proof, and the derivation of the concept of entropy from the Clausius' original approach. Second, current conclusions of reversed cycles are reviewed and the air compression refrigeration cycle is taken as an example. The analysis comparing two cycles within given temperature limits presented that for given two temperature limits, the COP of the reversed Carnot cycle is the minimum possible COP, which is different from current conclusions. The quality of volumetric work is then discussed, and a new reversed cycle named reversed p-V cycle is proposed, which operates between two given pressure limits. The analysis indicates that this cycle is the best reversed cycle operating between two given pressure limits. Based on these discussion, the theorem and principle for reversed cycles corresponding to the second law and the Carnot's theorem are derived and proved using the Clausius' approach. The performance of the newly proposed reversed p-V cycle is investigated and compared with the reversed Carnot cycle operating within the same temperature limits, and results present that the COP of the reversed p-V cycle is much higher than the COP of the reversed Carnot cycle within the same temperature limits. Finally, from the equation of an arbitrary reversed cycle, it can be seen that the volume has a similar physical interpretation in the reversed cycles to the entropy in thermodynamic cycles, and it can be named as the work-entropy. In summary, the reversed cycles are analyzed, and its theorem, principles and core physical quantity are investigated.
Engineering thermodynamics mainly focuses on the principles and methods for the heat-work conversion and to improve heat-work conversion efficiency. In current literatures, discussions are mainly focused on the heat-work cycles, which converts heat to work. Besides, the core physical quantity of heat-work cycles is entropy, which presents the heat-work conversion ability of the system. As for reversed cycles, the discussions are not quite detailed, and most of them applied the theory for heat-work cycles directly on reversed cycles. However, it's well known that heat cannot be fully converted to work in a reversible thermodynamic cycle, which leads an efficiency less than 1. For reversed cycles, the heat output from the cycle can be much more than the net work the cycle costs, which derives a coefficient of performance(COP) more than 1. This phenomenon implies the principles of heat-work conversion in ordinary heat-work cycles and reversed cycles are somehow different, and some problems are naturally drawn as follows:(1) Is the COP of the reversed Carnot cycle the maximum possible COP for all reversed cycles within two temperature limits?(2) Heat can be judged from its quality, i.e. its temperature, and does the mechanical work have its quality? To answer these questions, this work analyzed and discussed the theorem, principle, and core physical quantity of reversed thermodynamic cycles. First, the principle for ordinary thermodynamic cycles are briefly reviewed, including the Carnot theorem and its proof, and the derivation of the concept of entropy from the Clausius' original approach. Second, current conclusions of reversed cycles are reviewed and the air compression refrigeration cycle is taken as an example. The analysis comparing two cycles within given temperature limits presented that for given two temperature limits, the COP of the reversed Carnot cycle is the minimum possible COP, which is different from current conclusions. The quality of volumetric work is then discussed, and a new reversed cycle named reversed p-V cycle is proposed, which operates between two given pressure limits. The analysis indicates that this cycle is the best reversed cycle operating between two given pressure limits. Based on these discussion, the theorem and principle for reversed cycles corresponding to the second law and the Carnot's theorem are derived and proved using the Clausius' approach. The performance of the newly proposed reversed p-V cycle is investigated and compared with the reversed Carnot cycle operating within the same temperature limits, and results present that the COP of the reversed p-V cycle is much higher than the COP of the reversed Carnot cycle within the same temperature limits. Finally, from the equation of an arbitrary reversed cycle, it can be seen that the volume has a similar physical interpretation in the reversed cycles to the entropy in thermodynamic cycles, and it can be named as the work-entropy. In summary, the reversed cycles are analyzed, and its theorem, principles and core physical quantity are investigated.
引文
1 Wang B X.Engineering Thermodynamics(in Chinese).Beijing:Higher Education Press,2011.12-20[王补宣.工程热力学.北京:高等教育出版社,2011.12-20]
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3 Zeng D L,Ao Y,Zhang X M,et al.Engineering Thermodynamics(in Chinese).3th ed.Beijing:Higher Education Press,2002.40[曾丹苓,敖越,张新铭,等.工程热力学.第3版.北京:高等教育出版社,2002.40]
4 Moran M J,Shapiro H N,Boettner D D,et al.Fundamentals of Engineering Thermodynamics:SI Version.8th ed.New Jersey:John Wiley&Sons,2014
5 Wark K.Advanced Thermodynamics for Engineers.New York:McGraw-Hill,1995
6 Carnot S.Reflections on the Motive Power of Heat and on Machines Fitted to Develop that Power.New Jersey:John Wiley&Sons,1890
7 Müller I.A History of Thermodynamics:the Doctrine of Energy and Entropy.Berlin:Springer,2010
8 Clausius R.The Mechanical Theory of Heat,with its Applications to the Steam-engine and to the Physical properties of Bodies.London:John van Voorst,1867
9 Clausius R.The Mechanical Theory of Heat.London:Macmillan and Co,1879
10 Wu J,Guo Z Y.An exploration for the macroscopic physical meaning of entropy(in Chinese).Sci China Tech Sci,2010,53:1809-1816[吴晶,过增元.熵的宏观物理意义的探索.中国科学:技术科学,2010,53:1809-1816]
11 Napier S.Manual of Meteorology.Cambridge:Cambridge University Press,2015
12 Zhao T,Guo Z Y.Least action principle for reversible thermodynamic processes.In:Proceedings of the 1st Asian Conference on Thermal Sciences.March 2017,Jeju Island,Korea
13 Zhao T,Hua Y C,Guo Z Y.The Principle of Least Action for Reversible Thermodynamic Processes and Cycles.Entropy,2018,20:542
14 Guo Z Y,Zhao T,Xue T W.The performance analysis of reversed Carnot cycle and reversed p-V cycle(in Chinese).Sci China Tech Sci,2018,48:1190-1198[过增元,赵甜,薛提微.逆卡诺循环与逆p-V循环性能分析.中国科学:技术科学,2018,48:1190-1198]
15 Xue T W,Guo Z Y.The misunderstanding of Clausius statement of the second law of thermodynamics and its aftermath(in Chinese).Chin Sci Bull,2018,63:2666-2672[薛提微,过增元.热力学第二定律克劳修斯表述的误解及其后果.科学通报,2018,63:2666-2672]
2 Shen W D,Tong J G.Engineering Thermodynamics(in Chinese).4th ed.Beijing:Higher Education Press,2007.24[沈维道,童钧耕.工程热力学.第4版.北京:高等教育出版社,2007.24]
3 Zeng D L,Ao Y,Zhang X M,et al.Engineering Thermodynamics(in Chinese).3th ed.Beijing:Higher Education Press,2002.40[曾丹苓,敖越,张新铭,等.工程热力学.第3版.北京:高等教育出版社,2002.40]
4 Moran M J,Shapiro H N,Boettner D D,et al.Fundamentals of Engineering Thermodynamics:SI Version.8th ed.New Jersey:John Wiley&Sons,2014
5 Wark K.Advanced Thermodynamics for Engineers.New York:McGraw-Hill,1995
6 Carnot S.Reflections on the Motive Power of Heat and on Machines Fitted to Develop that Power.New Jersey:John Wiley&Sons,1890
7 Müller I.A History of Thermodynamics:the Doctrine of Energy and Entropy.Berlin:Springer,2010
8 Clausius R.The Mechanical Theory of Heat,with its Applications to the Steam-engine and to the Physical properties of Bodies.London:John van Voorst,1867
9 Clausius R.The Mechanical Theory of Heat.London:Macmillan and Co,1879
10 Wu J,Guo Z Y.An exploration for the macroscopic physical meaning of entropy(in Chinese).Sci China Tech Sci,2010,53:1809-1816[吴晶,过增元.熵的宏观物理意义的探索.中国科学:技术科学,2010,53:1809-1816]
11 Napier S.Manual of Meteorology.Cambridge:Cambridge University Press,2015
12 Zhao T,Guo Z Y.Least action principle for reversible thermodynamic processes.In:Proceedings of the 1st Asian Conference on Thermal Sciences.March 2017,Jeju Island,Korea
13 Zhao T,Hua Y C,Guo Z Y.The Principle of Least Action for Reversible Thermodynamic Processes and Cycles.Entropy,2018,20:542
14 Guo Z Y,Zhao T,Xue T W.The performance analysis of reversed Carnot cycle and reversed p-V cycle(in Chinese).Sci China Tech Sci,2018,48:1190-1198[过增元,赵甜,薛提微.逆卡诺循环与逆p-V循环性能分析.中国科学:技术科学,2018,48:1190-1198]
15 Xue T W,Guo Z Y.The misunderstanding of Clausius statement of the second law of thermodynamics and its aftermath(in Chinese).Chin Sci Bull,2018,63:2666-2672[薛提微,过增元.热力学第二定律克劳修斯表述的误解及其后果.科学通报,2018,63:2666-2672]