" /> 通过热力学与电学的类比加深对于熵的理解
 上海理工大学学报  2019, Vol. 41 Issue (4): 307-312 PDF

1. 上海理工大学 能源与动力工程学院，上海 200093;
2. 上海理工大学 理学院，上海 200093

A More In-Depth Understanding of Entropy by Drawing Analogy Between Thermodynamics and Electricity
WU Guobin1, HUANGFU Quansheng2, GU Zhengtian2
1. School of Energy and Power Engineering, University of Shanghai for Science and Technology, Shanghai 200093, China;
2. College of Science, University of Shanghai for Science and Technology, Shanghai 200093, China
Abstract: To make correct analogies between different branches of physics is an effective way to understand physics as a whole. By studying the concept of electric charge in electricity, the idea of thermal charge was introduced in thermodynamics. Entropy was then defined as quantity of thermal charge. Accordingly, it is now a physical quantity that is more understandable. Based on this, further comprehensive analogies were made between thermodynamics and electricity including the continuity and driving forces of electric current and entropy current, their relations with energy current as well as the entropy generated in both currents. Consequently, the analogies highlight the similarities and commonalities in the physical processes in thermodynamics and electricity, signify the harmony within the objective world, but also reveal the unique characteristics and differences between the two. Thus, we are allowed to understand entropy more in depth.
Key words: analogy     entropy     thermal charge     quantity of thermal charge     substance-like quantity

1 熵的百年艰辛求真探索之路

2 熵其实是一个容易理解的物理量

3 电流与熵流之间的类比 3.1 电流与熵流的连续性

 $\sum I = \mathop{{\int\!\!\!\!\!\int}\mkern-17.5mu \bigcirc}\limits_A {{ j} \cdot {\rm{d}}{{ A}} = - \frac{{{\rm{d}}q}}{{{\rm{d}}t}}}$ (1)

 $\sum {{I_S}} = \mathop{{\int\!\!\!\!\!\int}\mkern-17.5mu \bigcirc}\limits_A {{{ j}_{{S}}}\cdot {\rm{d}}{{{A}}} = \frac{{{\rm{d}}S'}}{{{\rm{d}}t}} - \frac{{{\rm{d}}S}}{{{\rm{d}}t}}}$ (2)

 图 1 熵流的连续性示意图 Fig. 1 Continuity of entropy currents

3.2 电流与熵流的驱动力

3.3 电流、熵流与能流之间的关系

 $P = \Delta UI$

 $P = \Delta T{I_S}$

 $P = T{I_S}$ (3)

 ${\eta _{\text{卡}} } = \frac{{{P_1} - {P_2}}}{{{P_1}}} = \frac{{{T_1} {I_S} - {T_2}{I_S}}}{{{T_1} {I_S}}} = 1 - \frac{{{T_2}}}{{{T_1}}}$ (4)

 图 2 热机的能流图 Fig. 2 Energy flow diagram of a heat engine
3.4 电流与熵流过程中的熵产生

 图 3 热传导过程中的熵产生 Fig. 3 Entropy production in heat conduction

4 结　论

 [1] HERRMANN F. 德国卡尔斯鲁厄物理教程: 热学、力学、电学(新物理教程•高中版)[M]. 上海: 上海教育出版社, 2010. [2] 皇甫泉生, 吴国玢, 顾铮. 浅析动量流与电流相关性质的类比[J]. 物理与工程, 2016, 26(2): 41–45. [3] 吴国玢, 章琢之. 德国卡尔斯鲁厄物理课程(KPK)的结构[J]. 大学物理, 2012, 31(10): 42-45. [4] 吴国玢. 浅谈德国KPK物理教材的基本特点[J]. 物理与工程, 2010, 20(5): 6-9. DOI:10.3969/j.issn.1009-7104.2010.05.003 [5] 程守洙, 江之永. 普通物理学[M]. 6版. 北京: 高等教育出版社, 2006. [6] 吴国玢. 关于德国KPK物理课程教学实验中若干问题的讨论[J]. 物理与工程, 2011, 21(3): 43-45, 51. DOI:10.3969/j.issn.1009-7104.2011.03.013 [7] POHLIG M, ROSENBERG J. Three chances for entropy[J]. Latin-American Journal of Physics Education, 2012, 6(SI): 49-58. [8] FALK G. Entropy, a resurrection of caloric-a look at the history of thermodynamics[J]. European Journal of Physics, 1985, 6(2): 108-115. DOI:10.1088/0143-0807/6/2/009 [9] FUCHS H U. Entropy in the teaching of introductory thermodynamics[J]. American Journal of Physics, 1987, 55(3): 215-219. DOI:10.1119/1.15216 [10] 吴国玢, 皇甫泉生. 关于如何理解物理量熵的若干思考[J]. 上海理工大学学报, 2018, 40(2): 103-109, 149. [11] FALK G. Was an der Physik geht jeden an?[J]. Physikalische Blätter, 1977, 33: 616-626. DOI:10.1002/phbl.v33.12 [12] EINSTEIN A, INFELD L. The evolution of physics[M]. New York: Simon & Schuster, 1967.