﻿ " /> 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

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