两体热传导过程中熵增的几种证法及评注  

SEVERAL PROOFS AND COMMENTARY ON ENTROPY INCREASE DURING TWO-BODY HEAT CONDUCTION

作　　者：何小勇 李品钧 叶海[1] HE Xiaoyong;LI Pinjun;YE Hai(School of Telecommunications Engineering and Automation,Dongguan University of Technology,Dongguan,Guangdong 523808;Department of Information Science,Zhanjiang Preschool Education College,Zhanjiang,Guangdong 524084)

机构地区：[1]东莞理工学院电信工程与智能化学院,广东东莞523808 [2]湛江幼儿师范专科学校信息科学系,广东湛江524084

出　　处：《物理与工程》2025年第1期42-45,共4页Physics and Engineering

基　　金：广东省本科高校教学质量与教学改革工程建设项目“光电子学课程教学改革研究”(粤教高函[2021]29号)。

摘　　要：孤立系统中两个不同温度物体的热接触过程是一个不可逆过程,因而在此过程中体系的熵会增加。现存教科书均未对此结论给出严格的证明,Lima发表的论文对此给出了一个优美而简洁的证明,但是其证明过程仍然存在两个问题:(1)假定物体的热容是一个常量,这在多数实际情况下并不成立;(2)证明过程中用到了一个关于函数曲线凹凸性的不等式,这个不等式对初学者而言仍然较为生僻。本文就第(1)个问题给出了另外两种较为严格且非常简单直观的证明,就第(2)个问题利用初等几何方法给出了另一种证明,供初学者参考。The process of thermal contact between two objects at different temperatures in an isolated system is an irreversible process,hence the entropy of the system will increase during this process.Existing textbooks do not provide a rigorous proof for this conclusion.Lima's published paper offers an elegant and concise proof,but there are still two issues with the proof:1.It assumes that the heat capacity of the object is a constant,which is not true in most real situations.2.The proof process uses an inequality about the concavity of a function's curve,which is still relatively obscure to beginners.This paper provides two alter-native proofs that are more rigorous and intuitively simple for the first issue,and for the second is-sue,it offers another proof using elementary geometric methods for reference by beginners.

关 键 词：热传导 熵增加原理 热力学第二定律 

分 类 号：O414.1[理学—理论物理]