热 学

热 学

Thermophysics

穆良柱

课程简介

• 课程名称：热学

• 学分：3

• 上课时间地点: 周一3-4 ，周四7-8(单周)，理教402

• 成绩评定：平时10；期中40；期末50.

• 助教：叶柄天，18811792232，yebingtian@126.com 韩兆宇，15652626191，heinsius@pku.edu.cn 李泽阳，13901221673，laser.li@pku.edu.cn

• 答疑时间和地点：预约，理教111

• 联系方式： 穆良柱，13681016237，muliangzhu@pku.edu.cn

教材与参考书

• 教材讲义 ppt讲义

刘玉鑫，《热学》，北京大学出版社，2016年4月；

习题，李椿《热学》，第二版，高等教育出版社，2008年。

• 参考书

(1)赵凯华、罗蔚茵，新概念物理教程《热学》,高等教育出版社,1998；

(2)包科达,《热物理学基础》，高等教育出版社，2002；

(3)陆果,《基础物理学》下卷，高等教育出版社，1997；

(4)林宗涵,《热力学与统计物理学》，北京大学出版社，2007。

• 1 热学简介 作业：

• 2 第零定律和温度 作业：1.8，1.10

• 3 状态方程 作业：1.25，1.32

• 4 物质微观图像 作业：7.1，7.3

• 5 理想气体微观初级理论 作业：2.14，2.20

• 6 麦克斯韦速度分布律 作业：3.19，3.25

• 7 麦玻分布与能均分定理 作业：3.24，3.30

• 8 基于量子力学的麦玻分布 作业：6.30

• 9 麦玻分布的检验与F-D分布、B-E分布 作业：

• 10 气体分子的碰撞 作业：4.8，4.12

• 11 气体的输运过程 作业：4.18，4.21

• 12 热力学第一定律 作业：5.12，5.16

• 13 热力学第一定律的应用 作业：5.24，5.29

• 14 卡诺定理与热力学第二定律 作业：6.7，6.8

• 15 克劳休斯不等式与熵 作业：6.27，6.24

• 16 热力学第二定律的应用和讨论 作业：6.28，6.29

• 17 热力学基本微分方程 作业：6.9，6.10

• 18 热力学理论的应用 作业：6.13，6.17

• 19 热辐射系统 作业：

• 20 液体表面的热力学 作业：8.2，8.5

• 21 相变现象及其热力学 作业：9.2，9.13

• 22 范氏气体与气液相变 作业：9.8，9.12

课程目录

课程进度

周数 日期 星期 地点 上课时间 进度 教学内容 习题（李椿《热学》第二版）

1 2月20日 周一 理教402 10:10-12:00 01 什么是物理？什么是热学？

2月23日 周四 理教402 15:10-17:00 02 温度与热力学第零定律 1.8，1.10 2 2月27日 周一 理教402 10:10-12:00 03 理想气体的状态方程 1.25，1.32 3 3月06日 周一 理教402 10:10-12:00 04 物质的微观图像 7.1，7.3

3月09日 周四 理教402 15:10-17:00 05 理想气体微观初级理论 2.14，2.20 4 3月13日 周一 理教402 10:10-12:00 06 麦克斯韦速度分布律及其验证 3.19，3.25 5 3月20日 周一 理教402 10:10-12:00 07 麦玻分布及其验证(能均分定理) 3.24，3.30

3月23日 周四 理教402 15:10-17:00 08 量子版本的麦玻分布及其验证 6.30 6 3月27日 周一 理教402 10:10-12:00 09 F-D统计与B-E统计及其应用

7 4月03日 周一 理教402 10:10-12:00 10 气体分子碰撞的微观描述 4.8，4.12 4月06日 周四 理教402 15:10-17:00 11 输运过程 4.18，4.21 4月09日 周日 理教111 18:00-21:00 答疑

8 4月10日 周一 理教402

10:10-12:00

12 期中考试

9 4月17日 周一 理教402 10:10-12:00 13 热力学过程与热力学第一定律 5.12，5.16 4月20日 周四 理教402 15:10-17:00 14 第一定律的应用 5.24，5.29 10 4月24日 周一 理教402 10:10-12:00 15 卡诺定理与热力学第二定律 6.7，6.8

4月25日 周二 理教303

18:40-20:30 16 克劳修斯不等式与热力学第二定律的熵表述6.27，6.24

13 5月15日 周一 理教402 10:10-12:00 17 第二定律的应用与讨论（其他表述，质疑，信息熵等）6.28，6.29 5月18日 周四 理教402 15:10-17:00 18 热力学基本微分方程（理想气体上的验证）6.9，6.10

14 5月22日 周一 理教402 10:10-12:00 19 热力学理论的应用（范氏气体，橡皮筋，磁介质）6.13，6.17 15 5月29日 周一 理教402 10:10-12:00 20 相变现象及其热力学 9.2，9.13

6月01日 周四 理教402 15:10-17:00 21 范氏气体与气液相变，连续相变理论，多元系统9.8，9.12 16 6月05日 周一 理教402 10:10-12:00 22 液体表面的热力学 8.2，8.5

6月11日 周日 理教111 18:00-21:00 答疑

17 6月12日 周一 理教402

10:10-12:00

23 期末考试

热学简介

• 什么是热学？ 关于热现象的研究。

热学研究对象 —热现象

热现象

加热一块未名湖的冰会发生什么？

热学的研究对象

热现象 热运动

和温度有 关的现象

大量粒 子组成 的系统

10 ²³

和大量微观粒子无规则热运动有关的现象

热现象的本质

300B.C.

500B.C.

热动说

热质说

1788

1798 1799 1840-1849 1850

热质说认为热是一种特殊的 物质，称之为caloric热质，

热质由没有重量的微细粒子 组成，可以从一个物体流向 另一个物体，其数量守恒

战 国

， 驺 衍

， 五 行 说

， 水

、 火

、 木

、 金

、 土

H er acl itus(

赫 拉 克 利 特

)

四 种 元 素

， 火

、 水

、 土

、 气

1600s

培根 胡克 牛顿 笛卡尔

伽利略 伽桑狄 玻意耳?

英国,化学兼 物理学家 J.Black(布莱 克)提出温度、

热量概念，

完善量热学，

提出热量守 恒

H. Davy (

戴维) 冰摩擦

英国著名业 余科学家，

焦耳，400余 次，热功当 量4.154J/cal

热是组成物质的 微观粒子运动的 表现，热是能量 的一种表现形式，

可以由其他功转 化而来

Rumford

克劳修斯，热

是分子热运动，

论文《关于我 们称为热的这 种运动》

美国,伦福 德伯爵, 大炮膛孔

Clausius Joule

热力学 系统 环境

粒子源 ^封闭系

热源

绝热系

功

力

开放系

孤立系

热力学系统

热力学

系统 ^成分 单元系

多元系

均匀

单相系

复相系

热力学系统

热力学 系统

热力学 系统 热力学

系统

热力学 系统

时间

热力学 系统 热力学

系统

平衡态 稳恒态

是

是

是

否

否

否

否

否 孤立

非孤立

热力学系统

平衡态

平衡态

没有外界影响 宏观性质长时间不变

宏观：静 微观：动

热动平衡 力学平衡

热平衡

化学反应 化学平衡

化学势

临界乳光现象 涨落 涨落理论

平衡态实际上是一个理想化的概念，因为在实际问题中，不存在完全没有外 界影响的系统；

但是如果外界条件的变化速率相对于系统自身由非平衡态趋向于平衡态的速 率( 弛豫 )足够缓慢的话，平衡态的概念就是实际情况的一个合理的抽象和近似。

最概然状态

平衡态

气缸中气体达到平衡 态的弛豫时间量级为 平均碰撞时间 10 ^-9 秒

活塞运动一次时

间为 10 ^-4 分钟

最简单的研究对象

孤立的 单元的 单相的

处于平衡态的

系统

气体中的输运过程

热传导现象

扩散现象 粘滞现象

Flow Direction Flow Direction

N ² O ²

valve

N ² O ²

valve

非 平 衡 态

近 平 衡 态

输 运 过 程

电 流

局域平衡假设，

即假设系统由一 系列达到平衡态 的微元组成，对 整个系统的描述 就是由对每一个 平衡态微元的描 述而组成的

偏离 平衡 态不 远的 系统

热力学过程

平衡态 不随时间变化 不与外界发生相互作用

热力学过程 随时间变化 与外界发生相互作用 准静态过程

quasi-steady process

可逆过程

reversible process

进行的足够缓 慢，以至于系 统连续经过的 每个中间态都 可近似地看成 平衡态的过程

一个系统由某一状态出发，经过 某一过程达到另一状态，如果存在另 一过程，它能使系统和外界完全复原

（即系统回到原来的状态，同时消除 了系统对外界引起的一切影响），则 原来的过程称为可逆过程；反之，如 果用任何方法都不可能使系统和外界 完全复原，则原来的过程称为不可逆 过程;

无摩擦的准静态过程是可逆过程

全球气候变暖

原子弹爆炸 不可再生资源

相变现象及其实验规律

等温压缩实验

熔解曲线

升华曲线 汽化曲线

• 1，从p-T图上看来，发生相变 时， p和T满足特定的关系 ，而 与体积无关(从p-V图上看来相变 只发生在一定的体积区间内)，

所以发生相变时独立状态参量 只有一个。

• 2，一般说来，物质从固体变为 液体，从液体变为气体，体积 都会膨胀(一个特例是水变成冰 体积会增大)，或者说 体积发生 变化。

• 3，物质发生相变时通常会吸放 热量，比如等温过程中，压缩 蒸气凝聚成水时，要放出热量，

这些被统称为相变潜热。

• 4， 临界点处体积气液两相体积

连续变化、没有相变潜热(熵连

续变化)、有临界乳光现象

热学内容简介

系统

平衡态

过程

近平 衡态

相变 平衡态

近平 衡态

相变 非平衡态

描述

规律

描述

规律

描述

规律 描述

规律 描述

规律

描述

规律

状态参量pTV 响应函数C、α、β、κ

第零定律

物态方程

做功W、传热Q U、H、S、F、G

卡诺定理

第一、二、三定律

局域平衡假设 流、梯度力 牛顿黏性、傅里叶热传

导、菲克扩散定律 相变现象、分类

平衡判据、条件 克拉珀龙方程、相变理论 粒子大小、位置、速度、质量、

动量、能量、角动量、自旋等；

粒子间相互作用；物质的量；

微观态 经典力学 等概率假设 各态历经假设 细致平衡原理 量子力学

M-B分布 B-E分布 F-D分布

碰撞截面、自由程、碰 撞频率；平均自由程、

平均碰撞频率 气体输运理论 玻尔兹曼方程 涨落理论 平均场、标度 律、重整化

统 计 平 均

微观 宏观

陆果，《基础 物理学》下卷

热学的研究方法和研究结论

热 力 学

统 计 物 理 学 宏观

微观

1840-1849

焦耳 热功 当量

迈耶

《论 无机 界的 力》

1842 1847

亥姆霍 兹《论 力的守 恒》

卡诺定理

《关于热 的动力的 思考》

1824

克劳修斯

《论热的 动力和由 此得出的 热学定律》

1850

汤姆孙

《论热 的动力 理论》

等三篇 论文

1851 1930s-40s 1960s-70s

昂萨格、

卡西米尔、

普里高津、

德格鲁特 等人发展 了非平衡 态热力学 的线形理 论

普里高津 学派耗散 结构理论，

哈根学派 (Haken)协 同学，解 释非平衡 热力学的 非线性理 论

克劳修斯

《论热的 动力理论 的主要方 程的各种 应用形式》

1865

克劳修 斯发表 了一篇 非常重 要的论 文《论 我们称 之为热 的运动》

1857

克劳修 斯《关 于气体 分子运 动的平 均自由 程》

1858 1866

麦克斯 韦《气 体的动 力理论》

1877

玻尔兹曼

《关于热 动力学第 二定律与 概率的关 系、或热 平衡定律》

1924–25

玻色、爱因 斯坦统计

1926–27

费米、狄 拉克统计

平衡态统计理论、非平衡态统计理论、涨落理论 热力学三定律，耗散结构理论等

1902

吉布斯

《统计 力学基 本原 理》,统 计系综 理论

1927

John von Neumann,

mathematical

foundations of quantum mechanics 量子统计力学

。。。

第零定律和温度

作业

• 1.8，1.10

我们的研究对象

孤立的 单元的 单相的

处于平衡态的

系统

状态参量

处于平衡态的系统，其宏 观性质不随时间变化，从 而相应描述该系统的可观 测量有确定的数值和意义

宏观 状态 温度T 参量

压强p 体积V 熵S 内能U 焓H

自由能F

吉布斯函数G 无

记 忆 性

物态方程 f(T,p,V)=0

态函数

响应 函数

C d Q

 dT 1

p

V V T

 _{ } ^{  } _

  

1

V

p p T

 _{ } ^{  } _

   1

T

T

V V p

 _{  } ^{  } _

  

相对压 力系数 体膨胀 系数

等温

压缩

系数

• 宏观状态参量按照随系统大小变化 的性质分为两类，强度量和广延量。

当系统的大小改变时，广延量的值 必然发生变化，而强度量则不变。

宏观状态参量的分类

+

=

1mol 1mol 2mol

压强p 温度T

体积V 熵S 内能U

压强p 温度T

体积V 熵S 内能U

压强p 温度T

体积2V 熵2S 内能2U

• 需要注意的是广延量通过适当的定义也可以变成 强度量，通常是将广延量除以物质的量。

• 而按照状态参量的本身性质，可以分为几何参量、

力学参量、化学参量、电磁参量以及热学特有的

热学参量 — 温度。

备注 广延量 强度量 几何 力学 化学 电磁 热学

熵S √

温度T √ √

体积V √ √

压强p √ √

物质的量 √ √

ln S k W dS d Q

T





摩尔质量 √ √

电场强度E √ √

磁场强度H √ √

极化强度P √ √

磁化强度M √ √

粒子数N √ √

化学势μ √

,

T p

G

 _{ } ^{ } N ^ _

  

内能U dU=TdS-pdV √

焓H H=U+pV √

亥姆霍兹自 由能F

F=U-TS √ 吉布斯函数

G

G=U+pV-TS √

备注 广延量 强度量 几何 力学 化学 电磁 热学

热容量C √ √

体膨胀系数 α √ √

C d Q

 dT

1

p

V

V T



_{ }^{ }_

  

相对压力系 数 β

√ √

等温压缩系 数 κ _T

√ √

1

V

p

p T

 _{ } ^{  } _

  

1

T

T

V

V p



_{  }^{ }_

  

温度 温标 第零定律

冷热程度 温度T 分子热

运动剧 烈程度

温度标定

1931(?9) Fowler

第零定律

1593 伽利略 验温器

1714

Fahrenheit

华氏温标

1742

Celsius

摄氏温标

1848,1854 Kelvin 热力学温标

？1940 理想气体温标 经验温标

寒冬摸铁 器和木器 冷水热水

宏观 微观

空气 气压p

温度

水银 体积V

温度t

测温物质

测温属性 固定点

炉火纯青

理想气体温标

0 (1 _p ) p  p  a t

0

0

0 o 0

lim 1

273.15 C

p a p

T T







0 273.15 T   t T   t

0

0 0

0 0 0

lim p

T T p p T T p

 p





Ideal Gas

一个标准大气压下水的冰点定 为0度，水的沸点定为100度

理想气体温标 符号T，单位K

1954年，固定点选为水 的三相点，T _tr =273.16K

p 摄氏温标

t

0 100

-1/a

p

p

0

-273.15

a p

p 0

N 2

N e

H 2

H e

1/273.15

p

t

0 100

-1/a

p

= -273.15 p

0

0 273.15 373.15 T

热力学第三定 律（有多种表

述方式，其中 一种是不可能 使一个物体经 过有限的步骤 冷却到绝对零 度的温度）告 诉我们-273.15

o

C是所有可能 达到温度的最 低极限，其本 身是达不到的

0

273.15

T   t T   t

热力学温标

2 2

1 1

( ) ( ) Q

Q





 



 ( )   

热力学温标 开尔文温标

2 1 2 1

1 Q Q / 1 /

      

2 1

1 T T /

  

以最低温度为零 点，称做绝对温 标，对应温度称 做绝对温度，现 统称热力学温度

卡诺定理：工作于两个 恒定温度之间的一切可 逆卡诺热机的效率与工 作物质无关，只是两热 源温度的函数。

1954年，水的 三相点273.16K

理想气 体温标

2 3 3 2

1 2

1 3 3 1

/ ( , )

( , )

/ ( , )

Q Q f

f Q Q f

     

 

1

3 1

3

( , ) Q f

Q    ² _{1 2}

1

( , )

Q f

Q    ² _{3 2}

3

( , ) Q f

Q   

Θ 3

Θ 1 Q

3

Q

1

Θ 3

Θ 2 Q

3

Q

2

1 2 2

1 1 1

QQ

1

Q

W

Q Q Q

   ^  

1

31

3

( , ) Q f Q   

2

32

3

( , ) Q f Q   

2

12

1

( , ) Q f Q    Θ 1

Θ 2 Q

1

Q

2

W

热力学第零定律

热平衡定律

实验事实

可以用一个温 度计去判定不 同的物体温度 是否相同

互为热平衡的热力学系 统具有一个数值相等的 状态函数，定义为温度 将A、B作为温度计测 量C的温度，则A、B应 有相同读数，这就是校 准不同温度计的依据。

T _A =T _C T _B =T _C

T _A =T _B

李椿《热学》P26-27

温度大观

存在着10 ⁹ 种生物大分子

如果温室效应使得平均气温 升高3度，海平面将上涨2-5 米，迫使10亿人背井离乡

冰河期下降10度，

大批物种灭绝

} 

Iter国际热核 聚变实验堆

冶金 纵火 液氧90K 液氮77K

1908Onnes液氦4K

1956莱顿大学 绝热去磁1.4mK

2000

Helsinki University of Technology

100pK 1898Dewar液氢20K

LHC

状态方程

作业

• 1.25，1.32

状态方程(物态方程) ( , , , ) 0 f p T V 

系统 描述

响应函数C、α、β、κ 状态参量pTV

Ideal Gas van der Waals Gas pure matter and …

理想气体的物态方程

Perfect Gas

1/ 273.15 1/ 273.15

p V









pVT

pV R T  

0 0 0

pV p V

T  T  R

Boyle's law

Charles's law Gay-Lussac's law

pV  p V 0 0 ⁰

0 0

(1 ) /

V V V t

V V T T



 



Avogadro constant

Boltzmann constant

5 0

0

1.01 10 273.15

p Pa

T K

 



标准状况

Avogadro’s law

0 22.414

V  L

微观模型

1 1

8.31

R  J mol  ^  K ^

23 1 23

6.02 10 , 1.38 10 /

A B

N   mol ^ k   ^ J K

B A

N R Nk

 N 

Robert Boyle

born January 25, 1627, Lismore Castle, County Waterford, Ireland died December 31, 1691, London, England British natural philosopher and theological writer, a preeminent figure of 17th-century intellectual culture. He was best known as a natural philosopher, particularly in the field of chemistry, but his scientific work covered many areas including hydrostatics, physics, medicine, earth sciences, natural history, and alchemy.

His prolific output also included Christian devotional and ethical essays and theological tracts on biblical language, the limits of reason, and the role of the natural philosopher as a Christian. He sponsored many religious missions as well as the translation of the Scriptures into several languages. In 1660 he helped found the Royal Societyof London.

Gay-Lussac, Joseph-Louis

born December 6, 1778, Saint-Léonard-de-Noblat, France died May 9, 1850, Paris

French chemist and physicist who pioneered investigations into the behaviour of gases, established new techniques for analysis, and made notable advances in applied chemistry.

Avogadro, Amedeo

lithograph, 1856 born August 9, 1776 , Turin, in the Kingdom of Sardinia and Piedmont died July 9, 1856, Turin, Italy

in full Lorenzo Romano Amedeo Carlo Avogadro, conte di Quaregna e Cerreto Italian mathematical physicist who showed in what became known as Avogadro's lawthat, under controlled conditions of temperature and pressure, equal volumes of gases contain an equal number of molecules.

例题：由响应函数得到状态方程

T p V p V

T V

T V ( ) ( )

lim ^{1 1}

0  

 



 

 

T V p V p

T p

T p ( ) ( )

lim ^{1 1}

0 









 

 

p T V T V

p V

p V ( ) ( )

lim ^{1 1}

0  

 



   

 

 p

 

1 0

1 3

1 3

10 10 10

















atm K K







1 6

1 2

~ 1

1 4

10 10 10

















atm K K







1 7

1 3

1 3

10 10 10

















atm K

K





 气体

液体

固体

例题：由响应函数得到状态方程

V dV dT

p

V dV dT p

T dp p

T V p p

T V

 ¹  )

, (





 

 







 

 

 







 



dp V

dT V

p dp dT V

T dV V

p T V V

p T



 



 

 







 

 

 







 

 ( , )

p T

T , 1 / , 1 / /

1  

  



T d

pV d

V dV T

dT p

dp

V dV dT p

T dp p

ln ln 









T d

pV d

p dp T

dT V

dV

p dp dT V

T dV V

ln ln 









混合理想气体的物态方程

1 1

1 1

1

B

p V m

R R N k

T 

   

2 2

2 2

2

B

p V m

R R N k

T 

   

B

pV m

R R Nk

T 

   

1 2

p  p  p 道尔顿分压定律

1 2

1 2

1 2

N N N

m m m

    

 

 

 1 2  1 2

1 2 2 1

m m

m m

  

 

 



平均摩尔质量

混合理想气体状态方程

van der Waals Gas and Onnes Equation

实际气体

Perfect Gas

Van der Waals Gas Onnes Equation

2 3

2 ( ) 3 ( )

B

p n B T n B T n

k T     ^{p a} ₂  ^{v b}  ^RT

v

    

 

 

pV  RT

van der Waals, 1873, doctoral treatise “On the Continuity of the Liquid and Gaseous State”

分子间相互作用 排斥与吸引

n=N/V数密度 位力系数

Kamerlingh Onnes

我很高兴把液体氦 送给我最尊敬的朋 友范德瓦尔斯，是 他的理论一直指导 了这个气体的液化

液体

相变

2

3 1 8

3 3

  



     

  

  

2

, 3 , 8

27 27

, ,

c c c

c c c

a a

p v b T

b Rb

p  p v  v T  T

  

  

范氏对比方程

李椿，《热学》，P50-52

Waals, Johannes Diederik van der

Dutch physicist,winner of the 1910 Nobel Prize for Physics for his research on

the gaseous and liquid states of matter. His work made the study of

temperatures near absolute zero possible.

A self-educated man who took advantage of the opportunities offered by the University of Leiden, van der Waals first attracted notice in 1873 with his doctoral treatise “On the Continuity of the Liquid and Gaseous State,” for which he was awarded a doctorate. In pursuing his research, he knew that the ideal-gas law could be derived from the kinetic theory of gases if it could be assumed that gas molecules have zero volume and that there are no attractive forces between them. Taking into account that neither assumption is true, in 1881 he introduced into the law two parameters (representing size and attraction) and worked out a more exact formula, known as the van der Waals equation. Since the parameters were distinct for each gas, he continued his work and arrived at an equation (the law of corresponding states) that is the same for all substances.

It was this work that brought him the Nobel Prize and also led Sir James Dewar of England and Heike Kamerlingh Onnes of The Netherlands to the determination of the necessary data for the liquefaction of hydrogen and helium.

Van der Waals was appointed professor of physics at the University of Amsterdam in 1877, a post he retained until 1907. The van der Waals forces, weak attractive forces between atoms or molecules, were named in his honour.

born Nov. 23, 1837, Leiden, Neth. died March 9, 1923, Amsterdam

Kamerlingh Onnes, Heike

born Sept. 21, 1853, Groningen, Neth. died Feb. 21, 1926, Leiden

Dutch winner of the Nobel Prize for Physics in 1913 for his work on low-temperature physics and his production of liquid helium. He discovered superconductivity, the almost total lack of electrical resistance in certain materials when cooled to a temperature near absolute zero.

From 1871 until 1873 Kamerlingh Onnes studied and

worked at Heidelberg University, notably with the German

physicists Robert Bunsenand Gustav Kirchhoff. Awarded a

doctorate by the University of Groningen (1879), he taught

at the Polytechnic School in Delft (1878–1882). From 1882

to 1923 he served as professor of experimental physics at

the University of Leiden.

例题

写出m摩尔范德瓦耳斯气体的状态方程

将范德瓦耳斯气体状态方程写成昂尼斯方程的形式，

求出其位力系数

 

2 2

p m a V mb mRT V

 

  

 

 

2

2 3

2 2

B A A B A

p b a b

n n n

k T N TN k N

 

      

 

纯物质的pVT图

纯物质 pVT系统

0.00004

0.00006

0.00008

0.0001

0.00012 200

300 400

500 600

-2 108 -1 108 0 1 108

0.00004

0.00006

0.00008

0.0001

0.00012 0.005

0.01

0.015

0.02 200

250 300

350 500000

1 106

0.005

0.01

0.015

0.02 0.005

0.01

0.015

0.02 200

250 300

350 500000

1 106

0.005

0.01

0.015

0.02

0.005 0.01 0.015 0.02

200 250

300 350 500000 1 10

6

0.005 0.01 0.015 0.02

理想气体

0.00004

0.00006

0.00008

0.0001

0.00012 200

300 400

500 600

-2 108 -1 108 0 1 108

0.00004

0.00006

0.00008

0.0001

0.00012

0.00004

0.00006 0.00008 0.0001 0.00012

200 300 400 500 600

-2 10 8 -1 10 8 0 1 10 8

0.00004

0.00006 0.00008 0.0001 0.00012

范氏气体

物态方程举例

( , ) ( )( 0 ) F T L  C T L  L

金属丝 磁介质

/ M  CH T

电介质

( / ) P  a b T E 

热辐射

4

3 p  a T

胡克定律 居里定律

物质微观图像

作业

• 7.1，7.3

物质的微观理论 —物质结构

Dalto n原子 模型

Brownian motion

1828

1897

JJThom son发现 电子

Ruthorford alpha粒子 散射实验

1919

Ruthorfo rd α粒子 轰击氮原 子，发现 质子

卢瑟福的 学生查德 威克用质 子轰击铍 核，发现 中子

1932

海森堡提 出原子核 由中子和 质子构成

高能电子对 核子结构的 探测表明内 部存在更小 的结构，被 称为部分子

盖尔曼提出 夸克模型，

提出用夸克 来构造各种 粒子

超对称 超弦

1800s

1911

2013 Higgs

1968 1961

LHC

1968--today

量子力学

电子显微镜可以直接看到原子

Thomson, Sir J.J.

born Dec. 18, 1856, Cheetham Hill, near Manchester, Eng. died Aug. 30, 1940, Cambridge, Cambridgeshire

in full Sir Joseph John Thomson English physicist who

helped revolutionize the knowledge of atomic structure by his discovery of the electron (1897). He received the Nobel Prize for Physics in 1906 and was knighted in 1908.

“浸入式”原 子模型:认为原 子是由带正电 的均匀连续体 和在其中运动 的负电子构成

Ruthorford alpha粒子散射实验

Feynman, Richard P.

born May 11, 1918, New York, New York, U.S. died February 15, 1988, Los Angeles, California

in full Richard Phillips Feynman American theoretical physicist who was widely regarded as the most brilliant, influential, and iconoclastic figure in his field in the post-World War II era.

Feynman remade quantum electrodynamics—the theory of the interaction between light and matter—and thus altered the way science understands the nature of waves and particles. He was co-awarded the Nobel Prize for Physics in 1965 for this work, which tied together in an experimentally perfect package all the varied phenomena at work in light, radio, electricity, and magnetism. The other cowinners of the Nobel Prize, Julian S. Schwingerof the United States and Tomonaga Shin'ichirōof Japan, had independently created equivalent theories, but it was Feynman's that proved the most original and far-reaching. The problem-solving tools that he invented—including pictorial representations of particle interactions known as Feynman diagrams—permeated many areas of theoretical physics in the second half of the 20th century.

Born in the Far Rockaway section of New York City, Feynman was the descendant of Russian and Polish Jews who had immigrated to the United States late in the 19th century. He studied physics at the Massachusetts Institute of Technology, where his undergraduate thesis (1939) proposed an original and enduring approach to calculating forces in molecules. Feynman received his doctorate at Princeton University in 1942. At Princeton, with his adviser,John Archibald Wheeler, he developed an approach to quantum mechanics governed by the principle of least action. This approach replaced the wave-oriented electromagnetic picture developed by James Clerk Maxwellwith one based entirely on particle interactions mapped in space and time. In effect, Feynman's method calculated the probabilities of all the possible paths a particle could take in going from one point to another.

During World War II Feynman was recruited to serve as a staff member of the U.S. atomic bomb project at Princeton University (1941–42) and then at the new secret laboratory at Los Alamos, New Mexico (1943–45). At Los Alamos he became the youngest group leader in the theoretical division of the Manhattan Project. With the head of that division, Hans Bethe, he devised the formula for predicting the energy yield of a nuclear explosive. Feynman also took charge of the project's primitive computing effort, using a hybrid of new calculating machines and human workers to try to process the vast amounts of numerical computation required by the project.

He observed the first detonation of an atomic bomb on July 16, 1945, near Alamogordo, New Mexico, and, though his initial reaction was euphoric, he later felt anxiety about the force he and his colleagues had helped unleash on the world.

At war's end Feynman became an associate professor at Cornell University (1945–50) and returned to studying the fundamental issues of quantum electrodynamics. In the years that followed, his vision of particle interaction kept returning to the forefront of physics as scientists explored esoteric new domains at the subatomic level. In 1950 he became professor of theoretical physics at the California Institute of Technology (Caltech), where he remained the rest of his career.

Five particular achievements of Feynman stand out as crucial to the development of modern physics. First, and most important, is his work in correcting the inaccuracies of earlier formulations of quantum electrodynamics, the theory that explains the interactions between electromagnetic radiation (photons) and charged subatomic particles such as electrons and positrons (antielectrons). By 1948 Feynman completed this reconstruction of a large part of quantum mechanics and electrodynamics and resolved the meaningless results that the old quantum electrodynamic theory sometimes produced. Second, he introduced simple diagrams, now called Feynman diagrams, that are easily visualized graphic analogues of the complicated mathematical expressions needed to describe the behaviour of systems of interacting particles. This work greatly simplified some of the calculations used to observe and predict such interactions.

In the early 1950s Feynman provided a quantum-mechanical explanation for the Soviet physicist Lev D. Landau's theory of superfluidity—i.e., the strange, frictionless behaviour of liquid helium at temperatures near absolute zero. In 1958 he and the American physicist Murray Gell-Manndevised a theory that accounted for most of the phenomena associated with the weak force, which is the force at work in radioactive decay. Their theory, which turns on the asymmetrical “handedness” of particle spin, proved particularly fruitful in modern particle physics. And finally, in 1968, while working with experimenters at the Stanford Linear Accelerator on the scattering of high-energy electrons by protons, Feynman invented a theory of “partons,” or hypothetical hard particles inside the nucleus of the atom, that helped lead to the modern understanding of quarks.

Feynman's stature among physicists transcended the sum of even his sizable contributions to the field. His bold and colourful personality, unencumbered by false dignity or notions of excessive self-importance, seemed to announce: “Here is an unconventional mind.” He was a master calculator who could create a dramatic impression in a group of scientists by slashing through a difficult numerical problem. His purely intellectual reputation became a part of the scenery of modern science. Feynman diagrams, Feynman integrals, and Feynman rules joined Feynman stories in the everyday conversation of physicists. They would say of a promising young colleague, “He's no Feynman, but . . .” His fellow physicists envied his flashes of inspiration and admired him for other qualities as well: a faith in nature's simple truths, a skepticism about official wisdom, and an impatience with mediocrity.

Feynman's lectures at Caltech evolved into the books Quantum Electrodynamics (1961) and The Theory of Fundamental Processes (1961). In 1961 he began reorganizing and teaching the introductory physics course at Caltech; the result, published as The Feynman Lectures on Physics, 3 vol. (1963–65), became a classic textbook. Feynman's views on quantum mechanics, scientific method, the relations between science and religion, and the role of beauty and uncertainty in scientific knowledge are expressed in two models of science writing, again distilled from lectures: The Character of Physical Law (1965) and QED: The Strange Theory of Light and Matter (1985).

Gell-Mann, Murray born September 15, 1929, New York, New York, U.S.

American physicist, winner of the Nobel Prize for Physics for 1969 for his work pertaining to the classification of subatomic particles and their interactions.

Having entered Yale University at the age of 15, Gell-Mann received his B.S. in physics in 1948 and his Ph.D. at the Massachusetts Institute of Technology in 1951. His doctoral research on subatomic particles was influential in the later work of the Nobel laureate (1963) Eugene P.

Wigner. In 1952 Gell-Mann joined the Institute for Nuclear Studies at the University of Chicago. The following year he introduced the concept of “strangeness,” a quantum property that accounted for previously puzzling decay patterns of certain mesons. As defined by Gell- Mann, strangeness is conserved when any subatomic particle interacts via the strong force—i.e., the force that binds the components of the atomic nucleus.

In 1961 Gell-Mann and Yuval Ne'eman, an Israeli theoretical physicist, independently proposed a scheme for classifying previously discovered strongly interacting particles into a simple, orderly arrangement of families. Called the Eightfold Way(after Buddha's Eightfold Path to Enlightenment and bliss), the scheme grouped mesons and baryons (e.g., protons and neutrons) into multiplets of 1, 8, 10, or 27 members on the basis of various properties. All particles in the same multiplet are to be thought of as variant states of the same basic particle. Gell-Mann speculated that it should be possible to explain certain properties of known particles in terms of even more fundamental particles, or building blocks.

He later called these basic bits of matter “quarks,” adopting the fanciful term from James Joyce's novel Finnegans Wake. One of the early successes of Gell-Mann's quarkhypothesis was the prediction and subsequent discovery of the omega-minus particle(1964). Over the years, research has yielded other findings that have led to the wide acceptance and elaboration of the quark concept.

Gell-Mann joined the faculty of the California Institute of Technology, Pasadena, in 1955 and was appointed Millikan professor of theoretical physics in 1967 (emeritus, 1993). He published a number of works, notable among which are The Eightfold Way (1964), written in collaboration with Ne'eman;

Broken Scale Variance and the Light Cone (1971), coauthored with K. Wilson; and The Quark and the Jaguar (1994).

Building Blocks of Hadron World

Proton Neutron (uud) (udd)

Mesons (q-q)

Exotics (qqqq-q,…) Molecules

Atoms

Electrons Nucleus

Hyperons (s…)

物质的微观理论 —相互作用

强相互作用 弱相互作用

电磁相互作用

物质的微观理论 —分子间相互作用

结合能 平衡位置

10 ^-10 m

0.1～5eV

共价键 离子键 金属键

范德瓦

尔斯键 氢键

分子间相互作用举例，

包科达《热物理学基

础》，P44-46

Perrin, Jean

born Sept. 30, 1870, Lille, France died April 17, 1942, New York, N.Y., U.S.

in full Jean-Baptiste Perrin French physicist who, in his studies of the Brownian

motion of minute particles suspended in liquids, verified Albert Einstein's explanation

of this phenomenon and thereby confirmed the atomic nature of matter. For this achievement he was honoured with the Nobel Prize for Physics in 1926.

Educated at the École Normale Supérieure, Paris, Perrin joined the faculty of the University of Paris (1898) where he became professor of physical chemistry (1910–40).

In 1895 he established that cathode rays are negatively charged particles (electrons).

His attempt to determine the mass of these particles was soon anticipated by the work of J.J. Thomson.

About 1908 Perrin began to study Brownian motion, the erratic movement of particles suspended in a liquid.

Einstein's mathematical analysis (1905) of this phenomenon suggested that the particles were being jostled by the randomly moving water molecules around them. Using the newly developed ultramicroscope, Perrin carefully observed the manner of sedimentation of these particles and provided experimental confirmation of Einstein's equations. His observations also enabled him to estimate the size of water molecules and atoms as well as their

quantity in a given value. This was the first time the size of atoms and molecules could be reliably calculated from actual visual observations. Perrin's work helped raise atoms from the status of useful hypothetical objects to observable entities whose reality could no longer be denied.

物质的微观理论 —分子热运动

爱因斯坦(1905年)和斯莫陆绰斯 基(Smoluchowski,1906年)、郎之 万(Langevin,1908年) 关于布朗运 动的理论工作，证明了布朗粒子 位移平方的平均值正比于时间t

1908年皮 兰(Perrin) 实验证实

Fig. 1 Fluctuation of HSI during the period Jan. 3, 1994 to Nov. 30, 2000. The period is characterized by the 1995

‘bearish market’ and the 1997-98 crash.

Steven Zhu

2 2

2 2 2 2

2

2 2 2

2 2

( )

2 2 ( )

2

, 0

B

d x dx

m F t

dt dt

d x dx dx

m m xF t

dt dt dt

d x d x

m k T

dt dt

x Tt m







 

 

      

 

 

cooling and trapping atoms using laser light

证实原子存在的人

赵凯华新概念《热学》P258-260

1911年布魯塞爾舉行的Solvay會議

Brownian motion

英国植物学家布朗(R. Brown)在显微镜下观察到 悬浮在静止液体里的花粉不停地做无规则运动。

Steven Chu 朱棣文

Chu served as the 12th United States Secretary of Energy from 2009 to 2013. At the time of his appointment as Energy Secretary, Chu was a professor of physics and molecular and cellular biology at the University of California, Berkeley, and the director of the Lawrence Berkeley National Laboratory, where his research was concerned primarily with the study of biological systems at the single molecule level.On February 1, 2013, he announced he would not serve for the President‘s second term and resigned on April 22, 2013. Chu is a vocal advocate for more research into renewable energy and nuclear power, arguing that a shift away from fossil fuels is essential to combating climate change. For example, he has conceived of a global "glucose economy", a form of a low-carbon economy, in which glucose from tropical plants is shipped around like oil is today.

Steven Chu (Chinese: 朱棣文; pinyin: Zhū Dìwén, born February 28, 1948) is an American physicist who is known for his research at Bell Labs and Stanford University in cooling and trapping of atoms with laser light, which won him the Nobel Prize in Physics in 1997, along with his scientific colleagues Claude Cohen-Tannoudji and William Daniel Phillips.

物质的等离子态？、气态、液态、固态、超密态（白矮 星、中子星、黑洞）

势能E _p 动能E _k

> ≈ <

• 气体---非凝聚态，分子位置相互间没有关联

直径10 ^-10 m

间距10 ^-9 m

273K时，N ₂ 平均速率400m/s H ₂ 平均速率1700m/s

物质的气态、固态、液态

“气体”

普通气体 电子气体 白矮星 中子星 光子气

固体晶格中的声子气

物质的气态、固态、液态

完美晶体

离子键 共价键 金属键

范德瓦耳斯键 氢键

物质的气态、固态、液态

晶体与对称性

7个晶系14种Bravais格子

旋转，镜面

32个点群 平移群

230个空间群

平移

完美的晶体只 具有1，2，3，

4，6次对称轴

准晶体

D. Shechtman, I. Blech, D. Gratias, and J.W. Cahn, "Metalic phase with long- range orientational order and no translational symmetry," Phys. Rev.

Lett. 53 (1984) 1951-1953.

1984年, Shechtman等在 寻找既轻又硬的Al合金 中,在急冷的Al-Mn合金 中获得了具有五重对称, 斑点明锐的电子衍射图, 定出其点群为m35.

准晶体

郭可信: 五 次、八次、

十二次对称

PenrosePattern

光子晶体

纳米材料

新型晶体

空位 间隙 杂质 位错

物质的气态、固态、液态

晶体中的缺陷

非晶体

流 体

0.00004

0.00006 0.00008 0.0001 0.00012

200 300 400 500 600

-2 10 ⁸ -1 10 ⁸ 0 1 10 ⁸

0.00004

0.00006 0.00008 0.0001 0.00012

分子间相互作用不 可忽略，又不像固 体那样紧密束缚，

可以用范德瓦耳斯 方程定性描述液体

液体---稠密的气体

物质的气态、固态、液态

液体---濒临瓦解的晶格

物质的气态、固态、液态

物质的气态、固态、液态

液晶，包科达，《热物理学基础》，P240-242

http://dept.kent.edu/spie/liquidcrystals/

表面张力

赵凯华，新概念教程《热学》，P56-58

理想气体微观初级理论

作业

• 2.14，2.20

大量事件的概率描述

例题：“热学”成绩

97,96,93,93,93,90,90,90, 90,88,88,87,87,87,86,86, 86,86,86,85,85,85,85,85, 85,83,83,82,82,82,82,82, 82,82,82,80,80,80,80,79, 79,79,79,79,79,79,78,78, 78,78,76,76,76,76,75,75, 75,75,75,75,75,75,75,73, 73,72,72,72,72,72,70,70,

69,68,68,66,65,64,64

个人成绩：枚举 离散型描述

随机变量x∈{60,61,…,100}

概率 ( ) ^{( ) ( )} ( )

x

n x n x P x  N  n x



( ) ( )

( )

xn x n x

x x

n x N

    

平均值

( ) 1 P x 



归一化

方差   ^{2 ( )} _{2 2}

( ) x x n x

x x

   ^ n x  



连续型描述

随机变量x∈R且60<x<100 概率 P x (   x dx )  f x dx ( )

( ) x   xf x dx 平均值

( ) 1 f x dx 



归一化

方差    ( x  x ) ² f x dx ( )

1 2 3 4 5 6 7 8 9 10

2 4 6 8 10 12 14

4. 7%

3.7 17%

3.3 10%

3. 15%

2.7 9%

2.3 10%

2. 10% 1.5 9%

1. 7%

0 6%

概率密度、分布 ^{f x ( )}

( , , )

( , , )

P x x dx y y dy z z dz f x y z dxdydz

     



( , , )

( ) ( ) ( )

x y z

P x x dx y y dy z z dz f x f y f z dxdydz

     



4. 11%

3.7 20%

3.3 13%

3. 19%

2.7 16% 2.3 9%

2. 6%

1.5 5%

平均3.0 方差0.45

平均79.81 方差55

1 2 3 4 5 6 7 8 9 10

5

10

15

20

理想气体的微观模型

理想气体微观模型

1，分子有质量、无体积，是质点；

2，除了相互碰撞的瞬间、以及和容器壁 碰撞的瞬间之外分子不再受到其他作用。

混乱，数量多 微观描述

坐标r 速度v 动量p 能量E

…

统计描述

宏观描述

体积 压强 温度 内能

…

随机变量可选r、v、p、E等

确定相应分布f(r)、f(v)、f(p)、f(E)等 求各种平均值

压强的统计解释

N, V, T

一个分子撞击器壁的后果,动量改变为2mv

_x

在时间 Δt内，速度为v的分子沿着v的方向走 了 vΔt，沿x方向走了v _x Δt，而在以ΔS为底面 积， vΔt为母线长，v _x Δt为高的圆柱体内的所 有速度为v，v _x >0的分子都会撞到ΔS上

, N ( ) _{x y z} v v dv f v dv dv dv

  V

( ) 0

x x y z v x

Sv t N f v dv dv dv

V ^

 

1 ( )

2 ^{x x y z}

Sv t N f v dv dv dv

  V

2

2 1 ( )

2

( )

x x x y z

x x y z

mv Sv t N f v dv dv dv dp V

t S mv N f v dv dv dv

V

 

  



2 1 2

( ) 2

x x y z 2 x

N N

p mv f v dv dv dv mv

V V

  

 

2 2 2 2 2

1 1 1

2 mv  2 m v ^x   v ^y v ^z  3 2 mv ^x

2 1 2

3 2

p N mv

 V

宏观量 冲量作用的 微观量 统计平均

p x

p x

p v x x

p v x x

1 3

N p v

 V 

温度的统计解释

B

p N k T

 V

2 1 2

3 2

p N mv

 V

2 2

1 1 1

2 mv ^x  3 2 mv 1 2 3

2 mv  2 k T ^B

1 2 1

2 mv ^x  2 k T ^B



1 2 1

2 mv ^y  2 k T ^B 1 2 1

2 mv ^z  2 k T ^B



微观量 宏观量

动能统 微观推导 计平均

状态方程

宏观状 态方程

能均分

热动说

道尔顿分压定律

设一个容器体积为V，总压强为p，温度为T，总粒子数为N，质 量为M。容器中盛有n种不同种类的气体，对于其中的任一种气 体，其体积为V，压强为p _i ，温度为T，粒子数为N _i ，质量为M _i

1 n

i i

p p



  ^{p i N i k T B}

 V

1

1 1

n

n n i

i i

i B B B

i i

N N N

p p k T k T k T

V V V



 

    

 

混合理想气体的状态方程

道尔顿 分压定律

第i种理想气

体状态方程

范氏气体状态方程修正参数的微观解释

𝑝 + 𝑎

𝑣 ² 𝑣 − 𝑏 = 𝑅𝑇

𝑏 = 𝑁 _𝐴 − 1 × 1 2 × 4

3 𝜋𝑑 ³

≈ 4𝑁 _𝐴 4

3 𝜋 𝑑 2

3

≈ 0.01L/mol

∆𝑝 = 𝜕Φ _𝑁

𝜕𝑉 ₀ = 𝑎 𝑉 ₀ ²

B A

b



u

B A

b



u

Φ _𝑁 = 1

2 𝑁 _𝐴 𝑁 _𝐴 − 1 𝜑 𝜑 =

𝑑

∞

𝜑 𝑟 4𝜋𝑟 ² 𝑑𝑟

𝑉 ₀ = − 𝜀 𝑉 ₀

4 3 𝜋𝑑 ³

𝑎 = 4𝜀𝑁 _𝐴 ² 4

3 𝜋 𝑑 2

3

He,𝜀 = 1.81 × 10 ⁻²² 𝐽, 𝑎 = 2.42 × 10 ⁻² 𝐽𝑚 ³ /𝑚𝑜𝑙 ²

𝑟 ≤ 𝑑, 𝜑 𝑟 = ∞, 𝑟 > 𝑑, 𝜑 𝑟 = −𝜀 𝑑/𝑟 ⁶

氧 氮 氢 氦 氩 𝐂𝐎 _𝟐 氨 𝐇 _𝟐 𝐎

𝑎/(𝑎𝑡𝑚 ∙ 𝐿 ² /𝑚𝑜𝑙 ² ) 1.36 1.35 0.245 0.032 1.35 3.60 4.19 5.48

𝑏/(10 ⁻² 𝐿/𝑚𝑜𝑙) 3.19 3.86 2.66 2.34 3.23 4.28 3.73 3.06

麦克斯韦速度分布律

作业

• 3.19，3.25