上游充通大 SHANGHAI JIAO TONG UNIVERSITY Chapter 10.Statistical Thermodynamics 1.Macrosates and Microstates宏观状态与微观状态 2.微观状态数与最可几分布 3. Boltzmann假定与配置熵 4.理想固溶体熵 5.第三定律 6.Gibbs公式 7.Boltzmann分布* 8.配分函数* 9.Fermi-Dirac分布* IAO TONG UNI David V.Ragone,Thermodynamics of Materials,John Wiley Sons,Inc.,1995,Vol.I,Chap 10 &Vol.II,Chap 2.. 江伯鸿，材料热力学，上海交通大学出版社，1999，第八章 徐祖耀，李麟，材料热力学，科学出版社，2000，第九第十章
Chapter 10. Statistical Thermodynamics 1. Macrosates and Microstates宏观状态与微观状态 2. 微观状态数与最可几分布 3. Boltzmann假定与配置熵 4. 理想固溶体熵 5. 第三定律 6. Gibbs 公式 7. Boltzmann 分布* 8. 配分函数* 9. Fermi-Dirac 分布*
上游充通大￥ SHANGHAI JIAO TONG UNIVERSITY Macroscopic thermodynamics microscopic thermodynamics/statistical thermodynamics Root-mean-square average rate of motion Macrosate/Microstate:宏观态/微观态 The time average of the properties of a system is equivalent to the instantaneous average over the ensemble of the microstates available to the system. Ensemble:系综 Microcanonical/canonical/macrocanonical::微/正则/巨 Degeneracy:简并度 Partition function:配分函数
上游充通大￥ SHANGHAI JIAO TONG UNIVERSITY Macroscopic thermodynamics Microscopic thermodynamcis 宏观世界 统计热力学 微观世界 (热力学) (量子力学) Statistical averaging Temperature,pressure,heat etc. Molecular motion,structures, No information about atomic vibrations. structures and quantum mechanics AO TONG U! Depend heavily on the quantum mechanics Constant P,T for a system at equilibrium Atoms or molecules are in motion,and their configurations are changing constantly
Macroscopic thermodynamics Microscopic thermodynamcis Temperature, pressure, heat etc. No information about atomic structures and quantum mechanics Molecular motion, structures, vibrations. Depend heavily on the quantum mechanics Statistical averaging Constant P, T for a system at equilibrium Atoms or molecules are in motion, and their configurations are changing constantly
上浒充通大率 SHANGHAI JIAO TONG UNIVERSITY 10.1 Average velocity of gas molecules momentum mvx Consider the x direction first Surface area=A -mv Here F is the average △I=Vx△t force during△t Fat=A,At号(2m或)9 PV =nNami =nRT P m晚 RT NAm m晚= T=7 R
10.1 Average velocity of gas molecules mvx -mvx 𝐹∆𝑡 = 𝐴𝑣 𝑥∆𝑡 𝑛𝑡 𝑉 2𝑚𝑣 𝑥 ( 1 2 ) F Δl=vxΔt Surface area= A 𝑃 = 𝐹 𝐴 = 𝑚𝑣 𝑥 2 𝑛𝑡 𝑉 𝑅𝑇 = 𝑁𝐴𝑚𝑣 𝑥 2 momentum Consider the x direction first
上游充通大￥ SHANGHAI JIAO TONG UNIVERSITY 2=呢十好+昭 2=3晚 1 mv2 kT 3 AIJIAO TONG UNI 1 3 (E〉= m2 2 二 2 kT