Contents of Today S.J.T.U. Phase Transformation and Applications Page 1/66 Review previous Macro-states and Micro-states Boltzman Hypothesis and the Third Law Boltzman Distribution Partition Function Ideal Gas etc. SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 19 Statistical
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 19 Statistical Page 1/66 Contents of Today Review previous Macro-states and Micro-states Boltzman Hypothesis and the Third Law Boltzman Distribution Partition Function Ideal Gas etc
统计热力学Contents S.J.T.U. Phase Transformation and Applications Page 2/66 统计热力学概述 Boltzmann假定、分布和配分函数 熵的统计概念/第二定律 热力学第三定律 理想气体的状态方程 晶体的热容 聚合物溶液的混合嫡 SJTU Thermodynamics of Materials Spring 2008 ©X.J.Jin Lecture 19 Statistical
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 19 Statistical Page 2/66 统计热力学Contents 统计热力学概述 Boltzmann假定、分布和配分函数 熵的统计概念/第二定律 热力学第三定律 理想气体的状态方程 晶体的热容 聚合物溶液的混合熵
Nomenclature S.J.T.U. Phase Transformation and Applications Page 3/66 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. SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 19 Statistical
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 19 Statistical Page 3/66 Nomenclature 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
Nomenclature (2) S.J.T.U. Phase Transformation and Applications Page 4/66 Ensemble:系综 Microcanonical/canonical/macrocanonical:微/正则/巨 Degeneracy:简并度 Partition function:配分函数 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 SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 19 Statistical
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 19 Statistical Page 4/66 Nomenclature (2) Ensemble：系综 Microcanonical / canonical / macrocanonical：微/正则/巨 Degeneracy：简并度 Partition function：配分函数 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
统计热力学 S.J.T.U. Phase Transformation and Applications Page 5/66 ·统计热力学 统计平均的方法研究大量微观粒子的力学行为，将统计力学应用于研 究热力学体系的宏观性质及其规律 统计热力学寻求的是在一定条件下对一切可能的微观运动状态的统计 平均值。 宏观世界 统计热力学 微观世界 (热力学) (量子力学) SJTU Thermodynamics of Materials Spring 2008 ©X.J.Jin Lecture 19 Statistical
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 19 Statistical Page 5/66 统计热力学 • 统计热力学 统计平均的方法研究大量微观粒子的力学行为，将统计力学应用于研 究热力学体系的宏观性质及其规律 统计热力学寻求的是在一定条件下对一切可能的微观运动状态的统计 平均值。 宏观世界 （热力学） 微观世界 （量子力学） 统计热力学
统计热力学基础：经典与统计 S.J.T.U. Phase Transformation and Applications Page 6/66 经典热力学 研究热现象基本规律的宏观理论，所研究对象是含有大量粒子的平衡体 系，是以在经验或实验数据基础上总结出的的三个定律为基础，利 用反应热、热容、熵等热力学函数，研究平衡体系各宏观性质之间 的相互关系，进而预示过程自动进行的方向和可能性。 统计热力学 研究热现象基本规律的微观理论，其研究对象仍是由大量微观粒子（包 括分子、原子和离子等)所组成的体系。 !从体系内部粒子的微观运动性质及结构数据出发，以粒子普遍遵循的 力学定律为基础，用统计的方法直接推求大量粒子运动的统计平均 结果，以得到平衡体系各种宏观性质的具体数值。 SJTU Thermodynamics of Materials Spring 2008 ©X.J.Jin Lecture 19 Statistical
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 19 Statistical Page 6/66 统计热力学基础：经典与统计 • 经典热力学 研究热现象基本规律的宏观理论，所研究对象是含有大量粒子的平衡体 系，是以在经验或实验数据基础上总结出的的三个定律为基础，利 用反应热、热容、熵等热力学函数，研究平衡体系各宏观性质之间 的相互关系，进而预示过程自动进行的方向和可能性。 • 统计热力学 研究热现象基本规律的微观理论，其研究对象仍是由大量微观粒子（包 括分子、原子和离子等）所组成的体系。 ！从体系内部粒子的微观运动性质及结构数据出发，以粒子普遍遵循的 力学定律为基础，用统计的方法直接推求大量粒子运动的统计平均 结果，以得到平衡体系各种宏观性质的具体数值
统计热力学基础：经典与统计 S.J.T.U. Phase Transformation and Applications Page 7/66 统计热力学：经典统计/量子统计 服从经典力学规律的微观粒子组成的体系称为经典粒子体系。 服从量子力学规律的微观粒子组成的体系称为量子粒子体系。 经典力学 “组合分析”理论和系综理论 同种粒子彼此可分辨 量子力学 Fermi-Dirac和Bose-Einstain以及系综理论 无法对全同粒子编号 SJTU Thermodynamics of Materials Spring 2008( X.J.Jin Lecture 19 Statistical
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 19 Statistical Page 7/66 统计热力学基础：经典与统计 统计热力学：经典统计/量子统计 服从经典力学规律的微观粒子组成的体系称为经典粒子体系。 服从量子力学规律的微观粒子组成的体系称为量子粒子体系。 经典力学 “组合分析”理论和系综理论 同种粒子彼此可分辨 量子力学 Fermi-Dirac和Bose-Einstain以及系综理论 无法对全同粒子编号
Average Velocity of Gas Molecules S.J.T.U. Phase Transformation and Applications Page 8/66 Monatomic,ideal gas in equilibrium with its pressure and temperature PV =nRT Cv 3 R 2 SJTU Thermodynamics of Materials Spring 2008( X.J.Jin Lecture 19 Statistical
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 19 Statistical Page 8/66 Average Velocity of Gas Molecules V RC 23 = Monatomic, ideal gas in equilibrium with its pressure and temperature = nRTPV
宏观态、微观态 S.J.T.U. Phase Transformation and Applications Page 9/66 宏观态 体系的状态由几个状态参数如温度、体积和内能来描述。 An isolated system at equilibrium at a given volume. ·微观态 需表征体系中所有粒子的状态，如所有分子的能量和速度。 Specify the position and velocity of all of the molecules in the system The rate of motion of molecules in air at macroscopic equilibrium v2=3kT/m=23.4×104m2/S2 v=483m/S SJTU Thermodynamics of Materials Spring 2008 ©X.J.Jin Lecture 19 Statistical
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 19 Statistical Page 9/66 宏观态、微观态 • 宏观态 体系的状态由几个状态参数如温度、体积和内能来描述。 An isolated system at equilibrium at a given volume. • 微观态 需表征体系中所有粒子的状态，如所有分子的能量和速度。 Specify the position and velocity of all of the molecules in the system 2 224 mkTv ×== /104.23/3 Sm = /483 Smv The rate of motion of molecules in air at macroscopic equilibrium
动态平衡 S.J.T.U. Phase Transformation and Applications Page 10/66 In order to compute the macroscopic average of a property .The property of each microstate .Which microstates the system can be in .The probability that the system will be in a given microstate Macrostate: stating the total number of particles in Macroscopic each box yields pressure Microstate: each way of realizing a given macro distribution Instantaneous pressure Each macrostate may be realized by a number of microstates Time> Figure 10.2 Instantaneous gas pressure as a function of time.(The magnitude of the variation of instantaneous gas pressure is exag- gerated for emphasis.) SJTU Thermodynamics of Materials Spring2008©X.J.Jin Lecture 19 Statistical
Phase Transformation and Applications S. J. T. U. SJTU Thermodynamics of Materials Spring 2008 © X. J. Jin Lecture 19 Statistical Page 10/66 动态平衡 In order to compute the macroscopic average of a property •The property of each microstate •Which microstates the system can be in •The probability that the system will be in a given microstate Macrostate: stating the total number of particles in each box yields Microstate: each way of realizing a given macro distribution Each macrostate may be realized by a number of microstates