上海交通大学：《材料加工原理 Principles of Materials Processing》教学资源（课件讲稿）凝固和铸造 Solidification and casting_Brief of statistic thermodynamics

先进材料疑固实验室 Laboratory of Advanced Materials Solidification 1896 1920 1987 2006 A B 50 50 30 20 0.04 0.03 10 001 0.02 00 0.005 0.010.0150.020.0250.03 0.0350.04 Conformational Change of HupA (A) PNAS110,4273-4278(2013) Brief of statistic thermodynamics Dr.Mingxu Xia 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

1896 1920 1987 2006 Brief of statistic thermodynamics Dr. Mingxu Xia PNAS 110, 4273-4278 (2013)

先进材料疑固实验室 Outline Laboratory of Advanced Materials Solidification Macro Micro thermodynamics Basic concept of statistical thermodynamics Entropy S Enthalpy H anced Materals o 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

Outline Macro & Micro thermodynamics Basic concept of statistical thermodynamics Entropy S Enthalpy H

Macro&Microscopic 先进材料疑固实验室 thermodynamics Laboratory of Advanced Materials Solidification Macroscopic thermodynamics: Be concerned with relative changes of macroscopic properties, such as P,T,Cp.m… Does not require any knowledge of the atomic nature of matters. Can ignore the existence of molecules,molecular complexity,and quantum mechanics ory o vanced Matera 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

Macro&Microscopic thermodynamics Macroscopic thermodynamics: Be concerned with relative changes of macroscopic properties, such as P, T, Cp,m… Does not require any knowledge of the atomic nature of matters. Can ignore the existence of molecules, molecular complexity, and quantum mechanics

Macro&Microscopic 先进材料疑固实验室 Laboratory of Advanced Materials Solidification thermodynamics Microscopic(statistical)thermodynamics: Attempts to compute absolute values of thermodynamic quantities based on a statistical averaging of such properties of individual atoms or molecules as the m,V,bond strength,vibration frequencies... Relies heavily on quantum mechanics,and knowledge of molecular motion and structures. 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

Macro&Microscopic thermodynamics Microscopic(statistical) thermodynamics: Attempts to compute absolute values of thermodynamic quantities based on a statistical averaging of such properties of individual atoms or molecules as the m, V, bond strength, vibration frequencies… Relies heavily on quantum mechanics, and knowledge of molecular motion and structures

先进材料疑固实验室 Basic concepts Laboratory of Advanced Materials Solidification A basic idea embodied in statistical thermodynamics is: Even when a material is in equilibrium on a macroscopic scale,it is dynamic on a microscopic scale. To be derived: Dynamic distribution Distribution consequences anced Materials Sol 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

Basic concepts A basic idea embodied in statistical thermodynamics is: Even when a material is in equilibrium on a macroscopic scale, it is dynamic on a microscopic scale. To be derived: Dynamic distribution Distribution consequences

先进材料疑固实验室 Macro&microstate link Laboratory of Advanced Materials Solidification Macrostate: Be characterized by a few state variables,such as T,V,and U etc. Be the state of all particles in the system. Passes very rapidly through many microstates during the observation time. For example: An atom in a solid vibrates at a frequency in the order of 1013 s-1 Gas molecules have velocities of order of 102 ms-1 When we observe a property of a system,we really see the average of this property in all of the microstates that the material passed through during the observation time. 上海充通大￥ SHANGHAI JIAO TONG UNIVERSITY

Macro&microstate link Macrostate: Be characterized by a few state variables, such as T, V, and U etc. Be the state of all particles in the system. Passes very rapidly through many microstates during the observation time. For example: An atom in a solid vibrates at a frequency in the order of 1013 s-1 Gas molecules have velocities of order of 102 ms-1 When we observe a property of a system, we really see the average of this property in all of the microstates that the material passed through during the observation time

先进材料疑固实验室 Main tasks Laboratory of Advanced Materials Solidification What we can do is To take advantage of the large number of the atoms in the system to make statistical descriptions of the behavior of the atoms that make up the material based on the microscopic behavior. What we really want is Statistical information regarding the motions of all particles in the system. vanced Mater 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

Main tasks What we can do is To take advantage of the large number of the atoms in the system to make statistical descriptions of the behavior of the atoms that make up the material based on the microscopic behavior. What we really want is Statistical information regarding the motions of all particles in the system

Main Results from Quantum 先进材料疑固实验室 Mechanics Laboratory of Advanced Materials Solidification Energy is quantized-energy of a system can only take on certain discrete values.Spectroscopy-Characteristic frequency of matters） Degeneracy of level g )--the number of states with the equal energy Shifting of particles from one state to another on the same level constitutes a new arrangement. 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

Main Results from Quantum Mechanics Energy is quantized—energy of a system can only take on certain discrete values. （Spectroscopy-Characteristic frequency of matters） Degeneracy of level（g）--the number of states with the equal energy Shifting of particles from one state to another on the same level constitutes a new arrangement

Results from Quantum 先进材料疑固实验室 Mechanics Laboratory of Advanced Materials Solidification A finite array of microstates satisfies two constraints ∑4=N=E=u Where: N:the number of particels; i:energy level; E:total energy of N particles; &,the energy of ith level nced Materials Soll 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

A finite array of microstates satisfies two constraints Where: N: the number of particels; i:energy level; E: total energy of N particles; εi : the energy of ith level Results from Quantum Mechanics

先进材料疑固实验室 Laboratory of Advanced Materials Solidification The number of microstates for each macrostate will be equal to the number of ways in which we can choose these Ni from N particles. Clearly,what is required here is a statistical treatment of the problem. ory of vanced Materials Solidl 上浒充通大学 SHANGHAI JIAO TONG UNIVERSITY

The number of microstates for each macrostate will be equal to the number of ways in which we can choose these Ni from N particles. Clearly, what is required here is a statistical treatment of the problem