大学物理（热学） Maxwell-Boltzmann Distribution Phase transition 2006-11-06.

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1 大学物理（热学） Maxwell-Boltzmann Distribution Phase transition

2 Maxwell-Boltzmann分布率

3 1866年，Maxwell承认他1860年的推导“may appear precarious” .
他又给出了另一个推导. 现在他考虑的是两个粒子碰撞的速度，而不是一个粒子的不同速度分量，存在统计的独立性. 这就意味着 接着，他指出平衡态的达到，只有在初始态 的碰撞数等于反过来的逆过程的碰撞数时才能发生. 碰到末态 这样

4 即 同时 类似于前面的推导，他得到

5 其中 1868年，Boltzmann将这种考虑推广到存在外力的情况， 这时能量守恒的条件应该是 即在势函数V(x)的情况.

6 然后Boltzmann采用Maxwell的推导方式，得到
其中 这就是著名的Maxwell-Boltzmann分布率.

7 Temperature Dependence of Chemical Reactions

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9 Phase Transition

10 PV=NkBT P – low, T –high

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15 Evaporation

16 In a Liquid

17 Saturated Vapor Pressure
1)Evaporation 2) Condensation Saturated Vapor Pressure

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19 Boiling

20 Boiling: PSVP=PExternal

21 Humidity

22 Partial Pressure Humidity
For: 30oC, PP of water in the air 21.0 torr, then

23 Dew or Fog or Rain might appear ! Dew point – as a measure of RH.
Supersaturation For: 30oC, PP of water in the air 21.0 torr, if T falls to 20oC (SVP=17.5 torr), then RH would exceed 100%, What would happen ? Dew or Fog or Rain might appear ! Dew point – as a measure of RH.

24 Van der Waals Equation of State

25 What would happen ? Van der Waals in 1873: 1) Finite size of molecules
2) Attractive forces between molecules What would happen ?

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28 14.1 Van der Waals’ equation (1873)
Van der Waals: items 14.1 Van der Waals’ equation (1873) Johannes Diderik Van der Waals ( ) Thesis 36years old; awarded 73 years old. Nobel Prize needs good work and longevity. On the continuity of the gas and liquid state. The importance of this conclusion from Van der Waals' very first paper can be judged from the remarks made by James Clerk Maxwell in Nature, "that there can be no doubt that the name of Van der Waals will soon be among the foremost in molecular science" and "It has certainly directed the attention of more than one inquirer to the study of the Low-Dutch language in which it is written" (Maxwell probably meant to say "Low-German", which would also be incorrect, since Dutch is a language in its own right). The Nobel Prize in Physics 1910 "for his work on the equation of state for gases and liquids"

29 Virial expansion

30 Van der Waals isotherms
Critical point

31  tilde Dimensionless version: where

32 Problems: 1. non-physical part (p < 0) 2. There is no solid phase. 3. Stability requires Positive slope part is not stable.