复旦大学《大学物理-热学》课件_第12次课.pdf

大学物理（热学）1)Maxwell-Boltzmann Distribution2)Phase transition2006-11-06MaxwellMaxwell-BoltzmannBoltzmann分布率的碰撞数等于反过来的逆过程的碰撞数时才能发生.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.1866年，Maxwell承认他1860年的推导“may appear precarious”.)()(),(2121vvvvffF=接着，他指出平衡态的达到，只有在初始态),(21vv),(21vv碰到末态这样他又给出了另一个推导.这就意味着),(),(2121vvvv=FF即)()()()(2121vvvv=ffff同时22221122221121212121vvvv+=+mmmm类似于前面的推导，他得到这时能量守恒的条件应该是1868年，Boltzmann将这种考虑推广到存在外力的情况，)exp()(22233vv=Nf其中mTkB22=2221211222121121)(2121)(21vvvv+=+mxVmmxVm即在势函数V(x)的情况.然后Boltzmann采用Maxwell的推导方式，得到+=)(21exp)(2xVhcfmvv其中TkhB1=这就是著名的Maxwell-Boltzmann分布率.Temperature Dependence Temperature Dependence of Chemical Reactionsof Chemical ReactionsPhase TransitionPV=NkBTP low,T highEvaporationIn a LiquidSaturated Vapor Pressure1)Evaporation2)CondensationBoilingBoiling:PSVP=PExternalHumidity%100Re22=OHofSVPOHofPPartialHumiditylativePartial PressureHumidityFor:30oC,PP of water in the air 21.0 torr,then%66%1008.310.21=torrtorrRHSupersaturationFor: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.Van der Waals Equation of StateVan der Waals in 1873:1)Finite size of molecules 2)Attractive forces between moleculesWhat would happen?14.1 Van der Waals equation()nRTnbVVnap=+2 The Nobel Prize in Physics 1910for his work on the equation of state for gases and liquidsJohannes Diderik Van der Waals(1837-1923)(1873)Van der Waals:126000 items11211+=VnbVnpanRTpVVirial expansion+=VnRTabnRT 1Critical pointVan der Waals isotherms0 ,022=TTVpVp ,CCCTVp2=VnanbVnRTp()TVVp81332=+Dimensionless version:where,Cppp tilde1.non-physical part(p 0)2.There is no solid phase.Problems:01 =TTpVV3.Stability requires Positive slope part is not stable.