麦克斯韦分子速率分布律与扩散方程、扩散系数的初浅推导

2011Vol.20No.11200111!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!COLLEGEPHYSICSNov.20012000-06-142001-03-121963.100044.O414.2A1000-0712200111-0016-041~3...!.1......!!##1!#122$!!+d!!!!+d!!d!!22!EX2.x=0.+-fxdx=ll+-x2fxdx=x2=!2fxf1=0.xfx+-=0l2fx.lxfx+--+-xf*xdx=l-+-xf*xdx=l32-3X!+-xx!fx+f*x[]dx=0f*x=-x!fxfx=Ce-x2/2!l+-Ce-x22!dx=lC=l2!\!fx=l2!\!e-x22!4fx=Ce-x2.!x1x1x1x.x.4x1xx212x1xf1x=l2!12\xeXp-12x212()xl2m12=32IT12x=12y=12zl2m12x=l2IT12x=IT/mf1x=m2!\ITe-l2m12x/IT1x1y1zf1yf1z.1x~1x+d1x1y~1y+d1y1z~1z+d1zf1xf1yf1zd1xd1yd1z=m2!()IT32e-m122ITd1xd1yd1z1~1+d17llld1xd1yd1z1d14!12d1f1d1=4!12m2!()IT32e-12m12ITd15mT.!.z=0x=0xz..14~6..!Nxii.i.z=N!xx2=1+2++N2=!2i+2!ii22i!2i=N2.i!i=0x2=N2z=N!x2=2!z6xz.2.3I1I2dIdx=-I1-I23dzdz/2!dzI1dSdz2!I2dSdz2!dzdSdNdN=I1-I22!dSdz=-22!dIdxdSdz22dN=-DdIdxdSdz77D=22!86x2=2!zx2=2Dz94#2Dzxx+dxfx=14!#Dze-x24Dz.z=0x=0N0x$0zxx+dxN0fxdxzxIxz=N04!#Dze-x24Dz10108120!n!t=D!2n!x211.1~3.3!!1.2!cos##$.2=#0!cos#2sin#d##0sin#d#=23!2!/$=18D=131!12#8$2.7....1.M.1978.2KitteIC.EIementaryStatisticaIPhysicsM.John-wiIay1958.21~25.3.M.1985.107~109.4LA.M.1986..5ChandrasekarC.StochasticProbIemsinPhysicsandChemistryJ.ReviewofModernPhysics1943151Chapter1andChapter2.6EinsteinA.InvestigationsontheTheoryofBrownianMovementM.EditedbyFurthRDoverPubIications1956.7RU.M.1957..AnelementaryDerivationofMaxwellsspeeddistributiondiffusioneguationandcoefficientofdiffusionTANGYingSHEShou-xianDepartmentofPhysicsNorthernJiaotongUniversityBeijing100044ChinaAbstractModeIIingtheGaItonBoarddemonstrationapparatusforstatisticaIdistributionGaussiandistri-butionfunctionMaxweIIsspeeddistributionIawdiffusioneguationandcoefficientofdiffusionarederivedbyeIementarycaIcuIus.KeywordsMaxweIIsspeeddistributiondiffusioncoefficientofdiffusion9111