复旦大学《大学物理》课件-第3讲(1).ppt

大学物理（热学）大学物理（热学）1)Mean Free Path 2)Diffusion,Thermal conductivity,and Viscosity 2006-10-12 Equilibrium distribution NvvvvN222212dn is the number of molecules xxxvvvdvy vy+dvy zzzvvvdin NnvNnviiid22Nvnvn222211ni the number of molecules of ivnear v among N molecules,how many are near v probability that one molecule is near v proportional to dvx.xxvvfdMeaning of dn/N ddd),(dzzyyxxzyxvvfvvfvvfNvvvnIsotropic assumption 2222zyxzyxvvvvvfvfvf22 exp xxvCvfThe solution is The probability should be normalized Nnd13223dexpd1xxvvCNnxxvvCdexp122xxvvCdexp12212 1each normalized d d dexp1),(d22223zyxzyxzyxvvvvvvNvvvn?mTkv 3B2Known 22223),(dNvvvnvvzyxwhile zyxzyxzyxvvvTkvvvmTkmNvvvnddd2exp2,dB22223BFor unit volume ,dzyxvvvnMaxwell velocity distribution zyxzyxvvvTkvvvmTkmnddd2exp2B22223B0vvTkmvTkmnvnd421exp2)(d2B223B0Maxwell speed distribution For one molecule,what speed is most possible?Most probable speed vvvfnd4)(20Among N molecules,what is the speed most molecules have in unit interval?021expddB22TkmvvvmTkvBm2vvvvvNvndexp14)(d22m2232mMaxwellian can be written as The average speed vvvvvvvd exp1422m20232mmTkB8xxvxde 4203mmTkmTkvBBm41.12mTkmTkvBB59.18mTkmTkvBBrms73.13 xDJm xTJQ thermal conductivity Fouriers law Conduction Transport phenomena Heat transfer:conduction convection thermal radiation diffusion viscosity Diffusion xDJm xvJyp Ficks law 6 Viscosity Microscopic theory of transport coefficients ymvTkvmm ,2321 ,B2pQM ,)()()()(dd61dxxnxxntvAFor mass transport,mnxmnxmntvAMdd61dxtvA2dd61 xvtAMJM31dddvD31TCTknVB23 VDCDSimilarly n21r=1.121010m sm1069.1 8m1068.2 kg1033.33B325B27mTkvTkpnmHydrogen under STP m1067.172)2(rK)(mW1071.8,sm1042.9225Dsm1028.1=25DExperimental results:)K(mW1068.1=2大学物理（热学）大学物理（热学）1)Mean Free Path 2)Diffusion,Thermal conductivity,and Viscosity 2006-10-12 Equilibrium distribution dn is the number of molecules vy vy+dvy in ni the number of molecules of near v among N molecules,how many are near v probability that one molecule is near v proportional to dvx.Meaning of dn/N Isotropic assumption The solution is The probability should be normalized 12 each normalized Known while For unit volume Maxwell velocity distribution Maxwell speed distribution For one molecule,what speed is most possible?Most probable speed Among N molecules,what is the speed most molecules have in unit interval?Maxwellian can be written as The average speed In an interval of Dt,number of collisions is Then mean free path is where the mean relative speed is Reference L.E.Reichl,A Mordern Course in Statistical Physics.University of Texas Press,Austin 1980 pp458 optional different from dimension Then mean free path is Only a factor analysis result.thermal conductivity Fouriers law Conduction Transport phenomena Heat transfer:conduction convection thermal radiation diffusion viscosity Diffusion Ficks law 6 Viscosity Microscopic theory of transport coefficients For mass transport,In general:Similarly r=1.121010m Hydrogen under STP Experimental results:2023/2/15 50 大学物理（热学）大学物理（热学）1)Review 2)Examples 3)Order and Disorder 2006-12-27 e=W/QH =1-QL/QH =1-TL/TH Clausius deduction(1865)QL/TL=QH/TH,QH/TH-QL/TL=0 (Q/T)=0 0TdQrev?TdQrev 0TdQrevT1 T2 T3 T4 T5 T6 T7(Q1/T1+Q2/T2)+(-Q2/T2+Q3/T3)+(-Q6/T6+Q7/T7)=0 TdQdS baTdQbaTdQIII)()(0)()(abTdQbaTdQIII Irreversible:e=W/QH=1-QL/QH QH/TH (Q/T)V1.Calculate the change in entropy(a)of the gas and(b)of the surrounding environment.(c)Evaluate DS for 1.00 mole,with V2=2.00 V1.Example 20-8 BAABTdQSSBAABTdQSS“Natural processes tend to move toward a state of greater disorder.”Second Law 等几率假定等几率假定 S=kBlnW 大学物理（热学）大学物理（热学）Maxwell-Boltzmann Distribution 2006-10-30 MaxwellMaxwell-BoltzmannBoltzmann分布率分布率 的碰撞数等于反过的碰撞数等于反过来的逆过程的碰撞数时才能发生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现在他考虑的是两个粒子碰撞的速度，而不而不是一个粒子的不同速度分量是一个粒子的不同速度分量，存在统计的独存在统计的独立性立性.1866年年，Maxwell承认他承认他1860年的推导年的推导“may appear precarious”.接着，他指出平衡态的达到接着，他指出平衡态的达到，只有在初始态只有在初始态 碰到末态碰到末态 这样这样 他又给出了另一个推导他又给出了另一个推导.这就意味着这就意味着 即即 同时同时 类似于前面的推导类似于前面的推导，他得到他得到 这时能这时能量守恒的条件应该是量守恒的条件应该是 1868年，年，Boltzmann将这种考虑推广到存在将这种考虑推广到存在外力的情况外力的情况，其中其中 即在势函数即在势函数V(x)的情况的情况.然后然后Boltzmann采用采用Maxwell的推导方式的推导方式，得得到到 其中其中 这就是著名的这就是著名的Maxwell-Boltzmann分布率分布率.大学物理（热学）大学物理（热学）1)Maxwell-Boltzmann Distribution 2)Phase transition 2006-11-06 MaxwellMaxwell-BoltzmannBoltzmann分布率分布率 的碰撞数等于反过的碰撞数等于反过来的逆过程的碰撞数时才能发生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现在他考虑的是两个粒子碰撞的速度，而不而不是一个粒子的不同速度分量是一个粒子的不同速度分量，存在统计的独存在统计的独立性立性.1866年年，Maxwell承认他承认他1860年的推导年的推导“may appear precarious”.接着，他指出平衡态的达到接着，他指出平衡态的达到，只有在初始态只有在初始态 碰到末态碰到末态 这样这样 他又给出了另一个推导他又给出了另一个推导.这就意味着这就意味着 即即 同时同时 类似于前面的推导类似于前面的推导，他得到他得到 这时能这时能量守恒的条件应该是量守恒的条件应该是 1868年，年，Boltzmann将这种考虑推广到存在将这种考虑推广到存在外力的情况外力的情况，其中其中 即在势函数即在势函数V(x)的情况的情况.然后然后Boltzmann采用采用Maxwell的推导方式的推导方式，得得到到 其中其中 这就是著名的这就是著名的Maxwell-Boltzmann分布率分布率.Temperature Dependence Temperature Dependence of Chemical Reactionsof Chemical Reactions Phase Transition PV=NkBT P low,T high Evaporation In a Liquid Saturated Vapor Pressure 1)Evaporation 2)Condensation Boiling Boiling:PSVP=PExternal Humidity Partial Pressure Humidi