-1 気体分子運動論による理想気体の粘性係数の導 …

1 3-1 . Maxwell- . v . Boltzmann .. 8k B T 1/ 2. v = .. m . x . u =. 1. x . 2 nd 2. y . y y .. y y + y .. y .. , , . y .. y y . y'+ .. y' .. A .. y' .. u+ uy' u u .. x .. v tA. nv tAmu .. 1. t nv tA. nv tAmu . 6. A t = nv tA. yx {( muy' mu+ ) + ( mu muy' )}. 6. yx y x . du du . u+ u Taylor u+ = uy' + u = uy' . dy y' dy y'. yx mnv mnv )+ # du & -+. yx = {(uy' u+ ) + (u uy' )} = * 2 % ( . 6 6 +, $ dy 'y' +/. " du % . yx = $ '. # dy &. mnv . = Maxwell-Boltzmann v . 3. 1/ 2. 2 mkB T . = . 3 d 2 . m . MT. Maxwell-Boltzmann . 1/2 1/2 .. 3-2 . , , .. y . y y y'+ .. y' . v t .. y' A. C . C+ Cy' C . v ! dC $. C+ = Cy' + # & t vA t C . C+ C . " dy %y' CvA t . Taylor . " dC %. C = Cy' $ ' . # dy &y' 1/6 . vA t {(Cy' C+ ) + (C Cy' )}.. 6. NA t N . vA t NA t =. 6. {(Cy' C+ ) + (C Cy' )}. " dC % " dC % " dC %. Taylor { } (C C+ ) + (C Cy' ) = C C+ = Cy' $ ' Cy' $ ' = 2 $ '.

2 Y'. # dy &y' # dy &y' # dy &y'. " dC % v (* " dC % ,* 1 " dC % A B . N Fick N = D $ ' = ) 2 $ ' - = v $ ' . # dy &y' 6 +* # dy &y' .* 3 # dy &y' . 1. D = v . v . 3. 8k B T 1/ 2 1. Maxwell-Boltzmann v = =. m 2 nd 2. 1/2. 1 ! 8k T $. D= # B &. 1 kB (J/K) T (K). 2 n (1/m3) m (kg). 3 " m % 2 nd D (m2/s). d (m) . n . n . PV = mRT m R = kB N A N A . mN P. m n= A. n=. V k BT. 1/2 3/2. 1 ! 8k T $ 1 k BT 2 ! k BT $ 1. D = # B & 2. = 2# &. 3" m % 2 d P 3d " % P m m . T T. D . P M. T 3/ M /.