気体の分子運動論

$\displaystyle f\Delta t$	$\textstyle =$	$\displaystyle mv_x - ( - mv_x ) = 2mv_x$	(1)
$\displaystyle N$	$\textstyle =$	$\displaystyle \frac{{v_x t}}{{2L}} 　壁への衝突回数$	(2)
$\displaystyle ft$	$\textstyle =$	$\displaystyle 2mv_x \times \frac{{v_x t}}{{2L}} = m\frac{{v_x ^{\rm 2} }}{L}t$	(3)
$\displaystyle v_x^2$	$\textstyle =$	$\displaystyle \frac{1}{3}\overline v ^2 　速度の等方性より$	(4)
$\displaystyle ft$	$\textstyle =$	$\displaystyle \frac{{m\overline v ^{\rm 2} }}{{{\rm 3}L}}t　　f = \frac{{m\overline v ^{\rm 2} }}{{{\rm 3}L}}$	(5)
$\displaystyle F$	$\textstyle =$	$\displaystyle N\frac{{m\overline v ^{\rm 2} }}{{{\rm 3}L}}　F = N_0 \frac{{m\overline v ^{\rm 2} }}{{{\rm 3}L}}　　アボガドロ数個　N_0　1(mol)$	(6)
$\displaystyle p$	$\textstyle =$	$\displaystyle \frac{F}{{L^2 }} = \frac{{N_0 m\overline v ^{\rm 2} }}{{{\rm 3}L^{\rm 3} }} = \frac{{N_0 m\overline v ^{\rm 2} }}{{3V}}$	(7)
$\displaystyle pV$	$\textstyle =$	$\displaystyle \frac{2}{3}N_0 \left( {\frac{{m\overline v ^{\rm 2} }}{2}} \right)$	(8)
$\displaystyle pV$	$\textstyle =$	$\displaystyle RT　　　　 1(mol)$	(9)
$\displaystyle RT$	$\textstyle =$	$\displaystyle \frac{2}{3}N_0 \left( {\frac{{m\overline v ^{\rm 2} }}{2}} \right)$	(10)
$\displaystyle \frac{{m\overline v ^{\rm 2} }}{2}$	$\textstyle =$	$\displaystyle \frac{3}{2}\frac{{RT}}{{N_0 }} = \frac{3}{2}kT　気体分子1個の運動エネルギー$	(11)
$\displaystyle \sqrt {\overline {v^2 } }$	$\textstyle =$	$\displaystyle \sqrt {\frac{{3R}}{{mN_0 }}T} = \sqrt {\frac{{3R}}{{M \times 10^{ - 3} }}T} 　　2乗平均速度　M：分子量$	(12)
$\displaystyle k$	$\textstyle =$	$\displaystyle \frac{R}{{N_0 }} 　　ボルツマン係数$	(13)
$\displaystyle U$	$\textstyle =$	$\displaystyle \frac{{m\overline v ^{\rm 2} }}{2} \times N_0 = \frac{3}{2}RT 　1(mol)$	(14)
$\displaystyle U$	$\textstyle =$	$\displaystyle \frac{3}{2}nRT 　n(mol)$	(15)