Consider many same particles are moving randomly in a constant pressure and constant temperature box. The average speed [tex]\overline{v}[/tex] of the particle can be calculated by maxwell distribution. Now assume the density of particles in the box is [tex]n[/tex], so in unit time, total number of particle hitting unit area of a wall is given by(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{1}{4}n\overline{v}[/tex]

I am thinking this problem, actually, we are considering a small volume in front of the wall being hit. The cross area of region is unit while the length of that region is [tex]d[/tex], so in time [tex]t[/tex]

[tex]\frac{d}{t} \approx \overline{v}[/tex]

Since not all particle inside that region will hit the wall, only those moving towards the wall will do. Well if we consider each particle in that region might have velocity along x, -x, y, -y, z, -z direction. So only one-eighth of them will along the direction towards the wall, so the expression we get should be

[tex]\frac{1}{8}n\overline{v}[/tex]

but why in many book, it is 1/4 instead?

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# Average velocity of particles and maxwell distribution

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