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A parallel beam of nitrogen molecules mo...

A parallel beam of nitrogen molecules moving with velocity `v = 400 m s^(-1)` imprings on a wall at an angle `theta = 30^(@)` to its normal. The concentration of molecules in the beam is `n = 9 xx 10^(18) cm^(-3)`. Find the pressure exerted by the beam on the wall, assuming that collisions are perfectly elastic.

Text Solution

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All the molecules contained in the cylinder of length v and inclined on the wall at an angle `theta` to the normal will strike the wall every second. Let `Delta` S be the base area of the cylinder.
The volume of the cylinder `= Delta S v cos theta`.
Therefore, the number of molecules striking `Delta S` every second `= (Delta S v cos theta xx n)`.
Change of momentum per molecule `= 2 mv cos theta`.
`:. Pressure = (Force)/(Area) = ((2 mv cos theta)(Delta S v cos theta xx n))/((Delta S cos^(2) theta)) = 2 mv^(2) n`
`:. p = 2 xx ((28)/(6.0 xx 10^(26))) (9 xx 10^(24)) xx 400^(2) xx cos^(2) 30^(@)`
`= 1.00 xx 10^(5) N m^(-2) = 1` atm
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