Impulse-momentum theorem and kinetic theory of gases

[member 392791]

Hello,

I am reading through my textbook and cannot wrap this idea around my head yet

Basically, when a molecule hits the wall of the container, it is reflected back.
ΔP = -mv_x -mv_x = -2mv_x = FΔt_collision

Then they say the collision occurs every 2d/v_x because that's the time it takes for the molecule to hit one side of the wall then come back. The time interval for this is Δt.

then they say that the average force over the time interval, and they say the change in momentum for this time interval us te same as that for the short duration of the collsion,

FΔt = -2mv_x

I don't understand why they say the time interval it takes for the molecule to go from one side of the wall to the other side and back is the same as the time interval of the collision.

 

[mfb]

No, that is not said. However, you have many particles, colliding all the time. So you are not interested in the time-dependence of the momentum transfers of a single particle - it is sufficient to calculate its average. And that is ("momentum transfer") / ("time between collisions").