Assumptions in the derivation of the kinetic theory of gases

[Miss_e101]

When deriving the kinetic theory of gases, we take the change in momentum of a particle as it hits one side of a box and divide it by the time over which the collision takes place. The time is derived by taking the total distance the particle traveled in the box (i.e. from one end, off the side and back again) divided by its velocity. However, why is it that we don't only take the time over which the collision with the wall occurred? Does this relate to the assumption that the size of the molecules is negligible compared with the size of the container?

Any assistance would be appreciated.

Cheers,
Miss_e101

 

[mjc123]

The rate of change of momentum is the momentum transfer per collision times the number of collisions per second. The latter quantity is equal to 1/(time between collisions), which is 1/(distance between collisions/velocity), assuming the time taken by a collision is negligible.