Kinetic equation of gases: time between collisions instead of time of colission?

[Vladimir_Kitanov]

I understand everything except why do we use time between collisions instead of time of colission?

 

[Vladimir_Kitanov]

And can it be done differently?

 

[TSny]

It's the average rate of change of momentum of one molecule due to collisions of the molecule against one wall that is of interest. Suppose you have a job that pays $5000 per month and you get paid on the last day of the month. So, you deposit $5000 each payday into your bank account. You wouldn't claim that your account is increasing at an average rate of $5000 per day. The average rate of increase of the account is $5000 divided by the the time between deposits (a month). Same with the molecule. Its average "deposit" of momentum-change against one wall is the momentum change of the collision divided by the time between collisions of that molecule with that wall.

You find this derivation in many introductory physics textbooks and it does get the idea across. However, we know that for a gas of many molecules, a single molecule will travel a very erratic path as it collides with other molecules. So, to me, this makes the derivation questionable. For a better derivation see for example here. More sophisticated derivations can be found in textbooks on statistical mechanics.