- #1

- Homework Statement:
- Question regarding derivation of pV = 1/3 Nmc^2

- Relevant Equations:
- $$\Delta t = 2L/v_{x}$$

This is such a small point but I just wondered if anyone could clarify.

It is easy to work out the time between successive collisions with one wall of the box, namely $$\Delta t = 2L/v_{x}$$However, if this time interval is for instance 1 second, then we could have either 1 or 2 collisions in this time interval depending on whereabouts the particle starts (i.e. could be at t=0 and t=1). These would result in different values for exerted force, but evidently this only is a problem at the beginning and end since double counting is definitely wrong.

My thinking was that when taking an average over a larger period of time - suppose n time intervals - the total time becomes [itex]n\Delta t[/itex] and if n becomes fairly large the calculated time interval for each collision [itex]\frac{n\Delta t}{n}[/itex] or [itex]\frac{n\Delta t}{n+1}[/itex] approach each other, so it doesn't matter if we count the first/last collisions.

Am I overcomplicating this?

It is easy to work out the time between successive collisions with one wall of the box, namely $$\Delta t = 2L/v_{x}$$However, if this time interval is for instance 1 second, then we could have either 1 or 2 collisions in this time interval depending on whereabouts the particle starts (i.e. could be at t=0 and t=1). These would result in different values for exerted force, but evidently this only is a problem at the beginning and end since double counting is definitely wrong.

My thinking was that when taking an average over a larger period of time - suppose n time intervals - the total time becomes [itex]n\Delta t[/itex] and if n becomes fairly large the calculated time interval for each collision [itex]\frac{n\Delta t}{n}[/itex] or [itex]\frac{n\Delta t}{n+1}[/itex] approach each other, so it doesn't matter if we count the first/last collisions.

Am I overcomplicating this?