Understanding the Ideal Gas Assumption: Time of Collision Negligibility

[The28]

Quick question I am trying to grapple with. I have been given the assumption the time of collision of the molecule with the wall is negligible compared to the time between collisions.

Is this compared to the time between collisions of molecule to molecule or from one wall to the other wall.

Where does this assumption come from?

There is something I am not understanding

 

[Drakkith]

I think it means that the duration of the collision itself is much faster than average duration between molecule-wall collisions. But don't quote me on that or bubble in C on your final exam just yet. Hopefully someone more knowledgeable in this area can verify this.

 

[BvU]

All assumptions come from the urge to justify the simplest possible approach to get concise formulas. Sometimes they are somewhat contradictory (non-interacting rigid spheres with zero volume do not collide with each other).
For your case I assume this is to justify assigning a single speed without taking into account the time needed to reverse it when a collistsion with a wall occurs. That way the pressure or the average kinetic energy comes out as a simple expression.

 

[DrStupid]

Is this compared to the time between collisions of molecule to molecule or from one wall to the other wall.

As there are no collisions between particles in an ideal gas it can be compared to the time between collisions with walls only.

 

[BvU]

As there are no collisions between particles in an ideal gas it can be compared to the time between collisions with walls only.

Somewhat inconsistent indeed, but for various issues we do need collisions between gas molecules. So we require that the total volume of the molecules is $\lll$ than the volume of the gas.