Time of Impact of Gas Molecules on the Inner Wall of a Pressure Vessel

[Zahid Iftikhar]

In derivation of relation for pressure of Gas ,(see pic below) the time for rate of change of momentum of molecules should be the time for which the wall of the vessel and the molecules kept interacting with each other, not the time between successive collisions. As circumscribed below, my confusion is how the time between two such collisions can be equal to the time of impact between the wall and the molecules. The time of impact has actually caused the change of momentum, thereby causing the pressure. I further argue, that let us suppose there are 100 or so molecules colliding just once on the wall, bounce back, and then never return (just assume), during this one-time collision, pressure has been exerted on the wall of the vessel. In this case, there is no time between successive collisions involved. I would be obliged if learned people on this forum help me to understand. High regards
Zahid

 

[Herman Trivilino]

I further argue, that let us suppose there are 100 or so molecules colliding just once on the wall, bounce back, and then never return (just assume), during this one-time collision, pressure has been exerted on the wall of the vessel.

In that case you would get a force exerted on the wall, and of course you could divide that force by the wall's area and get a pressure. But it would be a pressure pulse, and would last for a very short time. In that case, your reasoning is correct.

But if you go back and carefully read the derivation of the expression for the pressure of a gas in a box, you should see it stated that we are interested in a steady state pressure. There is a huge number of molecules colliding with the wall, and we are interested in the average pressure exerted on the wall due to the collisions. In this case we are interested in how often they collide and the number of such collisions.

There's a chapter-end problem in some textbooks where machine gun bullets are fired at Superman's chest. It's the same situation as above. To get the average force exerted on Superman we look at the frequency of collisions and the number and nature of the collisions.