Calculating Molecules in a punctured tire

  • #1
If a tire is punctured (or if any container full of air is holed) the air starts to leak out. Consider a small area A of the wall of the container. Show that the number of molecules striking this surface in a time interval Δt is


p is the pressure
m is the average mass of the air molecule
<Vx> is the average x-velocity of the molecules
Assume collisions with the wall are elastic

By having elastic collisions, the KE is conserved and none of the KE is transferred in any other form
In class, we showed that p= -ΔP/Δt
where P is the average molecular momentum

pressure (p)=F/A
therefore -ΔP/Δt=F/A
F=ma => -ΔP/Δt=(ma)/A

that is where I have gotten so far. Not sure if I am doing this right or where to go from here
Please help!
  • #2
I don't follow your formula p= -ΔP/Δt. Which p is momentum, which is pressure? The units don't seem to work out either way for me.

It seems to me you need to start with Force = ma = m*Δv/Δt.
From force, you can get pressure easily. m is related to the number of molecules and the molar mass. Δv would be double the average speed of the molecules. Solve for number of molecules and see if it looks anything like the desired formula!
  • #3
does m=M(molar mass)*N(number of particles)
and F=pA?
  • #4
Looks good! I think you are almost there.

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