Calculating Molecules in a punctured tire

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Homework Help Overview

The discussion revolves around calculating the number of air molecules escaping from a punctured tire, focusing on the relationship between pressure, force, and molecular motion. The subject area includes concepts from fluid dynamics and kinetic theory.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to derive a formula for the number of molecules striking a surface based on pressure and molecular velocity. Some participants question the clarity of the original poster's formula and the definitions of pressure and momentum. Others suggest starting from basic principles like force and its relationship to pressure, while also considering the connection between mass, molar mass, and the number of particles.

Discussion Status

The discussion is ongoing, with participants providing feedback and suggestions for clarification. Some guidance has been offered regarding the relationships between force, pressure, and molecular quantities, but there is no explicit consensus on the approach yet.

Contextual Notes

Participants are navigating through the definitions and relationships of physical quantities, and there may be confusion regarding the application of certain formulas and units. The original poster expresses uncertainty about their progress and seeks further assistance.

J.Welder12
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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

pAΔt/2m<Vx>

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!
 
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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!
 
does m=M(molar mass)*N(number of particles)
and F=pA?
 
Looks good! I think you are almost there.
 

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