Average velocity of gas molecules in a container

  • #1

Homework Statement


An ideal gas with molecules of mass m is contained in a cube with sides of area A. The pressure exerted by the gas on the top of the cube is P, and N molecules hit the top of the cube in a time
Δt. What is the average vertical component of the velocity of the gas molecules.


Homework Equations


F = ma P = f/A

The Attempt at a Solution



F = ma
F = mΔV /Δt
F = 2mV / Δt (ΔV = 2V since collisions are elastic)

Putting this into P = F/A leads to the correct answer but my problem is with the Δt. When used in the acceleration Δt should be the time that the molecules is in contact with the wall of the container and it seems to me to be unrelated to the Δt as specified in the question.

Thanks to anybody that can help clear this up.
 

Answers and Replies

  • #2
ehild
Homework Helper
15,543
1,909

Homework Statement


An ideal gas with molecules of mass m is contained in a cube with sides of area A. The pressure exerted by the gas on the top of the cube is P, and N molecules hit the top of the cube in a time
Δt. What is the average vertical component of the velocity of the gas molecules.


Homework Equations


F = ma P = f/A

The Attempt at a Solution



F = ma
F = mΔV /Δt
F = 2mV / Δt (ΔV = 2V since collisions are elastic)

Putting this into P = F/A leads to the correct answer but my problem is with the Δt. When used in the acceleration Δt should be the time that the molecules is in contact with the wall of the container and it seems to me to be unrelated to the Δt as specified in the question.

Thanks to anybody that can help clear this up.
The wall exerts bigger force on the molecule while in contact with it, but the pressure it exerts on the gas is also average quantity: the time average of the force exerted by unit area. It exerts some force f to one molecule during the collision , and zero between the collisions.
 
  • #3
The wall exerts bigger force on the molecule while in contact with it, but the pressure it exerts on the gas is also average quantity: the time average of the force exerted by unit area. It exerts some force f to one molecule during the collision , and zero between the collisions.
Thanks, Maybe I'm missing something that will seem obvious once it makes sense, but when considering the acceleration shouldn't we just consider the time that the molecule is actually in contact with the wall? It really doesn't seem right to me to use the same Δt.
 
  • #4
vela
Staff Emeritus
Science Advisor
Homework Helper
Education Advisor
14,843
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Instead of thinking in terms of acceleration, think of the force in terms of momentum delivered per unit of time. It's the momentum per collision divided by the time between collisions.
 

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