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Kinetic Theory of Gases

  1. Sep 20, 2009 #1
    1. The problem statement, all variables and given/known data

    A square box contain He at 25C. If the atoms collide with wall perpendicularly (90 degrees) at rate of 4.0E22 times/s, calculate pressure and force exerted on wall given area of wall 100cm^2 and speed of atoms =600 m/s

    2. Relevant equations
    PV=Nmv^2

    3. The attempt at a solution
    I'm not really sure what the N is... the question doesn't give the amount of He gas, so how do i know how many atoms there are? and the same for m...
    otherwise, i can find V from area given; velocity also given, then i can find pressure
     
  2. jcsd
  3. Sep 20, 2009 #2
    actually, for m, i can get from the molar mass and avogadro's number right?
    but i still don't get what N is...
     
  4. Sep 20, 2009 #3

    Borek

    User Avatar

    Staff: Mentor

    You don't need volume, gas density will be enough.

    --
    methods
     
  5. Sep 20, 2009 #4
    You could go to first principles:
    .What is the momentum of one molecule on hitting the wall?
    .What is the momentum when it bounces off?
    .What is the momentum change?(remember momentum is a vector)
    .Force is rate of change of momentum i.e.the total momentum change in 1 second so what is the force?
     
  6. Sep 20, 2009 #5

    ok, so the momentum of 1 molecule hitting the wall is mv(mass x velocity)
    when bounce off, the v is going to be in opposite direction so, change in momentum will be
    mv - m(-v) = 2mv

    so force = 2mv / time ? is this correct?
    I have no idea what's next ...
     
  7. Sep 20, 2009 #6
    So this is what i have:

    F = change in momentum /time
    F = 2mv /t

    velocity is given in the question=600m/s , time is given = 4.0X10^22 times/s
    m is i'm guessing the molar mass?
     
  8. Sep 21, 2009 #7
    Your equation gives the change in momentum of a single molecule in one second i.e. the force exerted by the single molecule.If there were N molecules the total force would be
    given by F=N2mv/t=2mv*N/t where N/t=number of collisions per second(4.0*10^22)
     
  9. Sep 21, 2009 #8

    okay, that makes sense. But i still don't really get how to find the mass of He, which has to be in grams right...?
     
  10. Sep 21, 2009 #9
    does the number of collision equals the number of molecules of He? If so, then i can get the # of moles from avogadro's number. Then with the moles, i can get grams of He using molar mass of He... can i do that?

    m = 4.0X10^22 molecules * (1 mol/6.022E10^23 molecules) * (4.003 g/mol) He
    =.266 g He
    can someone double check.. thanks!
     
  11. Sep 21, 2009 #10
    m in the equation stands for the mass of a single helium atom which you can find from the mass of one mol of He divided by Avagadros number.To find F in N and P in N/m^2(Pa) you need to express m in Kg.
     
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