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Kinetic Theory: How many molecules enter pinhole in vacuum?

  1. Dec 10, 2015 #1
    1. The problem statement, all variables and given/known data
    Pressure in vacuum is 10^-3 Torr. External Pressure is 1atm and 300K. Pinhole of 10^-10cm^2 made in vacuum. Assuming all molecules striking hole pass through, how many molecules leak into vacuum in 1hour?
    Answer: 10^17 molecules
    2. Relevant equations
    Flux = <v>*N/4V
    Rate = Flux times A

    3. The attempt at a solution
    I can make an DE: dN/dt = <v>N/4V*A and solve this but I have no info on N0, initial molecules. I also don't have volume. So I don't see how to obtain a numerical result.
     
  2. jcsd
  3. Dec 10, 2015 #2
    Ask yourself what pressure is.
     
  4. Dec 10, 2015 #3

    mfb

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    2016 Award

    Staff: Mentor

    You only need N/V, molecules per volume, which you can get with the given information.
    Alternatively, take an arbitrary volume, it will cancel out in the calculations anyway.
     
  5. Dec 10, 2015 #4
    I don't see how I can get this with the information
    P/kT = N/V = 2.45molecules/m^3 = ρ
    Also <KE> = 3/2KT = 6.21E-21J = m/2 *<v^2>.
    Now particles within vΔt make it to hole; also those within AvΔtρ make it.
    Now I'm stuck. I can't get v since I don't have m. Also I'm unsure whether to invoke a Maxwell Distribution to get all velocities.
     
  6. Dec 10, 2015 #5

    TSny

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    Gold Member

    Looks like they are only asking for an order-of-magnitude answer. So, you can use any reasonable value for the mass of a molecule.
     
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