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Unit conversions - ideal gas

  1. Jun 1, 2010 #1
    Can I please check if I've converted these units right? I'm doing a question and got the answer a few order of magnitudes out.

    Question: Argon has a collision cross section of 0.36nm^2. At what pressure is the mean free path of argon atoms equal to the length of the side of a 1cm^3 cubic container in which they are kept at a temperature of 10K?

    Given info
    ==========
    cross section = 0.36 nm^2
    volume of cube = 1 cm^3

    Conversions
    ==========
    cross section = 0.36 * 10^-18 m^2
    volume of cube = 10^-6 m^3
    length of one side of cube = 0.01 m

    Attempt
    =======

    mean free path = 1 / ((2^0.5) * cross section area * number of molecules )

    number of molecules =1 / ((2^0.5) * (0.36*10^-18) *0.01) = 1.96*10^20 molecules

    N = number of molecules

    pV = NkT
    p = (NkT)/V = ((1.96*10^20)*(1.38*10^-23)*10) / 10^-6
    = 2.71*10^4 Pa


    Given Solution
    ============

    0.027 Pa
     
  2. jcsd
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