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Find the rms speed of a dust particle.

  1. Sep 9, 2012 #1
    1. The problem statement, all variables and given/known data

    Dust particles are 13.0 micrometers in diameter. They are pulverized rock, with ρ=2540 kg/m3 . If you treat dust as an ideal gas, what is the rms speed of a dust particle at 18.0 C?

    2. Relevant equations

    ρ=m/v
    V=4/3∏r2
    vrms=√(3kT/m)

    3. The attempt at a solution

    OK:

    13 micrometers = 1.3*10-5 m, which makes radius 6.5*10-6 m

    Then, V=(4/3)∏(6.5*10-6)2=1.7697*10-10 m3

    m=ρv=(2540)(1.7697*10-10 m3)=4.495*10-7 kg

    vrms=√(3*(1.38*10-23)*(273+18))/(4.495*10-7 kg))
    =1.63*10-7 m/s

    This isn't right though, anyone see where I went wrong?
     
  2. jcsd
  3. Sep 9, 2012 #2
    Check the volume of a sphere.
     
  4. Sep 9, 2012 #3
    Thank you very much
     
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