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Particle physics / ideal gas problem

  1. Nov 20, 2009 #1
    1. The problem statement, all variables and given/known data
    Dust particles are approximately 11.0 micrometers in diameter. They are pulverized rock, with density 2500 kg/m^3. If you treat dust as an ideal gas, what is the rms speed of a dust particle at 23.0 degrees C?

    2. Relevant equations
    I have no idea.
    The only one I would bet money on is:

    [tex]v_{rms}=\sqrt{\frac{3k_{B}T}{m}}[/tex]

    3. The attempt at a solution
    I made a couple of far-reached guesses at this problem and came to the wrong answer. One method was to use the ideal gas law with pressure = 101325 Pa, and getting the number of particles to be 2.48*10^25. My main issue here is going from density and radius of a particle to a molecular mass or a correct number of particles. I am completely stumped by the problem and getting nowhere. If anyone could offer help, I would greatly appreciate it.
     
  2. jcsd
  3. Nov 20, 2009 #2

    jgens

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    Gold Member

    Well, show us your work for what you've done so far and maybe we'll be able to offer more help! I'll give you a couple of hints though: The absolute temperature of an ideal gas is proportional to its random translational kinetic energy. How might this help you solve the problem?
     
  4. Nov 20, 2009 #3

    ehild

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    Homework Helper
    Gold Member

    Your starting formula is OK,

    [tex]
    v_{rms}=\sqrt{\frac{3k_{B}T}{m}}
    [/tex]

    but why do you want the number of he particles? In the formula, m means the mass of a single particle. Given the diameter and density, it is easy to get.

    ehild
     
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