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Kinetic theory of gases - can someone check this please?

  1. Feb 18, 2006 #1
    i'm given that p= [tex]\frac{1}{3}\rho\overline{c^2}[/tex]

    without calculation, what happens to rms speed if pressure halved, temperature constant?

    firstly, just from rearranging the original equation, you get

    [tex]\overline{c^2}[/tex] = [tex]\frac{3p}{\rho}[/tex]

    square rooting both sides to get rms speed gives:

    rms speed = [tex]\sqrt{\frac{3p}{\rho}}[/tex]

    which rearranges to rms speed = 9 [tex]\sqrt{\frac{p}{\rho}}[/tex]

    then, using original equation, when pressure halved, you get:

    [tex]\overline{c^2}[/tex] = [tex]\frac{3p}{2\rho}[/tex]

    square rooting both sides to get rms speed gives:

    rms speed = [tex]\sqrt{\frac{3p}{2\rho}}[/tex]

    which rearranges to rms speed = [tex]\frac{9}{4}[/tex] [tex]\sqrt{\frac{p}{\rho}}[/tex]

    so is it ok to say that the rms speed is quartered?
     
    Last edited by a moderator: Feb 18, 2006
  2. jcsd
  3. Feb 18, 2006 #2

    Astronuc

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    Staff: Mentor

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