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Pressure for 2-D gas

  1. Jan 10, 2014 #1
    1. The problem statement, all variables and given/known data

    Find an expression for the pressure of a 2-D gas in terms of <v>.

    2. Relevant equations



    3. The attempt at a solution

    In 2D, velocity distribution is:

    [tex] f_{(v^2)} = (\frac{a}{\pi}) e^{-av^2} , a = \frac{m}{2kT} [/tex]

    Integrate all possible angles to get speed distribution and normalize to get speed distribution:

    [tex] w_{(v)} = 2a v e^{-av^2} [/tex]
    Number of molecules travelling between speed v and v+dv, at angles between θ and θ + dθ per unit area = [tex] n \frac {dθ}{2\pi}w_{(v)} dv[/tex]
    = [tex] n \frac{a}{\pi}ve^{-av^2} dv dθ [/tex]

    To find pressure, take the above expression * change in momentum of one molecule / (L dt)

    [tex] dP = \frac{n \frac{a}{\pi}ve^{-av^2} dv dθ * (L v cosθ dt) * (2mv cosθ) }{L dt} [/tex]

    Then we integrate v from 0 to ∞, θ from 0 to ∏/2.

    Is that right?
     
  2. jcsd
  3. Jan 11, 2014 #2

    TSny

    User Avatar
    Homework Helper
    Gold Member

    That looks right to me.
     
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