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Rms velocity and compression. Please help

  1. Dec 12, 2011 #1
    rms velocity and compression. Please help!!

    1. The problem statement, all variables and given/known data

    Explain why the rms velocity of a gas increases when it is adiabatically compressed.

    2. Relevant equations

    None

    3. The attempt at a solution

    I know that compressing a gas decreases the volume, but I don't know details on how it would effect rms velocity
     
  2. jcsd
  3. Dec 12, 2011 #2
    Re: rms velocity and compression. Please help!!

    Do you understand what adiabatically compressed means? If you don't, google it :-)
     
  4. Dec 12, 2011 #3
    Re: rms velocity and compression. Please help!!

    If you compress a gas adiabatically, no heat is transferred from the gas to its surroundings. You know that compressing a gas increases the temperature (and you can calculate by how much using your adiabatic relations).

    [itex]T*V^{γ-1} = constant[/itex]
    [itex]T_{0}*V_0^{γ-1} = T_1*(V_0 + ΔV)^{γ-1}[/itex]
    Thus
    [itex]T_1 = T_{0}*(V_0/(V_0 + ΔV))^{γ-1}[/itex]
    And
    [itex]ΔT = T_1 - T_0[/itex]

    Then
    [itex]ΔE = (3/2)N k_b ΔT= (1/2)N m (Δv)^2 [/itex]
    Or
    [itex] Δv = \sqrt{(3/2) (k_b ΔT)/m} [/itex]
     
    Last edited: Dec 12, 2011
  5. Dec 12, 2011 #4
    Re: rms velocity and compression. Please help!!

    And I was gonna make you figure it out yourself. :-(:wink:
     
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