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Adiabatic effusion and violation of energy conservation

  1. Dec 29, 2014 #1
    when the gas effuse out of an insulated container, its velocity is given by
    [tex]\sqrt{\frac{2\gamma RT}{(\gamma-1)M}} [/tex]
    (irodov's problem 2.42)

    This leads to the result that every mole of leaking gas has an energy of
    [tex]\frac{\gamma RT}{(\gamma-1)} [/tex]
    whereas we know the energy contained in 1 mole of gas is
    [tex]\frac{RT}{(\gamma-1)} [/tex]

    From where is this difference of energy coming out.

    Thanks for helping!!
     
  2. jcsd
  3. Dec 29, 2014 #2

    Bystander

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    Adiabatic. What's Tinitial? What's Tfinal?
     
  4. Dec 29, 2014 #3
    By adiabatic, I mean no heat given to the system.
    Also the process here is not in equilibrium all the time. Its a free expansion.

    I am posting the exact question I am referring to (from Irodov's Problems in general physics - 2.42):

    Ques: Find the rave v with which helium flows out of a thermally insulated vessel into vacuum through a small hole.
    The flow rate of the gas inside the vessel is assumed to be negligible under these conditions.
    The temperature of helium in the vessel is T = 1,000 K.

    Ans: v = [tex]\sqrt{\frac{2\gamma RT}{(\gamma-1)M}} [/tex] = 3.3 km/s
     
  5. Dec 29, 2014 #4

    Bystander

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    What's the Joule-Thompson inversion T for He?
     
  6. Dec 29, 2014 #5
    it is 51 K at 1 atm
     
  7. Dec 29, 2014 #6

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    How many hints do you want?
     
  8. Dec 30, 2014 #7
    Thanks Bystander. I got it. This happens only in case of real gas. For ideal gas rms effusion speed is same as rms speed of gas molecules.
     
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