Adiabatic effusion and violation of energy conservation

  • Thread starter mukul
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  • #1
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Main Question or Discussion Point

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!!
 

Answers and Replies

  • #2
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Adiabatic. What's Tinitial? What's Tfinal?
 
  • #3
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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
 
  • #4
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What's the Joule-Thompson inversion T for He?
 
  • #5
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it is 51 K at 1 atm
 
  • #6
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How many hints do you want?
 
  • #7
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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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