Adiabatic effusion and violation of energy conservation

[mukul]

when the gas effuse out of an insulated container, its velocity is given by
$$\sqrt{\frac{2\gamma RT}{(\gamma-1)M}}$$
(irodov's problem 2.42)

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

From where is this difference of energy coming out.

Thanks for helping!

 

[Bystander]

Adiabatic. What's T_initial? What's T_final?

 

[mukul]

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 = $$\sqrt{\frac{2\gamma RT}{(\gamma-1)M}}$$ = 3.3 km/s

 

[Bystander]

What's the Joule-Thompson inversion T for He?

 

[mukul]

it is 51 K at 1 atm

 

[Bystander]

How many hints do you want?

 

[mukul]

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.