Adiabatic effusion and violation of energy conservation

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Discussion Overview

The discussion revolves around the concept of adiabatic effusion of gas from an insulated container, specifically focusing on the energy differences observed during this process. Participants explore the implications of the equations provided in Irodov's problem regarding the velocity and energy of effusing gas, while also considering the conditions under which the process occurs.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested

Main Points Raised

  • One participant presents a formula for the velocity of gas effusing from an insulated container and notes a discrepancy in energy calculations between the energy of leaking gas and the energy contained in one mole of gas.
  • Another participant questions the initial and final temperatures of the system during the adiabatic process.
  • A participant clarifies that the process is adiabatic, meaning no heat is exchanged, and emphasizes that it involves free expansion, which may not be in equilibrium.
  • There is a mention of the Joule-Thompson inversion temperature for helium, which is provided by another participant.
  • A later reply indicates that the observed energy difference is relevant only for real gases, contrasting with ideal gases where the root mean square effusion speed aligns with the root mean square speed of gas molecules.

Areas of Agreement / Disagreement

Participants express differing views on the implications of the energy calculations and the conditions of the effusion process. There is no consensus on the source of the energy discrepancy or the applicability of the results to ideal versus real gases.

Contextual Notes

The discussion includes assumptions about the nature of the gas (ideal vs. real) and the conditions under which the effusion occurs, which may affect the interpretations of the energy calculations and the behavior of the gas.

Who May Find This Useful

This discussion may be of interest to those studying thermodynamics, gas dynamics, or related fields in physics, particularly in understanding the nuances of adiabatic processes and effusion phenomena.

mukul
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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!
 
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Adiabatic. What's Tinitial? What's Tfinal?
 
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
 
What's the Joule-Thompson inversion T for He?
 
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it is 51 K at 1 atm
 
How many hints do you want?
 
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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