Ideal Gas Law Equilibrium Requirements

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Discussion Overview

The discussion centers around the applicability of the ideal gas law under non-equilibrium conditions, specifically in the context of free expansion of an ideal gas. Participants explore the implications of particle interactions and velocity distributions during such expansions.

Discussion Character

  • Exploratory
  • Debate/contested
  • Technical explanation

Main Points Raised

  • One participant questions whether the ideal gas law is valid during non-equilibrium conditions, particularly in free expansion scenarios.
  • Another participant challenges the definition of volume in free expansion, suggesting that the ideal gas law (PV = MRT) may not hold.
  • A participant notes that the Maxwell-Boltzmann distribution may not apply during free expansion, citing the varying velocities of Ne atoms at different points in the gas cloud.
  • One participant explains that interactions among molecules maintain equilibrium before expansion, but during free expansion, the distribution of fast and slow molecules changes, leading to a non-Maxwellian distribution.
  • A later reply acknowledges the previous explanation and connects it to the principle of Occam's razor, suggesting that simpler explanations may often be correct.

Areas of Agreement / Disagreement

Participants express differing views on the validity of the ideal gas law and the Maxwell-Boltzmann distribution during free expansion, indicating that multiple competing perspectives remain without consensus.

Contextual Notes

Participants highlight limitations in defining volume during free expansion and the assumptions regarding particle interactions and velocity distributions, which remain unresolved.

0pt618
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It is well known that the ideal gas law applies only to an ideal gas, one consisting of particles infinitesimal in size and exhibits no interactions between the particles. Considering an ideal gas, is the ideal gas law valid under non-equilibrium conditions? For example, does the ideal gas law hold for all instants of in the free expansion of an ideal gas?

References, if available, would be appreciated.
 
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"Free"expansion? How do you define volume for such a condition? PV = MRT is then not valid.
The Maxwell-Boltzmann distribution is not valid either. Let's assume the expansion of a Ne
gas volume starts from an initial equilibrium state. At say 20 C the Ne atoms have an average
velocity of ~850m/s, but there are atoms with velocities close to 0 m/s and some which
move at over 2000 m/s. Clearly in a "free" expansion the velocity distribution at the boundaries of the
expanding Ne cloud will not be Maxwellian.
 
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Kazys, thank you. But why is it that "the velocity distribution at the boundaries of the gas will not be Maxwellian" in a "free" expansion?
 
My answer is simplistic, and because of that chances are that it is correct. Consider the Ne cloud before its free expansion. Within the could
the molecules interact, the probability is that fast ones loose energy, slow ones gain it. Equilibrium is maintained. At the edges the fast
molecules move faster in all directions including the outward directions. There they do not interact but keep moving. The slow ones
tag behind. Consequently the ratio of fast to slow molecules changes, thus it is no longer Maxwellian.
 
Thanks Kazys - this makes sense. As an aside, you are referring to Occam's razor, when you say the simple answer is usually the correct one, right?
 

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