Understanding the Ideal Gas Assumption: Time of Collision Negligibility

  • Context: Undergrad 
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Discussion Overview

The discussion revolves around the assumption that the time of collision of gas molecules with walls is negligible compared to the time between collisions. Participants explore the implications of this assumption in the context of ideal gas behavior, questioning its origins and validity.

Discussion Character

  • Exploratory
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • One participant seeks clarification on whether the negligible collision time refers to molecule-molecule collisions or wall collisions.
  • Another participant suggests that the assumption implies the collision duration is much shorter than the average time between molecule-wall collisions, but expresses uncertainty about this interpretation.
  • A third participant notes that assumptions in physics often aim to simplify calculations, mentioning that the ideal gas model assumes non-interacting rigid spheres, which leads to contradictions.
  • A later reply reiterates that in an ideal gas, the relevant comparison is between wall collisions, as there are no molecule-molecule collisions.
  • One participant acknowledges the inconsistency of the assumption but points out that collisions between gas molecules are still necessary for certain considerations, emphasizing the requirement that the total volume of the molecules is much less than the volume of the gas.

Areas of Agreement / Disagreement

Participants express uncertainty about the interpretation of the assumption and its implications, indicating that multiple competing views remain without a clear consensus.

Contextual Notes

Participants highlight limitations in the assumptions made in the ideal gas model, including the dependence on the definition of collisions and the implications of treating gas molecules as non-interacting.

The28
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Quick question I am trying to grapple with. I have been given the assumption the time of collision of the molecule with the wall is negligible compared to the time between collisions.

Is this compared to the time between collisions of molecule to molecule or from one wall to the other wall.

Where does this assumption come from?

There is something I am not understanding
 
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I think it means that the duration of the collision itself is much faster than average duration between molecule-wall collisions. But don't quote me on that or bubble in C on your final exam just yet. Hopefully someone more knowledgeable in this area can verify this.
 
All assumptions come from the urge to justify the simplest possible approach to get concise formulas. Sometimes they are somewhat contradictory (non-interacting rigid spheres with zero volume do not collide with each other).
For your case I assume this is to justify assigning a single speed without taking into account the time needed to reverse it when a collistsion with a wall occurs. That way the pressure or the average kinetic energy comes out as a simple expression.
 
The28 said:
Is this compared to the time between collisions of molecule to molecule or from one wall to the other wall.

As there are no collisions between particles in an ideal gas it can be compared to the time between collisions with walls only.
 
DrStupid said:
As there are no collisions between particles in an ideal gas it can be compared to the time between collisions with walls only.
Somewhat inconsistent indeed, but for various issues we do need collisions between gas molecules. So we require that the total volume of the molecules is ##\lll## than the volume of the gas.
 

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