Average relative velocity in calculating mean free path

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Discussion Overview

The discussion revolves around the use of the root mean square (rms) of relative velocity in the calculation of mean free path, particularly in the context of molecular collisions. Participants explore the implications of using different measures of relative velocity, including mean-relative-speed versus rms-relative-speed.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant questions the rationale behind using rms-relative-velocity instead of mean-relative-velocity in mean free path calculations.
  • Another participant suggests experimenting with mean-relative-velocity to observe the outcomes.
  • A participant clarifies that mean-relative-velocity would yield zero due to its vector nature and instead refers to mean-relative-speed, expecting it to be less than rms-relative-speed.
  • Another participant encourages reviewing notes on mean free path and suggests adjusting derivations if mean-speed is used instead of rms speed, implying that the choice of measure affects the results.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of using rms versus mean-relative-speed in calculations, indicating that there is no consensus on the best approach.

Contextual Notes

Participants note the need to adjust derivations when changing from rms speed to mean speed, highlighting the dependence on definitions and the implications of using different measures.

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Try it and see what happens when you use the mean-relative-velocity. ;)
 
Thanks Simon,

I'm not really following. The mean-relative-velocity would be 0 since velocity is a vector. I think I meant to say mean-relative-speed. I would expect the mean-relative-speed to be less than the rms-relative-speed but that's about it.

Thanks
 
Ri-ight - so, look through your notes about mean free path, where it is applied (say: brownian motion) and use your idea of the mean-speed instead of the rms speed. (You'll have to adjust the derivation to account for the difference.) See what you get.

I could go and just describe in words why the rms speed is preferred etc etc ... but that's a lot of typing when I can just make you do the math. You asked the question: are you prepared to find the answer?
 

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