Maxwell - Boltzman distribution

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Discussion Overview

The discussion revolves around the Maxwell-Boltzmann (M-B) distribution, specifically focusing on the speed distribution derived from the M-B probability function. Participants explore the integration of this distribution and the interpretation of the area under the probability curve.

Discussion Character

  • Technical explanation
  • Mathematical reasoning

Main Points Raised

  • One participant created a spreadsheet to plot the 3D speed distribution from the M-B probability function and noted a discrepancy in the area under the curve, suggesting a misunderstanding of its significance.
  • Another participant directed attention to an article that outlines properties of the M-B distribution, implying that an error may have occurred in the calculations of the first participant.
  • A third participant pointed out a normalization issue, referencing a specific source to support this claim.
  • The initial poster later reported that the area under the curve was approximately 0.98 after numerical integration, indicating a resolution to their earlier concern.

Areas of Agreement / Disagreement

While there was initial confusion regarding the area under the curve, the later response from the first participant suggests a resolution to their specific issue. However, the discussion does not indicate a consensus on the normalization process or the calculations involved.

Contextual Notes

Participants did not fully explore the assumptions behind the integration method or the definitions of normalization in this context, leaving some aspects unresolved.

mattT1227
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I made a spreadsheet to plot the 3d speed distribution from the MB probability function. It matches the peak and fall-off of published graphs. I then tried to integrate it by summing over interval widths times probability. I thought the area should be 1. My result is around 5 or 6. I've tried really small intervals, around 0.25 m/s, that didn't help. Must be I don't understand what the area under the probability curve represents.
 
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Thanks all. Problem solved. Area under curve is 0.98 by numerical integration, close enough.
 

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