Maxwell's velocity distribution

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SUMMARY

The discussion centers on Maxwell's velocity distribution, specifically addressing issues with file formats when sharing related documents. Users encountered problems when saving files in the wrong format, leading to errors in accessing content. The conversation highlights the importance of saving documents as "All files" to avoid issues and discusses the derivation of the Maxwell-Boltzmann (MB) distribution, emphasizing the need for proper normalization in mathematical functions. A simpler derivation using the central-limit theorem is mentioned but deemed not significantly easier than the standard approach.

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  • Understanding of Maxwell-Boltzmann distribution
  • Familiarity with file formats such as DOCX, PDF, and image files
  • Basic knowledge of probability functions and normalization
  • Awareness of the central-limit theorem in statistics
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  • Research the derivation of the Maxwell-Boltzmann distribution in statistical mechanics
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  • Investigate normalization techniques for probability density functions
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Students and educators in physics, particularly those studying statistical mechanics, as well as anyone involved in document sharing and formatting issues.

Ben Hom Chen
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I have some problem in the paragragh.
I save it as Word format.The link is below.
Thanks!

http://www.badongo.com/file/3337594"
 
Last edited by a moderator:
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I downloaded the file, which is a zip containing some xml docs I will not open. You won't get any help unless you show your problem and your work.
 
http://www.badongo.com/file/3383953

I upload my problem again.

And I found that when downloading it,badongo system set the default
file format as "zipped file",so some error would happen.

When saving file,we must change the saving format to"All files",then it can
be opened without error.

I hope my words can be understood><

Thx><
 
Last edited by a moderator:
Sorry, Ben, nothing has changed. I can't read the docx format. Try saving your document as PDF or .doc.
 
OK, I can see the pictures. THis is the standard undergraduate derivation of the MB distribution.

1. \vec{v}^2 = v_x^2 + v_y^2 + v_z^2

2. Hmm. Maybe this should be "f(\vec{v}^2) is the probability of finding a particle with squared velocity \vec{v}^2".

3. The function e^{ax} is not normalizable unless a < 0. By convention one gives 'a' a positive value and writes the equation with a negative sign.
 
Thx for your help.
At least I understand the third answer^^"
 
I never liked that derivation, which I have in the Pauli lectures in it's full clunkiness. In fact it's possible to derive the MB distribution using a much simpler heuristic argument and I'll be happy to dig it out and post it if you like.
 
Thank You,I want to check it out.

If it won't take you much time.
 
  • #10
Well, I found it but it's not simpler and relies on the central-limit theorem so maybe the standard derivation is the best after all.
 

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