Ideal gas - percentage of fraction of molecules

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Homework Help Overview

The discussion revolves around a problem related to the Maxwell-Boltzmann distribution in the context of kinetic theory of gases (KTG). The original poster expresses confusion regarding the application of concepts related to average, root mean square (RMS), and most probable speeds, specifically in relation to an entrance exam question about the fraction of molecules at certain speeds.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the relevance of the Maxwell-Boltzmann distribution and question the original poster's understanding of the necessary equations. There are inquiries about how to apply a specific equation from the textbook, including whether to find a fraction of molecules or to integrate the equation, along with considerations of limits for integration.

Discussion Status

Some participants have provided guidance on the interpretation of the equation and the approach to finding the fraction of molecules. There is an ongoing exploration of different values for speed and the corresponding intervals, indicating a productive direction in the discussion.

Contextual Notes

The original poster notes that their textbook only provides definitions and formulas without derivations, which may limit their understanding of the concepts needed to solve the problem.

Jahnavi
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Homework Statement


gas_percentage.jpg


Homework Equations

The Attempt at a Solution



Honestly speaking , I have absolutely no idea about this problem .This doesn't happen often .In the KTG chapter , only definition and formula of Average , RMS and Most probable speeds is given .

This question is for an entrance exam which requires minimum application of calculus . So I am guessing there is a formula for this problem which I am unaware of .

Please help me solve this problem in a simple way .
 

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Does your text not cover the Maxwell-Boltzmann distribution? Likely the Average , RMS and Most probable speed were derived using it.
 
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Jahnavi said:
Honestly speaking , I have absolutely no idea about this problem
You should know this does not count as an attempt -- so we're not allowed to help :rolleyes: .

Could it be you don't know what distribution you need for this ? i doubt that ...
 
Thanks @gneill for replying .

gneill said:
Does your text not cover the Maxwell-Boltzmann distribution? Likely the Average , RMS and Most probable speed were derived using it.

Please see the attached image from the textbook .As you can see nothing is derived .Only definitions and formula are given .
 

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Jahnavi said:
Please see the attached image from the textbook .As you can see nothing is derived .Only definitions and formula are given .
What about equation 24.13 at the bottom of the page?
 
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gneill said:
What about equation 24.13 at the bottom of the page?

OK . But I don't understand how to use this equation .

Do I need to find dN/N ? Or do I need to integrate this equation ? What will be the limits of N and v ?
 
Jahnavi said:
OK . But I don't understand how to use this equation .

Do I need to find dN/N ? Or do I need to integrate this equation ? What will be the limits of N and v ?

Yes, dN/N would be the fraction of molecules with speeds between v and v+dv. Since the range of speeds given is pretty narrow, you should be able to get a pretty good approximation using dv ≅ Δv . Integration would give you an exact result, but the integral might be a bit tricky.
 
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Should I go ahead with v = 323 and ∆v = 3 or v = 324 and ∆v = 2 ?
 
Jahnavi said:
Should I go ahead with v = 323 and ∆v = 3 or v = 324 and ∆v = 2 ?
The latter.
 
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Thank you gneill !
 

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