Maxwell-Boltzmann distribution help

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Homework Help Overview

The discussion revolves around applying the Maxwell-Boltzmann distribution of speeds to determine the fraction of F2 molecules at 500 K that have speeds within a specific range (240 to 250 m/s). Participants are exploring the implications of the distribution curve and integration in this context.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the need to integrate the Maxwell-Boltzmann equation between the specified speeds, with some expressing uncertainty about the integration process. Others suggest that integration may not be necessary due to the hint provided regarding linearity over the small range.

Discussion Status

The discussion is active, with participants questioning the necessity of integration and considering the implications of the hint about linearity. There is a suggestion that calculations could be simplified by evaluating the distribution at each velocity.

Contextual Notes

Participants are working under the assumption that the distribution curve is linear over the specified speed range, which may influence their approach to the problem. There is also a noted lack of confidence in integration skills among some participants.

Lily Wright
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Homework Statement


Use the Maxwell-Boltzmann distribution of speeds to find the fraction of F2 molecules at 500 K which have speeds in the range 240 to 250 m s -1
(HINT: determine the fraction of the total area under the distribution curve represented by the part between these two speeds. Assume that the distribution curve is linear over this small range)

Homework Equations


2}e^{-\frac{mv^{2}}{2KT}}dv.gif


The Attempt at a Solution


So I'm guessing I want to integrate this equation between 240 and 250 m s-1
So it simplifies to ∫v2e-mv2/2KTdv
I'm not very good at integrating so I genuinely have no idea what happens after that
 
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Lily Wright said:

Homework Statement


Use the Maxwell-Boltzmann distribution of speeds to find the fraction of F2 molecules at 500 K which have speeds in the range 240 to 250 m s -1
(HINT: determine the fraction of the total area under the distribution curve represented by the part between these two speeds. Assume that the distribution curve is linear over this small range)

Homework Equations


2}e^{-\frac{mv^{2}}{2KT}}dv.gif


The Attempt at a Solution


So I'm guessing I want to integrate this equation between 240 and 250 m s-1
So it simplifies to ∫v2e-mv2/2KTdv
I'm not very good at integrating so I genuinely have no idea what happens after that
You don't have to integrate if you use the given hint: "Assume that the distribution curve is linear over this small range"
 
Ah ok so would I just work it out for each velocity?
 

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