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Maxwell-Boltzmann distribution help

  • #1

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
 

Answers and Replies

  • #2
Redbelly98
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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
You don't have to integrate if you use the given hint: "Assume that the distribution curve is linear over this small range"
 
  • #3
Ah ok so would I just work it out for each velocity?
 
  • #4
Redbelly98
Staff Emeritus
Science Advisor
Homework Helper
Insights Author
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Yes.
 

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