Maxwell-Boltzmann distribution help

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SUMMARY

The discussion focuses on applying the Maxwell-Boltzmann distribution to determine the fraction of F2 molecules at 500 K with speeds between 240 and 250 m/s. Participants clarify that integration of the equation ∫v²e^(-mv²/2kT)dv is unnecessary due to the hint provided, which states that the distribution curve can be assumed linear over the specified range. Instead, users are advised to calculate the values directly for each velocity within the range.

PREREQUISITES
  • Understanding of the Maxwell-Boltzmann distribution
  • Basic knowledge of integration techniques
  • Familiarity with the concepts of temperature and molecular speeds
  • Knowledge of the ideal gas law
NEXT STEPS
  • Study the derivation of the Maxwell-Boltzmann distribution
  • Learn about the implications of temperature on molecular speed distributions
  • Explore numerical integration techniques for non-linear distributions
  • Investigate applications of the Maxwell-Boltzmann distribution in real-world scenarios
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Students studying thermodynamics, physicists analyzing molecular behavior, and educators teaching statistical mechanics concepts.

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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