Finding C from a speed distribution function.

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SUMMARY

The forum discussion focuses on solving a speed distribution function for gas particles represented by the equation fv = Cv/(v² + vo²)². The primary tasks include finding the constant C, calculating the most probable speed, and determining the fraction of particles moving faster than this speed. The most probable speed is derived as v = vo/√3 by taking the derivative of the function and setting it to zero. Additionally, to find the fraction of particles exceeding this speed, a definite integral of the function from vo/√3 to infinity is required.

PREREQUISITES
  • Understanding of speed distribution functions in statistical mechanics
  • Knowledge of calculus, specifically differentiation and integration
  • Familiarity with constants in mathematical functions
  • Basic concepts of gas particle behavior and thermodynamics
NEXT STEPS
  • Learn about normalization of probability distribution functions
  • Study the derivation of most probable speed in Maxwell-Boltzmann distribution
  • Explore definite integrals in the context of probability and statistics
  • Investigate the implications of constants in physical equations
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This discussion is beneficial for physics students, particularly those studying thermodynamics and statistical mechanics, as well as educators and researchers focusing on gas behavior and distribution functions.

Cantspel
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Homework Statement


Gas particles of a particular gas have a speed distribution function of

fv = Cv/(v2 +vo2)2

a. Find the value of C

b. Calculate the most probable speed

c. What fractions of the particles are moving faster than the most probable speed

Homework Equations

The Attempt at a Solution


[/B]
For problem a I don't even know where to begin, I know that C is probably a form of vo otherwise the function could end up being higher 1

I already got problem b by taking the derivative of the function and then setting it equal to 0
which got me

v = vo/√3

For problem c what I believe what I need to do is take the definite integral of f*dv between vo/√3 and infinity.
 
Last edited:
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Forgot to mention that vo and C are both constants.
 

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