Percentage error in Maxwellian distribution.

  • Thread starter debjit625
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Homework Statement


In computing the average kinetic energy of a molecule obeying Maxwellian distribution one use the formula ½mc2 .Calculate the percentage error incurred in the calculation.

The Attempt at a Solution


Here c is the average velocity of a molecule obeying Maxwellian distribution which I can calculate which is √(8KT/πm), but I have no idea how to calculate the percentage error so no attempt has been made.

Thanks
 

Answers and Replies

  • #2
BvU
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Hello debjit,

What equation did you use to calculate the average kinetic energy ?
Do you know the equation for the standard deviation ?
 
  • #3
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Thanks for the reply BvU.
I used Maxwell's velocity distribution to compute average or mean speed

Maxwell's velocity distribution
dNc = 4πN(m/2πkT)3/2e-(mc2/2kT)c2dc

From this I computed the average or mean speed
c' = 1/N ( o cdNc)

c' = √(8kT/πm)

"Do you know the equation for the standard deviation ?"
Well I am not very much good at the statistical part ,so if you kindly explain it it will be very helpful.

Thanks
 
  • #4
BvU
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Well I am not very much good at the statistical part ,so if you kindly explain it it will be very helpful
Well, you can always look it up ...
usually you do something like ##<x^2> - <x>^2##, so you're halfway already :smile:
 

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