Percentage error in Maxwellian distribution.

[debjit625]

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

 

[BvU]

Hello debjit,

What equation did you use to calculate the average kinetic energy ?
Do you know the equation for the standard deviation ?

 

[debjit625]

Thanks for the reply BvU.
I used Maxwell's velocity distribution to compute average or mean speed

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

From this I computed the average or mean speed
c' = 1/N ( _o ∫ ^∞ cdN_c)

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

 

[BvU]

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