# Percentage error in Maxwellian distribution.

• debjit625
In summary, the conversation discusses calculating the percentage error in computing the average kinetic energy of a molecule using the formula ½mc2. The conversation also includes the use of Maxwell's velocity distribution to compute the average or mean speed and the equation for standard deviation. The person asking the question is not familiar with the statistical aspect and asks for further explanation.

## 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

Hello debjit,

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

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

debjit625 said:
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