Maxwell Distrib: Determine Vrms & Temp

[itryphysics]

Homework Statement

A gas consisting of 15,200 molecules, each of mass 2.00×10^−26 kg , has the following distribution of speeds, which crudely mimics the Maxwell distribution:
Number of Molecules
1600
4100
4700
3100
1300
400
Speed
210
420
630
840
1050
1260

Determine V_rms for this distribution of speeds.
Given your value for V_rms , what (effective) temperature would you assign to this gas?

Homework Equations

V_rms = square root {Average V^2} or square root {3kT/m}

The Attempt at a Solution

So I squared all the values and then divided by the total number to obrain (Average velocity^2) and then took the square root ...the attempt failed..many thanks to anyone who helps!

 

[Doc Al]

So I squared all the values and then divided by the total number to obrain (Average velocity^2) and then took the square root ...the attempt failed..

You need to first find the weighted average of the squares of the speeds.

 

[malawi_glenn]

what do you mean by "squaring all values"?

Do you weight all speed^2 with their occurrence?

 

[itryphysics]

so the average of the squares of the speeds was 6.6885*10^5

 

[itryphysics]

what do you mean by "squaring all values"?

Do you weight all speed^2 with their occurrence?

sorry for the confusion...i meant squaring all speeds..

and I don't know wht you mean by your second question :S

 

[malawi_glenn]

sorry for the confusion...i meant squaring all speeds..

and I don't know wht you mean by your second question :S

then you did not do the weigted average.. look it up

 

[itryphysics]

square root { (3kT) /m}

is that the weighted average?

 

[malawi_glenn]

square root { (3kT) /m}

is that the weighted average?

no

http://mathworld.wolfram.com/WeightedMean.html

http://en.wikipedia.org/wiki/Weighted_mean

You did not have statistics in school yet?