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A question asked me to derive a symbolic expression for mean particle speed using the Max-Boltz equation. I know that Max-Boltz equation is a function of velocity (v).
The Max-Boltz equation is ##f=(\frac{m}{2\pi kT})^{3/2}4\pi v^2 exp(\frac{-mv^2}{2kT})##
Apparently the general formula for the average given a statistical function is ##\bar{v}=\int_{0}^{\infty}\frac{fvdv}{n}##
Here is what I don't understand:
1) Where did this formula come from? Does this formula only apply to statistical functions? What is a statistical function?
2) It turns out that division by the number of particles (n) is unnecessary for the Max-Boltz equation. What is reasoning behind this?
3) Why is the integration from zero to infinity? Clearly no particle can have infinite velocity...
Thank you again!
The Max-Boltz equation is ##f=(\frac{m}{2\pi kT})^{3/2}4\pi v^2 exp(\frac{-mv^2}{2kT})##
Apparently the general formula for the average given a statistical function is ##\bar{v}=\int_{0}^{\infty}\frac{fvdv}{n}##
Here is what I don't understand:
1) Where did this formula come from? Does this formula only apply to statistical functions? What is a statistical function?
2) It turns out that division by the number of particles (n) is unnecessary for the Max-Boltz equation. What is reasoning behind this?
3) Why is the integration from zero to infinity? Clearly no particle can have infinite velocity...
Thank you again!