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FallenLeibniz

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## Homework Statement

The problem that I am having stems from a problem given in the following way:[/B]

"a)Show that for a gas, the mean free path ##\lambda## between collisions is related to the mean distance between nearest neighbors ##r## by the approximate relation ##\lambda \approx r\frac{r^2}{\sigma}## where ##sigma## is the collision cross section."

## Homework Equations

a)Equation relating mean free path to molecule density and cross sectional area:

##\lambda \approx \frac{1}{n\sigma}##

---n is the number of molecules/number of collisions in a volume V that's

swept by the molecule during its travel

---##\sigma## is the collision cross section defined as ##\pi(2R)^2## where R is the radius of the molecule modeled as a sphere.

---n is the number of molecules/number of collisions in a volume V that's

swept by the molecule during its travel

---##\sigma## is the collision cross section defined as ##\pi(2R)^2## where R is the radius of the molecule modeled as a sphere.

## The Attempt at a Solution

[/B]After hours of working with it, I finally found that I can get the author's solution if I set the volume swept by the molecule approximately equal to the N cubes of length r...

##V_{swept_cyl} \approx V_{cubes}##

##(2\pi)(\sigma)(N)(\lambda) \approx N(r^3)##

However, I fail to see how this is totally justified in a physical context. Is it that we estimate that the cylinder is filled with those r length cubes as on average they (the neighbors) will be "about" that r distance away from the molecules the traveling one hits?

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