- #1

mitch_1211

- 99

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## Homework Statement

obtain an expression for the thermal conductivity of a gas at ordinary pressures. The thermal conductivity of Argon (atomic weight 40) at STP (standard temp and pressure) is 1.6e-2 W/mK. Use this to calculate the mean free path in Argon at STP. Express the mean free path in terms of an effective atomic radius for collisions and find the value of this radius.

Solid argon has a close-packed cubic structure in which if the atoms are regraded as hard spheres, 0.74 of the volume of the structure is filled. The density of solid argon is 1.6e3 km/m^3. Compare the effective atomic radius obtained from this information with your effective collision radius. Comment on your result.

## Homework Equations

[tex]\kappa = \frac{1}{3}C_{v}\lambda[/tex]

[tex]\lambda=\frac{k_{b}T}{\sqrt{2}\pi d^{2}p}[/tex]

[tex]\lambda[/tex]=mean free path

d = diametre

p = pressure

[tex]\kappa[/tex]=thermal conductivity

## The Attempt at a Solution

I know i can get the mean free path from [tex]\kappa = \frac{1}{3}C_{v}\lambda[/tex] as thermal conductivity is given. but what do i do about the Cv term?

I think i then calculate d from [tex]\lambda=\frac{k_{b}T}{\sqrt{2}\pi d^{2}p}[/tex] and this is my "effective atomic radius for collisions"

Do i then simply multiply 0.74 by the given density to work out the "effective atomic radius"?

mitch