Blundell Thermal Physics · Problem 9.2

Transport properties in gases

Physics — Statistical Mechanics · thermal-conductivity-mean-free-path

Problem

Obtain an expression for the thermal conductivity of a gas at ordinary pressures. The thermal conductivity of argon (atomic weight 40) at STP is 1.6×10−21.6\times10^{-2} W m−1^{-1} K−1^{-1}. 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 regarded as hard spheres, 0.74 of the volume of the structure is filled. The density of solid argon is 1.6×1031.6\times10^{3} kg m−3^{-3}. Compare the effective atomic radius obtained from this information with your effective collision radius. Comment on your result.

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