The thermal conductivity of gases in confined spaces or at very low pressures is quite different from diffusion at atmospheric pressure. The motion of the gas is governed by collisions of the gas particles with the container walls, not with other molecules. For a container of radius, \(r_{o}\), derive an expression for the thermal conductivity of a gas using kinetic theory and assuming that wall collisions are all-important. Start from equation (3.90) and alter the value of the mean free path. What implications does your result have for designing insulation materials?

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Thermal W k = (3.90) 2 V conductivity mK