A gap of width between two parallel plates is filled with helium (molar mass ) at a…

PHYSICS · Multi-part · Fermi University Physics · Thermal, Statistical & Complex Systems · Kinetic theory and transport in gases · Kinetic theory and transport in gases

Thermal Physics, Ch Collisions, mean free path and transport in gases

Problem

A gap of width

4.0\,\mathrm{mm}

between two parallel plates is filled with helium (molar mass

4.003\,\mathrm{g\,mol^{-1}}

) at a pressure of

1.00\times10^{5}\,\mathrm{Pa}

. The mean temperature of the gas is

300\,\mathrm{K}

and the two plate temperatures differ by

25\,\mathrm{K}

. Treat the helium as an ideal gas of hard spheres of diameter

d = 0.21\,\mathrm{nm}

; helium is monatomic, so

f = 3

active degrees of freedom per atom. Radiation and convection are ignored, and the temperature gradient is taken as uniform across the gap. ((a)) Estimate the mean free path of a helium atom. ((b)) Estimate the thermal conductivity of the gas. ((c)) Using your estimate, find the heat flux across the gap in

\mathrm{W\,m^{-2}}

. Give each answer to two significant figures.

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