Pyrex glass $($the stuff we use in chem lab for

beakers and flasks$)$ is impermeable to all

gases except He$.$ Natural gas often contains a

fair bit of $He,$ and we wish to remove $($most$)$ of

the He before the natural gas can be used as

a fuel. Suppose the gas is contained in a

Pyrex tube $($see figure$).$ If the length of the

tube is $L,A$ is He$,P$ is Pyrex, and $D_{AP}$ is the

diffusion coefficient for He in Pyrex, show

that the rate at which He will leak out of the

tube is given by

$W_A=2L\frac{D_{AP}(c_{A1}-c_{A2})}{ln(\frac{R_2}{R_1})}$

where $c_{A1}$ and $c_{A2}$ are the concentrations of helium at the inner and outer wall of

the Pyrex, respectively.