Question $3$

$1$ During cold weather periods, vapor in a room diffuses through the dry wall and condenses

in the adjoining insulation. The scenario is shown in a diagram on Figure $3.$Having vapor condensing on adjoining insulation decreases the thermal resistance and degrades

the insulation. Consider a condition at which the vapor pressure in the air at $25\backslash$deg C inside a roomis $3$ kPa, and the vapor pressure in the insulation is negligible. The $3-$m$-$high and $10-$m$-$wide

solubility of water vapor in the wall material of approximately

dry wall is $12-$mm thick with

$0\mathrm{.}007$ kmol$/$m$^3.$bar, and diffusion coefficient of water vapor in the wall is $0\mathrm{.}2$ x $10-9$ m$^2/$s$.$

Determine the mass diffusion rate of water vapor through the wall.