The diffusion of water vapor through plaster boards and its condensation in
the wall insulation in cold weather are of concern since they reduce the
effectiveness of insulation. Consider a house that is maintained at
\(20^{\circ} \mathrm{C}\) and 60 percent relative humidity at a location where
the atmospheric pressure is \(97 \mathrm{kPa}\). The inside of the walls is
finished with \(9.5\)-mm-thick gypsum wallboard. Taking the vapor pressure at
the outer side of the wallboard to be zero, determine the maximum amount of
water vapor that will diffuse through a \(3-\mathrm{m} \times 8-\mathrm{m}\)
section of a wall during a 24-h period. The permeance of the \(9.5\)-mm-thick
gypsum wallboard to water vapor is \(2.86 \times 10^{-9} \mathrm{~kg} /
\mathrm{s} \cdot \mathrm{m}^{2} \cdot \mathrm{Pa}\).