A water-resistant sheet used for water-proofing applications is formed from an impermeable polymeric material. The microstructure of the sheet is engineered to provide open pores of diameter D = 10 µm that extend through the entire thickness of the L = 100-µm-thick sheet. The pore diameter is large enough to allow water vapor to be transferred through the pore, but is sufficiently small to prohibit liquid water from penetrating through the sheet. a) Determine the rate (mol/s) at which water vapor is transmitted through a single pore when saturated liquid exists on the top of the sheet and moist air at a relative humidity of 50% exists on the bottom side of the sheet at temperature of T = 298 K and a pressure of P = 1 atm. At 298 K, the diffusion coefficient for water vapor through air is, .DAB = 0.26 x 10-4 m2/s.

b) Determine the rate (mol/s) at which water vapor is transmitted through a single pore in the absence of advection. Comment on the results.

c) Investigate the sensitivity of the transfer rate, both including and neglecting advection, to temperature. Consider a temperature range from 300 K to 360 K. Comment on the results.