(Solved): 2) Water vapour is diffusing at steady-state through stagnant air in a conical stack (Figure 1) at ...

2) Water vapour is diffusing at steady-state through stagnant air in a conical stack (Figure 1) at \( 54^{\circ} \mathrm{C} \) and \( 1.0 \) bar. The height of the stack is \( 10 \mathrm{~m} \), and its diameter changes from \( 80 \mathrm{~cm} \) at the bottom to \( 40 \mathrm{~cm} \) at the top. The partial pressure of water vapour at the bottom of the stack is \( 2500 \mathrm{~Pa} \), and the partial pressure of water vapour at the top of the stack is \( 500 \mathrm{~Pa} \). The diffusivity of water in air at this temperature is \( 3 \times 10^{-5} \mathrm{~m}^{2} / \mathrm{s} \). Calculate a) The molar rate of transfer of water vapour in \( \mathrm{kg} / \mathrm{h} \). b) The molar fluxes of water vapour at the top of the stack and at the bottom.