After graduating from the University of Delaware, Joe Blue Hen installs an indoor swimming pool in his house. The length and the width of this swimming pool are 30 m and 10 m, respectively. The...

After graduating from the University of Delaware, Joe Blue Hen installs an indoor swimming pool in his house. The length and the width of this swimming pool are 30 m and 10 m, respectively. The temperature is held constant at 20 ◦C, and the humidity of the air 1 m above the water is set to 50%. To determine the rate at which the pool must be replenished with water, Joe conducts an experiment using an Arnold diffusion cell. In this experimental setup, bone-dry air flows over the top of the cell, while liquid water resides on the bottom of the vessel. The initial distance between the bone-dry air and the water is 10 cm, and the pressure in the cell is 1 bar. After conducting an experiment, Joe finds that the liquid–vapor interface falls at a rate of 20 m/hr. Help Joe with the following:

a. Derive a model equation that relates the rate of drop in liquid level in the Arnold cell to the diffusivity.

b. Find the diffusivity of water vapor in air.

c. Compare the value that you calculated with the literature value of 0.260 cm2/s.

d. Determine the rate at which Joe should be adding water to his swimming pool.

e. Suggest a source of uncertainty for this estimate. Is it most likely high or low?