Problem $2(20$ points$)$

A capillary is filled with water at the bottom and water vapor diffuses out of the capillary.

At a given time, $t,$ the water level from the top is $z.$ As diffusion proceeds, the water level

drops slowly.

a$.$ Write an appropriate equation for the flux of water vapor through the capillary.

Assume a water vapor concentration $c_1$ at the water surface and a water vapor

concentration $c_2$ at the top of the capillary. $(10$ points$)$

b$.$ Derive the equation for the time $t_f$ for the level to drop from a starting point of $z_0$

at $t=0$ to $z_f$ at $t=t_f.(10$ points$)$