Air at $25C,1$atm and a dew$-$point temperature of $0C$ flows steadily past the

open end of a vertical tube filled with water at $25C.$ The tube has a length of

$6$ inch, an inside diameter of $0\mathrm{.}083$ inch, and the liquid level is $0\mathrm{.}5$ inch below

the mouth of the tube.

Air $25C,1$ atm and

temperature $=0C$

a$)$ What is the mole fraction of $H_{2}O$ in the air immediately above the surface

of liquid water? Clearly state any assumption you make.

b$)$ What is the mole fraction of $H_{2}O$ in the air far above the mouth of the

tube?

c$)$ Find the diffusivity of the $H_2\frac{O}{?}$ Air system at $25C$ and $1$atm, if the

diffusivity is known at $0C$ and $1$atm

d$)$ Calculate the initial rate of evaporation of $H_{2}O$ as $\frac{g}{h}.$

e$)$ Plot the initial mole$-$fraction profile of $H_{2}O$ in the stagnant air layer in

the tube. $($Use Figure $1$ to plot your results.

f$)$ How long will it take for the liquid level in the tube to drop $3$ inches.

Solve using $N_A=\frac{{}_W}{M_W}\frac{dz}{dt}$

g$)$ Plot the tube liquid level as a function of time for this period. Use

Figure $2$ to plot your results.