As a finishing step in your monoclonal antibody production process, you lyophilized $($freeze$-$dried$)$ your

pharmaceutical product. However, you realized that even though you have solidified your pharmaceutical

formulation, the $2cm2cm$ cake with a thickness of $1cm$ still contains some liquid water. In its current

state, the cake contains $80wt\%$ solid product and $20wt\%$ water, with a total mass of $2\mathrm{.}5g.$ You decide to

use tray drying to remove the extra water from your product. This step will be accomplished by flowing

warm air parallel to the lyophilized cake, as shown in the figure below. The water must transfer from the

cake through a boundary layer formed by the air flowing over the surface. During the water evaporation

process, your tray warms beneath the cake and maintains it at a temperature of $25C.$ The vapor pressure

exerted by water at this temperature is a constant $23\mathrm{.}8mmHg.$ The air you are using to dry the cake is also

at $25C$ and $1\mathrm{.}0$atm$(760mmHg)$ total system pressure.

The rate of water evaporation from the cake is limited by convective mass transfer. The flow of air is

sufficient to ensure that relative to the rate of water evaporation, the concentration of water in the bulk

drying gas $(c_{w,})$ can be assumed to be near zero. You may assume that any resistances associated with the

molecular diffusion of water through the lyophilized cake may be neglected. The water evaporation process

occurs at steady state until all the water is evaporated.

warm air $(\{$:$25C1(atm))$

A$.$ What are the source and the sink for mass transfer in this system?

B$.$ Perform a material balance on the water to find an expression for the time required $(\{$:$t_f)$ to transfer all of

the water out of the cake. Express the result in terms of the initial moles of water in the cake $(n_{w0}),$ the

molar flux of water out of the cake $(N_w)$ and the cake surface area $(A).$

C$.$ What is the initial molar amount of water in the cake, in gmole?

D$.$ If the convective mass$-$transfer coefficient is $1\mathrm{.}0c\frac{m}{s},$ how long will it take to evaporate all of the water

from the cake?

E$.$ What velocity $v_{}$ is needed to achieve $\frac{?}{\text{b}\text{a}\text{r}}(k{)}_c=1\mathrm{.}0c\frac{m}{s}?$ Use $v=0\mathrm{.}15c\frac{m^2}{s}$ and $D=0\mathrm{.}25c\frac{m^2}{s}$ for

water vapor in air.Provide clear and detailed stepsProvide clear and detailed steps: