A tunnel dryer is to be used to dry $30I\frac{b}{h}$ of raw cotton $($dry basis$)$ with a countercurrent flow of $1,800l\frac{b}{h}$ of air $($dry basis$).$ Cotton enters at $70F$ with a moisture content of $100\%($dry basis$)$ and exits at $1500F$ with $10\%$ moisture $($dry basis$),$ and air enters at $200F$ and $1$atm with a relative humidity of $10\%.$ The specific heat of dry cotton can be taken constant at $0\mathrm{.}35Bt\frac{u}{l}b-F.$ Calculate:

a$)$ rate of evaporation of moisture;

b$)$ outlet temperature of the air;

c$)$ rate of heat transfer.

$[25$marks$]$