Question $1$:

A single$-$effect evaporator is concentrating a feed of $9072k\frac{g}{h}$ of a $10wt\%$ solution of NaOH in water to a product of $50\%$ solids. The pressure of the saturated steam used is $42$kPa $($gage$)$ and the pressure in the vapor space of the evaporator is $20$kPa $($abs$).$ The overall heat$-$transfer coefficient is $1988\frac{W}{m^2}.$ K$.$ Calculate the steam used, the steam economy in $kg$ vaporized $\frac{?}{kg}$ steam, and the area for the following feed conditions:

a$.$ Feed temperature of $288\mathrm{.}8K(15\mathrm{.}6C).$

b$.$ Feed temperature of $322\mathrm{.}1K(48\mathrm{.}9C).$