A single$-$effect evaporator is used to concentrate a solution from $10\%$ solids to $50\%$ solids at a flow rate of $7$ kg$/$h$.$ Heating is done with saturated steam at $198\mathrm{.}5$ kPa and the condensed steam leaves the evaporator as saturated liquid. The evaporation process takes place at $12\mathrm{.}35$ kPa. The overall heat transfer coefficient is $3000$ W$/$m$2$K$.$ The solution feed temperature is $294$ K$,$ the specific heat capacity of the $10\%$ solution is $3\mathrm{.}76$ kJ$/$kgK$,$ the specific heat capacity of the $50\%$ solution is $3\mathrm{.}14$ kJ$/$kg K$.$ The boiling point elevation $($KNY$)$ of the solution is given by the equation KNY $($oC$)=10-1\mathrm{.}2$x$,$ depending on the solution concentration.

a$)(10$ P$)$ Required amount of steam,

b$)(10$P$)$Required heat transfer surface lie,

c$)(5$ P$)$ Evaporator capacity

d$)(5$P$)$Steameconomics

calculate.