A sodium hydroxide solution with $20\%$ content will be concentrated to $50\%$ by a single$-$effect

evaporator. The feeding flow rate is $9070$ kg per hour with a temperature of $37\mathrm{.}8$C$.$ The gauge pressure

of the steam is to be $138$ kPa $(1\mathrm{.}38$ bar$)$; the absolute pressure in the vapor space is to be $13$ kPa $(0\mathrm{.}133$

bar$).$ The overall coefficient is $1400$ W$/$m$2$

$$C$.$ By using the D$$hring lines for sodium hydroxide solution

given in Figure $1$ and steam table to find boiling point of water under $13$ kPa $(1\mathrm{.}38$ bar$),$ heat of

vaporization of steam under $138$ kPa $(0\mathrm{.}133$ bar$).$

a$.(10)$ The consumed amount of steam

b$.(5)$ The economy

c$.(5)$ The required heating surface.