A two$-$stage parallel feed evaporator is used to concentrate a sugar $($sucrose$)$

solution from $5\%$ mass at the inlet to $20\%$ mass at the outlet. A total flow of

$20000$ kg hr$-1$ feed at $20$C is divided equally between the two parallel stages.

Saturated steam is provided at $150$C$.$ There is no sub$-$cooling of the condensate.

Assume that the following information is known for stage $1,$ which operates at higher

pressure than stage $2$:

$$ Temperature of vapour leaving stage $1$ is $106\mathrm{.}7$C

$$ Boiling point rise for stage $1$ is $1\mathrm{.}15$C

$$ Flowrate of vapour leaving stage $1$ is $8092$ kg hr$-1$

a$)$ Calculate the mass fraction of sugar in the liquid leaving stage $2$

b$)$ What is therefore the composition in the liquid leaving stage $1?$

Data:

Surface area of heat exchanger of each stage $=50$ m$2$

Overall heat transfer coefficient of each stage $=2\mathrm{.}8$ kW m$-2$ K$-1$

Specific heat capacity for all gases $=1\mathrm{.}8$ kJ kg

$-1$ K$-1$

Specific heat capacity for all solutions $=4\mathrm{.}2$ kJ kg$-1$ K$-1$

Heat of vaporisation of water at $0$C $=2\mathrm{.}5$ MJ kg$-1$

Molar mass of sucrose $=342$ g mol$-1$

Antoine coefficients for water: A $=18\mathrm{.}304,$ B $=3816\mathrm{.}4,$ C $=-46\mathrm{.}13$

$($P in mmHg$,$ T in K$,$ log to base e$)$

Ans: Q$3$: a$)$ w$2=0\mathrm{.}162$; b$)$ w$1=0\mathrm{.}262]$