$1)$ a$)$ A single stage evaporator is to concentrate $25,000$ kg$/$hr of an aqueous slurry at

$20$C from $10$ to $50\%$ w$/$w solids. Saturated steam is available at $120$C and the

pressure in the evaporator is $0\mathrm{.}2$ atm. The heat transfer area of the unit is $85\mathrm{.}4$ m$2$assuming

there is no boiling point rise or sub$-$cooling of the condensate.

Specific heat capacity for water vapour $=1\mathrm{.}8$ kJ kg$-1$ K$-1$

Specific heat capacity for water and slurry $=4\mathrm{.}2$ kJ kg$-1$ K$-1$

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

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

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$)$

It is decided that the system in should be replaced by two stages in a forwardfeed arrangement, with each stage having only half the heat$-$exchange area of the

original stage. The feed and product flow rates and compositions remain the same,

and an identical steam temperature is used.

$($i$)$ Make an approximate analysis by considering the contributions of sensible

heat terms to energy balances to be negligible. Thus calculate the new:

$$ Flow rate of steam required

$$ Temperatures of the two evaporation stages

$$ Steam economy

Ans : T$1=61\mathrm{.}9$C$,$ T$2=3\mathrm{.}83$C$,$ S$=10000$ kg hr$-1$

Steam Economy $=2\mathrm{.}0$