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A triple effect forward feed evaporator concentrates a sugar solution from $8$ mass $\%$

to $35\%.$ The feed enters at $30000k\frac{g}{h}$ at $27C$ and the pressure in the vapour space

of the third effect is $16$ kPa $.$ Fresh saturated steam is available at $205$ kPa $.$ The liquid

heat capacity is given by $C_p=4\mathrm{.}19-2\mathrm{.}55(k\frac{J}{k}g.K)$ where x is the mass fraction of

sugar. It can be assumed that the BPR$\text{'}$s can be neglected. The overall heat transfer

coefficients are: $U_1=3\mathrm{.}123$;$U_2=1\mathrm{.}987$ and $U_3=1\mathrm{.}136k\frac{W}{m^2}.K.$

$1\mathrm{.}4.$ Determine the heat balance around each evaporator.