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AN$01$

a plant is primarily used to crystallize calcium chloride with a feed solution of $1800$ kg at $315$ K which containing $35$ mass $\%$CaCl $2.$ The solution cooled to $300$ K in a counter flow SwensonWalker crystallizer where CaCl $26$H $2$ O crystals are removed. The solubility of the salt at $300$ K is $20$ kgCaCl$/100$ kgH $2$ O $.$ The heat the solution is $12300$ kJ$/$kmol and the average heat capacity $($Cp$)$ of the solution is $4\mathrm{.}18$ kJ$/$kgK and the heat of crystallization is $133\mathrm{.}5$ kJ$/$kg $.$ The cooling water enters at $280$ K and leaves at $290$ K $.$ The overall heat transfer coefficient U is $0\mathrm{.}15$ kW$/$m $2$ K and the available heat transfer area per unit length is $1\mathrm{.}5$ m $2/$m $.$ Determine the length of the crystallizer. Assume that evaporation is negligible. Atomic mass Ca$=40$ g$/$mol$,$Cl$=35\mathrm{.}5$ g$/$mol$,$O$=16$ g$/$mol

$1\mathrm{.}1.$ Use yield method to determine the yield of crystals from cooling crystallizer. $1\mathrm{.}2.$ Estimate how much heat must be removed from the system. $1\mathrm{.}3.$ Determine the length of the crystallizer.