Freeze concentration is used to produce a fruit-juice concentrate. A stream of fresh juice containing 12 wt% soluble solids in water at 20°C is combined with a recycle stream to form a pre-concentrate, which is fed to a crystallizer. The mixture is cooled in the crystallizer to —7°C, thereby crvstalh7ing 20,000 kg/h of ice. A slurry leaves the crystallizer containing 10 wt% ice and is fed to a tilter. The filtrate, which contains 45 wt% dissolved solids, is removed as the process product. The remaining slurry, which contains all the ice and some concentrate (also containing 45% dissolved solids. is sent to a separator that cleanly removes all of the ice. The residual liquid is the recycle stream that combines with the fresh feed to form the pre-concentrate.

(a) Determine the rates (kg/h) at which fresh fruit juice is fed and concentrate is produced and the mass flow rate (kg/h) and solids concentration of the pre-concentrate.

(b) Calculate the cooling requirement (kW) for the freezer, assuming that the temperature of the recycle stream is 0°C and the heat capacity of all solutions is 4.0 U/(kg∙°C).