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A cooling crystallizer has a feed of 1,000 lb/h of 32.5 wt% MgSO4 in water at 120F. This solution is cooled to 70F to form crystals of the heptahydrate. The feed of the specific heat is approximately constant over the temperature range at 0.72 Btu/lbF. The solubility of MgSO4 in water at 70F is 30 lb salt/100 lb water. Assume: a heat of crystallization value of 100,000 Btu/lbmol hydrated crystal Required: a. Estimate the yield of crystals (Ib) and heat removal rate (Btu/h). b. Consider the crystallizer is to be a scraped-surface unit with 3 ft2 of cooling surface per foot of running length of crystallizer. Cooling will be provided by a countercurrent flow of chilled water entering the cooling jacket at 60F and leaving at 85F. The overall heat-transfer coefficient, U, is expected to be 20 Btu/hr ft2 F. What length of crystallizer is needed