A 10 wt% aqueous solution of NaOH at 100°F and a flow rate of 30,000 lb/h is to be concentrated to 50 wt% by evaporation using saturated steam at 115 psia. 

(a) If a single-effect evaporator is used with U = 400 Btu/h-ft²-°F and a vapor-space pressure of 4 inches Hg, determine the heat-transfer area and the economy. 

(b) If a doubleeffect evaporator system is used with forward feed and U₁ = 450 Btu/h-ft²-F, U₂ = 350 Btu/h-ft²-F, and a vapor-space pressure of 4 inches Hg in the second effect, determine the heattransfer area of each effect, assuming equal areas, and the overall economy.