A \(3.0-\mathrm{m}^{3}\) cooling crystallizer is operating over a temperature range that gives \(\mathrm{C}_{\mathrm{in}}=82 \mathrm{~kg}\) solute \(/ 100 \mathrm{~kg}\) water and \(\mathrm{C}_{\text {out }}=35 \mathrm{~kg}\) solute \(/ 100 \mathrm{~kg}\) water. \(\mathrm{W}_{\text {in }}=266 \mathrm{~kg}\) water/h. No hydrates are formed. Density of concentrated feed \(=1200 \mathrm{~kg} /\). Currently we are adding 2.97 \(\mathrm{kg} / \mathrm{h}\) of seed crystals with an average size of \(\mathrm{L}_{\mathrm{S}}=0.021 \mathrm{~mm}\) to the feed and producing product crystals that are too small. We are told to increase product crystals to \(\mathrm{L}_{\mathrm{p}}=0.24 \mathrm{~mm}\). Keep magma density \(\mathrm{M}_{\mathrm{T}}\), weight of product crystals \(\mathrm{W}_{\mathrm{p}}\), and outlet volumetric flow rate \(\mathrm{Q}_{\text {out }}\) constant.

a. What are the current values of \(Q_{\text {out }} \mathrm{m}^{3} / \mathrm{h}, \mathrm{M}_{\mathrm{T}} \mathrm{kg} / \mathrm{m}^{3}, \mathrm{~W}_{\mathrm{p}} \mathrm{kg} / \mathrm{h}, \Delta \mathrm{L}_{\text {growth }} \mathrm{mm}\), and product crystal size \(\mathrm{L}_{\mathrm{p}} \mathrm{mm}\) ?

b. What size crystallizer and what weight of seeds \(\mathrm{kg} / \mathrm{h}\) are required to produce crystals of the desired size?