A stream of $100.K\frac{g}{m}in$ of a $80\mathrm{.}0\%($weight basis$)$ of sucrose in water at $90C$ flows into a crystallizer. In this crystallizer water is removed by evaporation under vacuum. The evaporation results in a drop of temperature in the crystallizer to $30C.$ Under the operating conditions, water is evaporated at a rate of $10\mathrm{.}0K\frac{g}{m}in.$

a$)$ Draw a fully labeled flowchart for the process.

b$)$ Perform a degree of freedom analysis and determine the number of degrees of freedom.

c$)$ Calculate the percentage of sucrose $($relative to sucrose in the input stream$)$ that is crystallized.

The solubility of sucrose in water is given in the chart below.

Solubility of sucrose $($sugar$)$ in water