An orange is placed on a plate and heated by solar

Question

Chemical Reaction Engineering/ Kinetics Question.

An orange is placed on a plate and heated by solar radiation at a heating rate Q (J/cm³). Some of the sugar (S) inside the fruit is caramelized (soft solid) during the heating at a rate of caramelization r_C= k_CC_s (mol S / cm³min). At the same moment, as a result of the heating, water (W) evaporates at a. constant vaporization rate r_W(mol W / cm³ min). Due to the disruption of the orange pulp, some of the juice leaks out at a volumetric flow rate of L (cm^3 / min).

a). Write the molar balances for Sugar (S) and Water (W) along with their units and the molar balance equation (for ex: IN - OUT + GENERATION = ACCUMULATION) for these.

b). Find an expression for the variation of volume of juice in the orange as a function of time.

c) From part a, derive two differential equations that would calculate the variation of sugar and water concentrations in the juice left as a function of time.