Liquid sugar is produced by stirring the solution in a tank as shown in Figure 1. The tank has a capacity of 1000 m3. The tank has one inlet and one outlet. Initially the tank contains 800 m3 of fresh water with 2 kg of sugar dissolved in it. Process 1 is described by liquid sugar with concentration of 5 kg/m3 flows into the tank with a volumetric flow rate of 3 m3/hr. The mixture inside the tank leaves at a rate of 3 m3/hr. When the amount of sugar in the tank reaches 500 kg, second process (Process 2) takes place, in which the inlet flow of liquid sugar is cut off and being replaced by fresh water. The fresh water flows into the tank with inlet volume flow rate of 2 m3/hr and outflow volume flow rate of 4 m3/hr.
Figure 1. Mixing tank for liquid sugar production
i. State the physical law which describes the change of mass of salt with respect
to time?
ii. Formulate and find the unique solution for the differential equation, which describes the change of change of mass of salt (dx1dt) with respect to time for Process 1. State the related initial value.
iii. Calculate the time when the Process 2 starts.
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