Question

A solution containing 0.03 mol/L of sugar in water is fed to a holding tank that initially has 200 L of pure water, in addition to microbes that eat sugar. The sugar disappears

at a rate (r= 0.055cs) proportional to its own concentration (ܿcs). The volumetric feed to the tank is increased linearly from 0 to 35 liters per second over a ten‐second period, and

remains constant thereafter at 35 L/s until the tank isfilled to a desired level.

(a) What are the values for the sugar concentration in the tank and the total volume of liquid in the tank after a 60‐second period of time?

(b) Create a pair of plots (or a single unified plot) showing the tank volume and sugar concentration in the tank over the span of 0 to 60 seconds. You may use the plotting

method of your choice!

(c) Display the entire program code used for your problem solution in Polymath.

Answer 1

(c) This part can be solved by pasting above solution in polymath software with the help of ODE equation and putting initial guess value as given in solution as follows:

dV/dt=V1

V1(0)=0

V(0)=200

dCs/dt=((V1/V)*Cs1-(0.055*Cs))

Cs1=0.03

V1(0)=0

Then select graph and table, click the green triangle to run or draw the graph.