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Mathematical modeling using linear first order equations

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Two tanks each hold 3 liters of salt water and are connected by two pipes (see figure below) the salt water in each tank is kept well stirred. Pure water flows into tank A at a rate of 5 liters per minute and the salt mixture exits tank B at the same rate.
Salt water flows from tank A to tank B at the rate of 9 liters per minute and flows from tank B to tank A at the rate of 4 liters per minute. If tank A initially contains 1 Kg of salt and tank B contains no salt, find the quantities of salt in tank A and tank B respectively, at any time t ≥ 0.

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Let CA and CB be the concentration of salt in tank A and B (kg of salt/L)
Initial Volume of tank VA = VB = 3 (liters)
Perform material balance for each tank:
Rate of change of material = Rate of mass in - Rate of mass out
Tank A:
Tank B:
Equipped with the two differential ...

Solution Summary

The solution provides very detailed theory for developing governing equations of continuous flow stirred tank reactors. It then provides explanations and calculations for the final answer in a 3-page Word document.