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A 2000-liter tank initially contains 400 liters of pure water. Beginning at t = 0, an aqueous solution containing 1.00 g/L of potassium chloride flows into the tank at a rate of 8.00 L/s and an outlet stream simultaneously starts flowing at a rate of 4.00L/s. The contents of the tank are perfectly mixed, and the density of the feed stream and of the tank solution, p(g/L), may be considered constant. Let V(t) (L) denote the volume of the tank contents and C(t)(g/L) the concentration of potassium chloride in the tank contents and outlet stream.
(a) Write a total mass balance on the tank contents convert it to an equation for dV/dt. and provide an initial condition. Then write a potassium chloride balance, convert it to an equation of the form dC/dt = f(C, V), and provide an initial condition. (See Example 11.4-1)
(b) Without solving either equation, sketch the plots you would expect to obtain for V versus I and C versus t, briefly explain your reasoning.
(c) Solve the mass balance equation to obtain an expression for V (t). Then substitute for V in the potassium chloride balance and solve for C (t). Calculate the KCI concentration in the tank at the moment the tank overflows.
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