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3. 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 4.00 L/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(1)(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. (b) Without solving either equation, sketch the plots you would expect to obtain for V versus t and C versus 1. Briefly explain your reasoning. (c) Solve the mass balance equation to obtain an expression for V(1). Then substitute for V in the potassium chloride balance and solve for C(t). Calculate the KCl concentration in the tank at the moment the tank overflows. Stream F1 8.00 L/s 1.00 g/L of KCI 2000 L 400 L water at t=0 Stream F2 4.00 L/s

3. 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 4.00 L/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(1)(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. (b) Without solving either equation, sketch the plots you would expect to obtain for V versus t and C versus 1. Briefly explain your reasoning. (c) Solve the mass balance equation to obtain an expression for V(1). Then substitute for V in the potassium chloride balance and solve for C(t). Calculate the KCl concentration in the tank at the moment the tank overflows. Stream F1 8.00 L/s 1.00 g/L of KCI 2000 L 400 L water at t=0 Stream F2 4.00 L/s

Introduction to Chemical Engineering Thermodynamics
Introduction to Chemical Engineering Thermodynamics
8th Edition
ISBN:9781259696527
Author:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Publisher:J.M. Smith Termodinamica en ingenieria quimica, Hendrick C Van Ness, Michael Abbott, Mark Swihart
Chapter1: Introduction
Section: Chapter Questions
Problem 1.1P
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3. 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 4.00 L/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(1)(L) denote the volume of the tank contents and C(1)(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. (b) Without solving either equation, sketch the plots you would expect to obtain for V versus t and C versus 1. 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 KCl concentration in the tank at the moment the tank overflows. Stream F1 8.00 L/s 1.00 g/L of KCI 2000 L 400 L water at t=0 Stream F2 4.00 L/s
Transcribed Image Text:3. 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 4.00 L/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(1)(L) denote the volume of the tank contents and C(1)(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. (b) Without solving either equation, sketch the plots you would expect to obtain for V versus t and C versus 1. 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 KCl concentration in the tank at the moment the tank overflows. Stream F1 8.00 L/s 1.00 g/L of KCI 2000 L 400 L water at t=0 Stream F2 4.00 L/s
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