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Determine at what time the tank starts to overflow and the acid concentration in the tank

Determine at what time the tank starts to overflow and the acid concentration in the tank

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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A tank with 2000 L total capacity initially contains 1000 L of a 10 wt.% acid solution. A feed stream of

fresh water enters the tank at a constant rate of F = 20 L/min. At time t = 0 a pump starts sucking

solution out of the tank at a constant rate P = 10 L/min. If the tank reaches its maximum capacity

then it will start to overflow, such that the combined overflow and exit flow via the pump exactly

match the inlet flow. You may assume that the acid solutions and pure water all have a constant

density of 1 kg/L.

Answer the following questions:

  1. Write the initial value problem (differential equation with initial conditions) that describes

how the total mass of solution varies with time.

  1. Write the initial value problem (differential equation with initial conditions) that describes

how the concentration of acid in the tank varies with time.

  1. Determine at what time the tank starts to overflow and the acid concentration in the tank at

that point in time.

  1. Determine how long it takes for the acid concentration in the tank to drop to 0.1 wt.%.
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