   Chapter 6.4, Problem 37E

Chapter
Section
Textbook Problem

Mixture In Exercises 35-38, consider a tank that at time t = 0 contains v 0 gallons of a solution of which, by weight, q 0 pounds is soluble concentrate. Another solution containing q 1 pounds of the concentrate per gallon is running into the tank at the rate of r 1 gallons per minute. The solution in the tank is kept well stirred and is withdrawn at the rate of r 2 gallons per minute.A 200-gallon tank is full of a solution containing 25 pounds of concentrate. Starting at time t = 0 , distilled water isadmitted to the tank at a rate of 10 gallons per minute, and the well-stirred solution is withdrawn at the same rate.(a) Find the amount of concentrate Q (in pounds) in the solution as a function of t.(b) Find die time at which the amount of concentrate in the lank reaches 15 pounds.(c) Find die amount of concentrate (in pounds) in die solution as t → ∞ .

a)

To determine

To Calculate: The amount Q of concentrate in the solution as a function of t.

Explanation

Given:

A 200-gallon tank is full of solution contains 25 pounds of concentrate starting at time t=0, distilled water is admitted to the tank at the rate of 10 gallons per minute and well stirred solution is withdrawn at the same rate.

Formula Used:

dQdt+r2Qv0+(r1r2)t=q1r1

Calculation:

Consider

dQdt+r2Qv0+(r1r2)t=q1r1

v0=200gallons

at t=0q0=25pounds

r1=10gallons/minute

q1=0(Distilled water)

r2=10gallons/minute

Substituting these values in equat

b)

To determine

To Calculate: The time when amount of concentrate in tank reaches 15 pounds.

c)

To determine

To Calculate: Theamount of concentrate (in pounds)in the solution as t.

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