A tank has initially 10 lb of salt dissolved in 100 gal of water. A solution containing a variableconcentration of salt enters the tank with the rate 5 gal/min and a well-mixed solution exits the tankwith the same rate. The concentration of salt in the solution entering the tank is given by the formulac(t) = 0.5e-t/10, where the concentration is in lb/gal and time is in minutes. Find the formula for theamount of salt in the tank as a function of time?

Answered: Image /qna-images/answer/2a24f11c-5b09-4a7e-b4b7-6b75bbe02c8e.jpg

Answered: A tank has initially 10 lb of salt…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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There's a tank containing 50 L of a solution into which 10 g of salt is dissolved in. A solution that contains 2g/L of salt flows into the tank at a rate of 4L/min and the well stirred mixture flows out at a rate of 2L/min. Find the following. What is the concentration of salt in the tank after 30 mins?
The air in a room 15 ft by 12 ft by 12 ft is 4% carbon monoxide. Starting at t = 0, fresh air containing no carbon monoxide is blown into the room at a rate of 300 ft³/min. If air in the room flows out through a vent at the same rate, when will the air in the room be 0.01% carbon monoxide? The air in the room will be 0.01% carbon monoxide after (Round to two decimal places as needed.) minutes.
A tank initially contains 50 gal. of fresh water. Brine (water in which a certain number of pounds of salt have been dissolved), containing 2 lb/gal of salt, flows into the tank at the rate of 2 gal/min and the mixture kept uniform by stirring runs out at the same rate. How long will it take to increase from 40 lbs. to 80 lbs.?
A certain amount of an indissoluble substance containing 2 kg of salt in its pores is subjected to the action of 30 liters of water. After 5 min, 1 kg of salt dissolves. Within how long will 99% of the initial amount of salt dissolve? The rate of dissolution is proportional to the amount of salt that does not dissolve and to the difference between the concentration at the given instant and the concentration and the concentration of the saturated solution (1 kg for 3 litres). Give the result in minutes. The Answer should be: 10.47
A large tank is filled to capacity with 600 gallons of pure water. Brine containing 2 pounds of salt per gallon is pumped into the tank at a rate of 6 gal/min. The well-mixed solution is pumped out at the same rate. Find the number A(t) of pounds salt in the tank at time t.
A tank contains 200 liters of fresh water. Brine containing 2.5 N/L of dissolved salt runs into the tank at the rate of 8 L/min and the mixture kept uniform by stirring runs out at 4 liters/min. What is the amount of salt when the tank contains 320 liters of brine? 487.5 N 287.5 N 387.5 N 416.7 N
A swimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. Starting at t=0, city water containing 0.002% chlorine is pumped into the pool at a rate of 6 gal/min. The pool water flows out at the same rate. What is the percentage of chlorine in the pool after 1 hour? When will the pool water be 0.004% chlorine? What is the percentage of chlorine in the pool after 1 hour? After 1 hour the pool will be % chlorine. (Round to four decimal places as needed.)
A swimming pool whose volume is 10,000 gal contains water that is 0.03% chlorine. Starting at t = 0, city water containing 0.002% chlorine is pumped into the pool at a rate of 5 gal/min. The pool water flows out at the same rate. What is the percentage of chlorine in the pool after 1 hour? When will the pool water be 0.004% chlorine?

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