A tank used for toxic chemical experiments has a capacity of 1500 litres. It initially contains 600 litres of water well mixed with 5 grams of toxic chemical. Water enters the tank at a rate of 9 litres/hour carrying the toxic chemical with a concentration of 1/5(1+cos(t)) grams/litre. If the solution in the tank leaves at a rate of 6 litres/hour, how much of chemical is in the tank when the tank overflows. Assume the water and toxic chemical are well mixed inside the tank. Hint: concentration is the amount of chemical in the tank at any time (e.g. grams/hour) over the volume of water in the tank at any time (e.g. litres/hour). Also, there is a net increase of well mixed solution in the tank.

A tank used for toxic chemical experiments has a capacity of 1500 litres. It initially contains 600 litres of water well mixed with 5 grams of toxic chemical. Water enters the tank at a rate of 9 litres/hour carrying the toxic chemical with a concentration of 1/5(1+cos(t)) grams/litre. If the solution in the tank leaves at a rate of 6 litres/hour, how much of chemical is in the tank when the tank overflows. Assume the water and toxic chemical are well mixed inside the tank. Hint: concentration is the amount of chemical in the tank at any time (e.g. grams/hour) over the volume of water in the tank at any time (e.g. litres/hour). Also, there is a net increase of well mixed solution in the tank.

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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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.

Question

A tank used for toxic chemical experiments has a capacity of 1500 litres. It initially contains
600 litres of water well mixed with 5 grams of toxic chemical. Water enters the tank at a rate
of 9 litres/hour carrying the toxic chemical with a concentration of 1/5(1+cos(t)) grams/litre.
If the solution in the tank leaves at a rate of 6 litres/hour, how much of chemical is in the tank
when the tank overflows. Assume the water and toxic chemical are well mixed inside the tank.
Hint: concentration is the amount of chemical in the tank at any time (e.g. grams/hour) over
the volume of water in the tank at any time (e.g. litres/hour). Also, there is a net increase of
well mixed solution in the tank.

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