At t=0, a 600 liter tank initially contains 50 grams of salt dissolved in 300 liters of water. Then, water that contains 2 grams of salt per liter is poured into the tank at a rate of 5 liters per minute. The solution in the tank is constantly stirred so the salt concentration is uniform at any given time t. Water leaves the tank at a rate of 2 liters per minute. Think a bit about this scenario and answer these questions just to ensure you understand it well. Which solution is "saltier" - the water in the tank at t=0, or the water that will flow into the tank? When will the tank overflow? Now, build a differential equation that models the rate of change of the amount of salt in grams, in the tank at time t. Think through this carefully. Solve the differential equation. Use your solution to find how much salt will be in the tank after 1 hour.
At t=0, a 600 liter tank initially contains 50 grams of salt dissolved in 300 liters of water. Then, water that contains 2 grams of salt per liter is poured into the tank at a rate of 5 liters per minute. The solution in the tank is constantly stirred so the salt concentration is uniform at any given time t. Water leaves the tank at a rate of 2 liters per minute. Think a bit about this scenario and answer these questions just to ensure you understand it well. Which solution is "saltier" - the water in the tank at t=0, or the water that will flow into the tank? When will the tank overflow? Now, build a differential equation that models the rate of change of the amount of salt in grams, in the tank at time t. Think through this carefully. Solve the differential equation. Use your solution to find how much salt will be in the tank after 1 hour.
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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Transcribed Image Text:At t=0, a 600 liter tank initially contains 50 grams of salt dissolved
in 300 liters of water. Then, water that contains 2 grams of salt per
liter is poured into the tank at a rate of 5 liters per minute. The
solution in the tank is constantly stirred so the salt concentration is
uniform at any given time t. Water leaves the tank at a rate of 2
liters per minute.
Think a bit about this scenario and answer these questions just
to ensure you understand it well. Which solution is "saltier" -
the water in the tank at t=0, or the water that will flow into the
tank? When will the tank overflow?
Now, build a differential equation that models the rate of
change of the amount of salt in grams, in the tank at time t.
Think through this carefully.
Solve the differential equation. Use your solution to find how
much salt will be in the tank after 1 hour.
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