A tank contains 8 L. (liters) of water in which is dissolved 32 g (grams) of chemical. A solution containing 2 g/L of the chemical flows into the tank at a rate of 4 L/min, and the well-stirred mixture flows out at a rate of 2 L/min. i. With an aid of a diagram, construct a mathematical model for this process of chemical y(t) at time t in the tank. ii. Find the amount of chemical at time t. iii. Use the Euler's method to approximate the yearly amount for r = [0,5] iv. Calculate the true error for each minute.
A tank contains 8 L. (liters) of water in which is dissolved 32 g (grams) of chemical. A solution containing 2 g/L of the chemical flows into the tank at a rate of 4 L/min, and the well-stirred mixture flows out at a rate of 2 L/min. i. With an aid of a diagram, construct a mathematical model for this process of chemical y(t) at time t in the tank. ii. Find the amount of chemical at time t. iii. Use the Euler's method to approximate the yearly amount for r = [0,5] iv. Calculate the true error for each minute.
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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![Question 4:
A tank contains 8 L (liters) of water in which is dissolved 32 g (grams) of chemical. A solution
containing 2 g/L of the chemical flows into the tank at a rate of 4 L/min, and the well-stirred
mixture flows out at a rate of 2 L/min.
i. With an aid of a diagram, construct a mathematical model for this process of chemical y(t)
at time t in the tank.
ii. Find the amount of chemical at time t.
iii. Use the Euler's method to approximate the yearly amount for 1 € [0,5]
iv. Calculate the true error for each minute.
v. Determine the amount of chemical in the tank after 20 minutes.
vi. What is the concentration of chemical in the tank at that time?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c044b69-454e-4f9e-8cd6-567ae6231ec2%2Fadc102d1-3a1e-411c-8778-aacb7b3fd32a%2Foxp98m_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Question 4:
A tank contains 8 L (liters) of water in which is dissolved 32 g (grams) of chemical. A solution
containing 2 g/L of the chemical flows into the tank at a rate of 4 L/min, and the well-stirred
mixture flows out at a rate of 2 L/min.
i. With an aid of a diagram, construct a mathematical model for this process of chemical y(t)
at time t in the tank.
ii. Find the amount of chemical at time t.
iii. Use the Euler's method to approximate the yearly amount for 1 € [0,5]
iv. Calculate the true error for each minute.
v. Determine the amount of chemical in the tank after 20 minutes.
vi. What is the concentration of chemical in the tank at that time?
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