Initially 5 grams of salt are dissolved in 30 liters of water in a tank. Brine with salt concentration 3 grams per liter is added at a rate of 3 liters per minute. Thetank is well mixed and drained at 3 liters per minute so that the volume of liquid in it remains constant.14012010080604020///68.1012time t in minutesLet s be the grams of salt in the tank at time t. What is the differential equation satisfied by s?How long does the process have to continue until there are 45 grams of salt in the tank?Your answer should be either exact or accurate to at least 6 decimal digits.minutesgrams of salt

Answered: Image /qna-images/answer/bacea01d-95fe-4064-a424-20370a9ef181.jpg

Answered: Initially 5 grams of salt are dissolved…

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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The water temperature T in a tank takes 20 minutes to decrease from 100°C to 60°C. The temperature of the surrounding air is kept constant at To=23°C. a) Assuming that the rate of temperature decrease is proportional to the difference of current water temperature and constant air temperature, find the differential equation describing water temperature as a function of time. b) Solve the differential equation subject to the initial condition. c) Find the coefficient of proportionality and relaxation time of temperature.
6. Train E travels west toward Chicago station at 120 miles per hour while a second train N travels north away from Chicago station at 90 miles per hour. At time t = 0 train E is 10 miles east of Chicago station and train N is 20 miles north of Chicago station. Determine the rate at which the distance between the two trains is changing when t=0.
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Please solve and explain this differential equ
Newton's Law of Cooling states that the rate at which the temperature of a cooling object decreases and the rate at which a warming object increases are proportional to the difference between the temperature of the object and the temperature of the surrounding medium. The differential equation formula is given as: dT = k (T – A) dt - T = temperature of object at time t А ambient temperature (aka temperature of the surrounding medium) k = constant of proportionality Okay, now here's the problem. A glass of delicious orange soda (with an initial temperature of 34°F) is placed in a room with a constant temperature of 72°F. One hour later, the temperature of the orange soda is 52°F. Find the exact simplified value of k. Hint: solve the differential equation for T and note that A is a constant.
Tank A initially contains 500 Litres of a brine solution with a concentration of 0.5 kg perlitre and tank B contains 500 Litres of water. Solution is pumped from tank A to tank B ata rate of 4 Litres /min and from tank B to tank A at a rate of 8 Litres /min. The tanks are keptwell stirred. Let the number of kilograms of salt in tank A be A1 after t minutes and B1in tank B.(a) Write down equations showing, respectively, the concentrations C1 and C2 inthe tanks after t minutes.(b) Write down two differential equations to show how A1 and B1 vary with time.(c) What is the relation between A1 and B1?(d) Eliminate B1 between the two equations in (b) and solve the resulting equationfor A1.(e) What is the concentration in tank A after 10 minutes?
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5. Suppose that sodium pentobarbital is used to anesthetize a dog. The dog is anesthetized when its bloodstream contains at least 45 milligrams (mg) of sodium pentobarbitol per kilogram of the dog's body weight. Suppose also that sodium pentobarbitol is eliminated from the dog's bloodstream at a rate which is proportional to the amount of sodium pentobarbitol in the bloodstream and that after 5 hours half of the initially prescribed sodium pentobarbitol is elliminated from the bloodstream. Set up and solve an initial value differential equation. What single dose should be administered in order to anesthetize a 50-kg dog for 1 hr?

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