Concept explainers
Stirred tank reactions For each of the following stirred tank reactions, carry out the following analysis.
- a. Write an initial value problem for the mass of the substance.
- b. Solve the initial value problem.
23. A 500-L tank is initially filled with pure water. A copper sulfate solution with a concentration of 20 g/L flows into the tank at a rate of 4 L/min. The thoroughly mixed solution is drained from the tank at a rate of 4 L/min.
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- 3b. Find the concentration of the syrup in the tank at time t.arrow_forward2. 1500-gallon tank initially contains 2271.2472 L of water with 2.267962 kg of salt dissolved in it. Water enters the tank at a rate of 9 gal/hr. and the water entering the tank has a salt concentration of 0.5(1 + cost) lbs/gal. If a well mixed solution leaves the tank at a rate of 6 gal/hr., how much salt is in the tank when it overflows?arrow_forward. A dolphin tank at Sea World is being filled. The tank has a volume of 50,000 liters. In order not to keep the dolphins in their small holding pools too long, they are released into the large tank when it is half full. Pure water is being pumped into the tank at 100 L/min. The dolphins release waste into the tank at a rate of 200 mg/min. Even though the tank is being filled, the waste removal system is operating and pumps 2 L/min of fluid from the tank. A) Derive a differential equation for the amount of waste in the tank as time goes on. B) Solve the differential equation (as much as possible by hand). C) How much waste will be in the tank when it finally fills? D) Once the tank fills, only the waste removal system is operating, so 2 L/min of water is removed from the tank, cleaned, and then returned to the tank. Derive a differential equation for the amount of waste in the tank after it fills. E) Solve the new differential equation. F) What is the long term outlook for the amount of…arrow_forward
- 0.5 kg/L Pollutant Pure Water 15 L/min 5 L/min 1000 L 15 L/min 1000 L Pure Water with 5 kg pollutant Tank A Tank B 20 L/min For the figure shown, consider the following: • Two tanks are connected by a pipe with flow rate of 15L/min. • Tank A and Tank B each contains 1000L volume of liquid. • A pollutant with concentration of 0.5kg/L is discharged to Tank A at a rate of 15L/min, while pure water is discharged to Tank B at a rate of 5L/min. • There is an outflow of 20L/min from Tank B. • Initially, the amount of the pollutant in Tank A and in Tank B are zero and 5kg, respectively. • It is assumed that the pollutant is well mixed in each tank at any time t. Let yA(t) and yB(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively. Determine the particular solution of the corresponding system of ODES using Method of Undetermined Coefficients. What is the final equation of yA(t)? What is the final equation of yB(t)?arrow_forwardA tank contains 200 gallons of fresh water. Brine containing 2 lbs/gal of salt enters the tank at 4 gpm and the mixture, kept uniform by stirring, runs out of at 3 gpm. Find the amount of salt in the tank after 30 minutes.arrow_forward(b) In an oil refinery, a storage tank as shown in Figure 1 contains 2000 gal of gasoline that initially has 100 lb of an additive dissolved in it. Gasoline containing 2 lb of additive per gallon is pumped into the tank at a rate of 40 gal/min. The well-mixed solution is pumped out at the same rate. Determine the amount of the additive in the tank 20 min after the pumping process begins. 40 gal/min containing 2 lb/gal 40 gal/min containing lb/gal 2000 Figure 1 Hint: Let y be the amount (in pounds) of additive in the tank at time t. The differential equation modeling of the mixture process is given by dy dt = 80- y 50' y(0) = 100arrow_forward
- Xenon gas is used in an experiment. The amount of gas needed is shipped in a 0.50-liter container. The pressure that the xenon exerts on the containers is 0.80 atm. For the experiment, the xenon must exert 5.0 atm. If the scientist wants to use all the xenon in the 0.50-liter container, into what size container does the xenon need to be transferred to be at the desired pressure? O 0.080 L O 0.80 L O 1.5 L O 15 Larrow_forwardA) Determine the mass of salt in the tank after t min B) When will the concentration of salt in the tank reach 0.02 kg/L?arrow_forwardA tank was initially filled with 100 gal of salt solution containing 1 lb of salt per gallon. Fresh brine containing 2 lbs of salt/gal runs into the tank at a rate of 5 gal/min, and the mixture, assumed uniform, runs out at the same rate. At what time will the concentration of the salt in the tank become ? Select one: O a. 55 min O b. 28 min O c. 32 min O d. 14 minarrow_forward
- A tank containing chocolate milk initially contains a mixture of 460 gallons of milk and 40 gallons of chocolate syrup. Milk is added to the tank at the rate of 8 gallons per minute and syrup is added at a rate of 2 gallons per minute. At the same time, chocolate milk is withdrawn at a rate of 10 gallons per minute. Assuming perfect mixing of milk and syrup, determine how much syrup will be in the tank after 10 minutes. O A. 55.50 gal. O B. None of the choices O C. 50.88 gal. O D. 60.23 gal. O E. 23.90 gal.arrow_forwardSolve each questionarrow_forwardDetermine the total differential, dz. f(x, y) = xyebzy. Factor each part completely. dz = %3Darrow_forward
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell