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.
24. A 1500-L tank is initially filled with a solution that contains 3000 g of salt. A salt solution with a concentration of 20 g/L flows into the tank at a rate of 3 L/min. The thoroughly mixed solution is drained from the tank at a rate of 3 L/min.
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Chapter 9 Solutions
Calculus, Early Transcendentals, Single Variable Loose-Leaf Edition Plus MyLab Math with Pearson eText - 18-Week Access Card Package
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University Calculus: Early Transcendentals (3rd Edition)
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Glencoe Math Accelerated, Student Edition
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- A tank contains 200 liters of brine holding 50 kg of salt in solution. Water containing 125 g of salt per liter flows into the tank at the rate of 12 liters per minute, and the mixture, kept uniform by stirring, flows out at the same rate. Find the time it takes for the concentration in the tank to be equal to 0.23 kg/L. Topic: Applications of 1st Order DEarrow_forwardA tank initially contains 200 liters of fresh water. Brine containing 2.5 N/liter of dissolved salt runs into the tank at the rate of 8 liters/min and the mixture kept uniform by stirring runs out at the same rate. After 15 minutes, what is the concentrations of the salt in the mixture? 1.8 N/L 2.1 N/L 0.82 N/L O 1.1 N/Larrow_forward9. A large tank contains 100 gallons of brine in which 10 lbs. of salt is dissolved. Brine containing 0.2 lbs. of salt to the gallon runs into the tank at the rate of 6 gal/min. The mixture, kept uniform by stirring, runs out of the tank at the rate of 4 gal/min. Find the amount of salt in the solution in the tank at the end of t min.arrow_forward
- 1. A tank initially holds 80 gal of a brine solution containing - Ib of salt per gallon. At t = 0, another brine solution containing 1 lb of salt per gallon is poured into the tank at the rate of 4 gal/min while the well stirred mixture leaves the tank at the rate of 8 gal/min. a. Find the amount of salt in the tank at any time t. b. Determine when the tank will be empty. c. Determine when the tank will hold 40 gal of solution. d. Find the amount of salt in the tank when the tank contains exactly 40 gal solution. e. Determine when the tank will contain the most salt.arrow_forward1. A tank initially holds 80 gal of a brine solution containing Ib of salt per gallon. At t = 0, another brine solution containing 1 Ib of salt per gallon is poured into the tank at the rate of 4 gal/min while the well stirred mixture leaves the tank at the rate of 8 gal/min. a. Find the amount of salt in the tank at any time t. b. Determine when the tank will be empty. c. Determine when the tank will hold 40 gal of solution. d. Find the amount of salt in the tank when the tank contains exactly 40 gal of solution. e. Determine when the tank will contain the most salt.arrow_forwardBrine containing 3 lbs per gal of salt enters a large tank at the rate of2 gal/min and the mixture well stirred leaves at 1.5 gal/min. If the tankcontains initially 100 gal of water, with 4 lbs of dissolved salt.a. Find the mount of salt in the tank at any time t in minutes.b. Find the amount of salt in the tank after 4 mins.arrow_forward
- . A large mixing tank currently contains 300 gallons of water, into which 8 pounds of sugar have been mixed. A tap will open, pouring 20 gallons of water per minute into the tank at the same time sugar is poured into the tank at a rate of 2 pounds per minute. Find the concentration (pounds per gallon) of sugar in the tank after t minutes.arrow_forwardA 500 gal capacity tank initially contains a salt solution consisting of 200 gal of water and 3 lbs of salt/gal. A solution of 2 Ib/gal flows in at the rate of 3 gal/min and the resulting mixture flows out at the rate of 2 gal/min. What is the concentration in the tank when it starts to overflow? O 2.352 Ib/gal O 1.873 lb/gal O 1032 lb O 2.064 lb/galarrow_forwardA tank contains 1000L of pure water. Brine that contains 0.02kg of salt per liter enters the tank at a rate of 5L/min. Also, brine that contains 0.07kg of salt per liter enters the tank at a rate of 10L/min. The solution is kept thoroughly mixed and drains from the tank at a rate of 15L/min. Answer the following questions. 1. How much salt is in the tank after t minutes? Answer (in kilograms): S(t) = ... 2. How much salt is in the tank after 5 hours? Answer (in kilograms):arrow_forward
- Algebra: Structure And Method, Book 1AlgebraISBN:9780395977224Author:Richard G. Brown, Mary P. Dolciani, Robert H. Sorgenfrey, William L. ColePublisher:McDougal Littell
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