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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.
26. A one-million-liter pond is contaminated by a chemical pollutant with a concentration of 20 g/L. The source of the pollutant is removed, and pure water is allowed to flow into the pond at a rate of 1200 L/hr. Assuming the pond is thoroughly mixed and drained at a rate of 1200 L/hr, how long does it take to reduce the concentration of the solution in the pond to 10% of the initial value?
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Chapter 9 Solutions
Calculus: Early Transcendentals (3rd Edition)
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University Calculus: Early Transcendentals (3rd Edition)
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Calculus: Early Transcendentals (2nd Edition)
Calculus and Its Applications (11th Edition)
Glencoe Math Accelerated, Student Edition
- A large, perfect cube of ice sits in the merciless Australian sun. It is melting. Each of its edges shrinks at 2 mm/min. How quickly does the volume of the ice cube decrease when it weighs 8 kg? (Hint: Assume that the specific volume of ice is the same as that of liquid water, which in turn we assume to be 1 litre/kg = 1000 cm /kg.) O 0.24 kg / min 240 kg / min 2.4 kg / min 24.0 kg / min 1600.0 kg / min 80.0 kg / min O 1.6 kg / min O 16.0 kg / min O 0.08 kg / min O 0.8 kg / min None of the other options.arrow_forwardPlease answer a & b. thank you! A tank initially holds 100 gal at brine solution containing 0.25 lb of salt per gallon. Pure water flows into th tank at thee rate of 2 gal/min, and the well-stirred mixture runs out at the same rate. Find a.) the amount of salt in the tank at any time t and b.) the time require for half the salt to leave the tank.arrow_forward1. A tank initially holds 100 gallons of brine solution containing 20 lbs. of salt. At t = 0, fresh water is poured into the tank at the rate of 5 gal/min., while the well- stirred mixture leaves the tank at the same rate. Find the amount of salt in the tank at any time t. 2. A tank 100 gallon capacity is initially full of water. Pure water is allowed to run into the tank at a rate of 1 gallon per minute, and at the same time containing one-fourth pound of salt per gallon flows into the tank also at a rate of 1 gallon per minute. The mixture flows out at a rate of 2 gallons per minute (it is assumed that there is perfect mixing). Find the amount of salt in the tank after t minutes. 3. The rate of growth of an investment is proportional to the amount of the investment at any time t. The initial investment is $1000 and after 10 years the balance is $3320.12. What is the particular solution? 4. The limiting capacity of the habitat of wildlife herd is 750. The growth rate dN/dt of the herd…arrow_forward
- Determine the total differential, dz. f(x, y) = xyebzy. Factor each part completely. dz = %3Darrow_forwardH.W. 1) Calculate the volume of cylinder has 15 m height and 8 m diameter. 2) If we have other cylinder with the same height but it volume greater than first cylinder by 20%, how long its radius? 3) Write a program to calculate the volumetric and mass flow rate of a liquid flowing in a pipe with a velocity equal to 0.5 m/s. Knowing that the diameter of this pipe is 0.1 m and the density of this liquid is 890 kg/m³ ? 4) For the following distillation column write a code to find the value of stream B and the compositions of stream D? D=80 X% ? S%? T%? Z% ? F=100kg 15% X 25% S 40% T 20% Z B=? 15% X 25% S 40% T 20% Z 9 5) Compute the reaction rate constant for a first-order reaction given by the -E/RT Arrhenius law k = A e at a temperature T = 500 K. Here the activation energy is E=20 kcal/mol and the pre-exponential factor is A=10¹3 s¹. The ideal gas constant is R=1.987 cal/mol K.arrow_forward6. A cylindrical tank that is 30 feet high with a radius of 5 feet is filled with water. At time t = 0, water is pumped out of the spigot at a rate of r(t) = (130 – 5t) feet/minute. a. How long will the water continue to be pumped at this rate? b. Using the time calculated in part a. above, determine the total volume of water pumped and the depth of the water in the container when pumping is complete.arrow_forward
- A) 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_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_forwardPlease show work. Thanks!arrow_forward
- 0.5 kg/L Pollutant Pure Water 15 L/min 5 L/min 1000 L 15 L/min 1000 L | with 5 kg pollutant Pure Water 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 100OL 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. • Itis assumed that the pollutant is well mixed in each tank at any time t. Let yA(t) and ye(t) be the amount of the pollutant at any time t in Tank A and Tank B, respectively. 1. Setup the system of ODES for the two tanks to determine the amount of pollutant in Tank A and Tank B at any time t. 2. Determine the complementary solution of the corresponding system of ODES.arrow_forwardThe volume of a cube decreases at a rate.1 of 15 m/sec. Find the rate at which the side of the cube changes when the side of the .cube is 5 marrow_forward1. Oil is being pumped into a huge cylindrical oil drum with diameter 3 m and length 6 m at a rate of 3 L / s. At what rate is the depth of the oil rising when the depth of the oil is 1 m? Note: 1L = 1000 cm³ 3 m 1 m = 100 cm 6 marrow_forward
- Calculus: Early TranscendentalsCalculusISBN:9781285741550Author:James StewartPublisher:Cengage LearningThomas' Calculus (14th Edition)CalculusISBN:9780134438986Author:Joel R. Hass, Christopher E. Heil, Maurice D. WeirPublisher:PEARSONCalculus: Early Transcendentals (3rd Edition)CalculusISBN:9780134763644Author:William L. Briggs, Lyle Cochran, Bernard Gillett, Eric SchulzPublisher:PEARSON
- Calculus: Early TranscendentalsCalculusISBN:9781319050740Author:Jon Rogawski, Colin Adams, Robert FranzosaPublisher:W. H. FreemanCalculus: Early Transcendental FunctionsCalculusISBN:9781337552516Author:Ron Larson, Bruce H. EdwardsPublisher:Cengage Learning
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