Homework Help is Here – Start Your Trial Now!
Math
Advanced Math
17. A pond initially contains 1,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.01 grams of this chemical per gallon flows into the pond at a rate of 300 gal/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. a. Write a differential equation for the amount of chemical in the pond at any time. b. How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? c. Write a differential equation for the concentration of the chemical in the pond at time t. Hint: The concentration is c = a/v = a(t)/106.

17. A pond initially contains 1,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.01 grams of this chemical per gallon flows into the pond at a rate of 300 gal/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. a. Write a differential equation for the amount of chemical in the pond at any time. b. How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? c. Write a differential equation for the concentration of the chemical in the pond at time t. Hint: The concentration is c = a/v = a(t)/106.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
See similar textbooks
icon
Related questions
Question

17

 

/// #117217317 FIGURE 1.1.10 Problem 16. 17. A pond initially contains 1,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.01 grams of this chemical per gallon flows into the pond at a rate of 300 gal/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. 1.2 //// a. Write a differential equation for the amount of chemical in the pond at any time. b. How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? c. Write a differential equation for the concentration of the chemical in the pond at time t. Hint: The concentration is c = a/v = a(t)/106. 18. A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential equation for the volume of the raindrop as a function of time. 19. Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (the ambient air temperature in most cases). Suppose that the ambient temperature is 70°F and that the rate constant is 0.05 (min)-¹. Write a differential equation for the temperature of the object at any time. Note that the differential equation is the same whether the temperature of the object is above or below the ambient temperature. olutions of b. lo N 21 the text For lar that the a 0 i In ea given beha of ya of the can e G G G P 0 b G 2 Ser Aer Mor
Transcribed Image Text:/// #117217317 FIGURE 1.1.10 Problem 16. 17. A pond initially contains 1,000,000 gal of water and an unknown amount of an undesirable chemical. Water containing 0.01 grams of this chemical per gallon flows into the pond at a rate of 300 gal/h. The mixture flows out at the same rate, so the amount of water in the pond remains constant. Assume that the chemical is uniformly distributed throughout the pond. 1.2 //// a. Write a differential equation for the amount of chemical in the pond at any time. b. How much of the chemical will be in the pond after a very long time? Does this limiting amount depend on the amount that was present initially? c. Write a differential equation for the concentration of the chemical in the pond at time t. Hint: The concentration is c = a/v = a(t)/106. 18. A spherical raindrop evaporates at a rate proportional to its surface area. Write a differential equation for the volume of the raindrop as a function of time. 19. Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between the temperature of the object itself and the temperature of its surroundings (the ambient air temperature in most cases). Suppose that the ambient temperature is 70°F and that the rate constant is 0.05 (min)-¹. Write a differential equation for the temperature of the object at any time. Note that the differential equation is the same whether the temperature of the object is above or below the ambient temperature. olutions of b. lo N 21 the text For lar that the a 0 i In ea given beha of ya of the can e G G G P 0 b G 2 Ser Aer Mor
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,
SEE MORE TEXTBOOKS