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The contents of a tanker truck carrying a liquid organic waste are spilled accidentally into a small lake. The resulting initial concentration of the waste in the lake is 300 mg/1. The volume of the lake is 105 m³. A stream that flows into and out of the lake has a flow rate of 1200 m³/d. If the organic waste in solution undergoes first-order photochemical decay (r = kC) with a k value of 0.008 d-1, determine the time required for the concentration of the waste in the lake to be reduced to 10 percent of the initial value.

The contents of a tanker truck carrying a liquid organic waste are spilled accidentally into a small lake. The resulting initial concentration of the waste in the lake is 300 mg/1. The volume of the lake is 105 m³. A stream that flows into and out of the lake has a flow rate of 1200 m³/d. If the organic waste in solution undergoes first-order photochemical decay (r = kC) with a k value of 0.008 d-1, determine the time required for the concentration of the waste in the lake to be reduced to 10 percent of the initial value.

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
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The contents of a tanker truck carrying a liquid organic waste are spilled accidentally into a small lake. The resulting initial concentration of the waste in the lake is 300 mg/l. The volume of the lake is 105 m³. A stream that flows into and out of the lake has a flow rate of 1200 m³/d. If the organic waste in solution undergoes first-order photochemical decay (r = kC) with a k value of 0.008 d-1, determine the time required for the concentration of the waste in the lake to be reduced to 10 percent of the initial value.
Transcribed Image Text:The contents of a tanker truck carrying a liquid organic waste are spilled accidentally into a small lake. The resulting initial concentration of the waste in the lake is 300 mg/l. The volume of the lake is 105 m³. A stream that flows into and out of the lake has a flow rate of 1200 m³/d. If the organic waste in solution undergoes first-order photochemical decay (r = kC) with a k value of 0.008 d-1, determine the time required for the concentration of the waste in the lake to be reduced to 10 percent of the initial value.
Expert Solution
Step 1

1st we will form a differential equation for amount of waste after t days and then solve it to get actual amount after t days . 

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