In a chemical plant, two connected tanks each contain a suspension of solid precipitate. The liquid in the tanks is caused to flow back and forth between the tanks, resulting in varying concentrations of the precipitate in each tank.
The concentrations in tank 1 and tank 2, measured relative to a fixed positive reference concentration, are given by
respectively at time
 . They are governed by the following pair of first order, coupled differential equations:
where a = -5, b = 9, c = -27, d = 31
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(i) |
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Find the concentrations of the precipitate in each tank if the initial concentrations in tank 1 and tank 2 are
and
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For this part of the question give the concentration in tank 1 as a function of t.
Omit the "
= " (8 marks)
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| Your Answer: |
3/2e^(4t)+1/2e^(22t) |
| Comment: | The particular solution required in this part is
= " "
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(ii) |
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What is
as a function of t?
Omit the "
= "
(8 marks)
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| Your Answer: |
3/2e^(4t)+3/2e^(22t) |
| Comment: | The particular solution required in this part is
= " "
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(iii) |
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What is the concentration in tank 1 at t = 0.04?
Give your answer to AT LEAST TWO PLACES OF DECIMALS. Put in this value only
ie. omit the "
= " (2 marks) |
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| Your Answer: |
2.965716159 |
| Comment: |
= 2.965716159
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(iv) |
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What is the concentration in tank 2 at t = 0.04?
Give your answer to AT LEAST TWO PLACES OF DECIMALS. Put in this value only
ie. omit the "
= " (2 marks) |
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| Your Answer: |
5.376615865 |
| Comment: |
= 5.376615865
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