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A tank contains 150 liters of fluid in which 40 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into th
Question
A tank contains 150 liters of fluid in which 40 grams of salt is dissolved. Brine containing 1 gram of salt per liter is then pumped into the tank at a rate of 3 L/min; the well-mixed solution is pumped out at the same rate. Find the number A(t) of grams of salt in the tank at time t.
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Physics
3 years
2021-09-05T16:58:32+00:00
2021-09-05T16:58:32+00:00 1 Answers
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Answers ( )
Answer:
The number A(t) of grams of salt in the tank at time t is![Rendered by QuickLaTeX.com A(t) = 150 - 110 e^{-\frac{t}{50} }](https://documen.tv/wp-content/ql-cache/quicklatex.com-ee7719639d5e0f2fd7b6787060d4cb6b_l3.png)
Explanation:
Knowing
First we have to find the Rin and Rout
Rin = (concentration of the salt inflow) * (input rate of brine)
Rin = 1 g/L * 3 L/min = 3 g/L
Rout = (concentration of the salt outflow) * (output rate of brine)
Rout = (
) * (3 L/min) = ![Rendered by QuickLaTeX.com \frac{A(t)}{50} g/min](https://documen.tv/wp-content/ql-cache/quicklatex.com-095c7c7aae44533920da960f78b05557_l3.png)
Substituting this results
Thus, integration factors is
Applying the initial conditions
A(0) = 40
c = 150 – 40 = 110
Now, substitute this result in the solution to get