Hi,So here's a mixing problem/initial value problem:A tank with a capacity of 4000 L is full of a mixture of water and chlorine with a concentration of 0.005 g of chlorine per liter.  In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 40 L/s.  The mixture is kept stirred and is pumped out at a rate of 100 L/s.  Find the amount of chlorine in the tank as a function of time.  Let y be the amount of chlorine in grams and t be the time in seconds.Thanks!

Question
Asked Apr 25, 2019
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Hi,

So here's a mixing problem/initial value problem:

A tank with a capacity of 4000 L is full of a mixture of water and chlorine with a concentration of 0.005 g of chlorine per liter.  In order to reduce the concentration of chlorine, fresh water is pumped into the tank at a rate of 40 L/s.  The mixture is kept stirred and is pumped out at a rate of 100 L/s.  Find the amount of chlorine in the tank as a function of time.  Let y be the amount of chlorine in grams and t be the time in seconds.

Thanks!

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Expert Answer

Step 1

The amount of liquid in the tank at time t is 4000 - 60t.

If y is the amount of chlorine in the tank at time t, then concentration of chlorine at time t is y/(4000 - 60t) g/lit.

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Step 2

Now use initial condition ...

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