Question

A brine solution of salt flows at a constant rate of

8

​L/min into a large tank that initially held

100

L of brine solution in which was dissolved

0.2

kg of salt. The solution inside the tank is kept well stirred and flows out of the tank at the same rate. If the concentration of salt in the brine entering the tank is

0.02

​kg/L, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach

0.01

​kg/L?

Answer 1

is salt content at time t

Then

So

Integrating factor is

Multiplying by this we get

So via product rule

So that

And so

Which is

And so is the general solution

Initial condition means

So that is the mass of salt in tank after t minutes

It will reach 0.01 kg/L (i.e. 1 kg salt) in minutes

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