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A brine solution of salt flows at a constant rate of ​l/min into a large tank that initially held l of pure water. The solution inside the tank is kept well stirred and flows out of the tank at a rate of ​l/min. If the concentration of salt in the brine entering the tank is ​kg/l, determine the mass of salt in the tank after t min. When will the concentration of salt in the tank reach ​kg/l?.

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snehashish65

To reach 01.kg/L concentration of salt in the tank will take around 18.9 min.

What is concentration in a solution?

The concentration of a solution is a measure of the amount of solute that has been dissolved in a given amount of solvent or solution.

A concentrated solution is one that has a relatively large amount of dissolved solute. A dilute solution is one that has a relatively small amount of dissolved solute.

The concentration ,C(t) of salt at time t is given by the mass x(t) at time t divided by the volume t + 100 at time t.

That is C(t) = x(t)/ (t+100)

So that,

C(t) = 0.2 -  [tex]\frac{2 * 10^4}{(t + 100)^4}[/tex]

The concentration of salt is 0.1 kg/L ,

we solve C(t) =0.1 ,

Giving the equation,

0.10.2 - [tex]\frac{2 * 10^4}{(t + 100)^4}[/tex]

t = [tex]100\sqrt[4]{2} -100[/tex]

≈ 18.9  minutes

Therefore,

To reach 01.kg/L concentration of salt in the tank will take around 18.9 min.

Learn more about concentration of solution here:

https://brainly.com/question/24316606

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