A tank contains 60 kg of salt and 2000 L of water. A solution of a concentration

Question

A tank contains 60 kg of salt and 2000 L of water. A solution of a concentration 0.015 kg of salt per liter enters a tank at the rate 9 L/min. The solution is mixed and drains from the tank at the same rate.

(a) What is the concentration of our solution in the tank initially?
concentration = ____________ kg/L

(b) Find the amount of salt in the tank after 4.5 hours.
amount = ____________ kg

(c) Find the concentration of salt in the solution in the tank as time approaches infinity.
concentration = ____________ kg/L

Explanation / Answer

(a) 60 kg / 2000 L = 0.03 kg/L

(b) Initial Salt content = 60 kg

Amount of salt after 4.5 hrs = initial salt - ((concentration*water)(1-e^((rate/water)*time in minutes)))

= 60-30(1-e^((9/2000)*4.5*60))

=38.901 kg

(c) If it drains at the same rate, then at infinity we can assume that all the initial salt has been removed, and there is only the solution of the concentration entering present. Hence, the final concentration at infinity is 0.015 kg/L as given in the question.

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