A tank contains 100 kg of salt and 2000 L of water. A solution of a concentratio

Question

A tank contains 100 kg of salt and 2000 L of water. A solution of a concentration 0.025 kg of salt per liter enters a tank at the rate 6 L/min. The solution is mixed and drains from the tank at the same rate.

A tank contains 100 kg of salt and 2000 L of water. A solution of a concentration 0.025 kg of salt per liter enters a tank at the rate 6 L/min. The solution is mixed and drams from the tank at the same rate. What is the concentration of our solution in the tank initially? concentration Find the amount of salt in the tank after 4.5 hours, amount = Find the concentration of salt in the solution in the tank as time approaches infinity, concentration =

Explanation / Answer

(a) 100 kg / 2000 L = 0.05 kg/L

(b) Initial Salt content = 100 kg
Salt introduced during the 4.5hr lapse: 6 L/min * 0.025 kg/L * 270 min/hr = 40.5 kg
Total Salt Content = 1000 kg + 40.5 kg = 140.5 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 0.025 kg/L as given in the question.

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