Question

Salt water flows at a constant rate of 6 L/min into a tank that initially held 100 L of salt solution in which was dissolved 0.3 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 solution entering the tank is 0.03 kg/L. a) Dtermine the mass of salt in the tank after t min. b) When will the concentration of salt in the tank reach 0.02 kg/L? a) Determine the mass of salt in the tank after t min. mass= Пkg b) When will the concentration of salt in the tank reach 0.02 kg/L? minutes. The concentration of salt in the tank will reach 0.02 kg/L after (Round to two decimal places as needed.)

Answer 1

오 Too 50 3x 100 50 -3t. e 50 50 50 3 14xct) suopresend the amount of fault (ash kg), at any time, times Input sate ( 6 bula) Co.03k912) = GMT Output rote: (61 min) (100 kgl.) - Game DE: dx = 9-32 at 50 50 The general solution for your differential equ. of u lincah with ult) eso , so doling we got IF Y (t) - Ja estat -34 (Axeso to x + c = 3 + ce so Using the waitial Caudition the value of equationaue when t=0, x= 0.3, therefore 0.3= 3+c = c =-27 Hence, X(t) = q 3-271-3 when the concentration of salt wh the trup scoach ocelyn Hence, X6t) - 3-87e Concentration 0.02 kg IL ils the same as 2 = 0.02 => x=d Suebetitelte red in solution yeld. 2= 3.2.76 37 270-34-1 e-3tos) e o = 0.370 - 100 50

Taking log on both side, therefore pa ang -3t -0.9942 50 t= 16:57