Engineering Board Exam Reviewer · Applications: Cooling, Heating, and Mixture Problems · medium

A tank holds 100 L of pure water. Brine containing 0.5 kg of salt per liter flows in at 4 L/min, and the well-mixed solution flows out at 4 L/min. How many kilograms of salt are in the tank after 25 minutes?

  1. 18.39 kg
  2. 50 kg
  3. 49.08 kg
  4. 31.61 kg

Answer

D. 31.61 kg

Solution

dA/dt=0.5(4)-4A/100=2-0.04A. With A(0)=0: A=50≤ft(1-e-0.04t ). At t=25: A=50(1-e-1) 31.61 kg.

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