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

A tank initially contains 100 liters of brine with 5 kg of dissolved salt. Brine containing 0.2 kg/liter enters at 3 liters/min, and the well-mixed solution leaves at the same rate. Set up the differential equation for the amount of salt Q(t) in the tank.

  1. dQ/dt=0.6-0.03Q
  2. dQ/dt=0.6-0.01Q
  3. dQ/dt=0.2-0.03Q
  4. dQ/dt=0.6Q-0.03

Answer

A. dQ/dt=0.6-0.03Q

Solution

Rate in =0.2(3)=0.6 kg/min. Rate out =Q/100(3)=0.03Q kg/min. So dQ/dt=0.6-0.03Q.

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