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

A 50-liter tank contains pure water. Brine with 2 kg/liter of salt flows in at 4 liters/min, and the mixture flows out at the same rate. Find the differential equation for Q(t).

  1. dQ/dt=8-0.08Q
  2. dQ/dt=8-0.04Q
  3. dQ/dt=2-0.08Q
  4. dQ/dt=8Q-0.08

Answer

A. dQ/dt=8-0.08Q

Solution

Rate in =2(4)=8 kg/min. Rate out =Q/50(4)=0.08Q kg/min. So dQ/dt=8-0.08Q.

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