Engineering Board Exam Reviewer · Applications: Cooling, Heating, and Mixture Problems · hard
A tank holds 100 L of brine with 50 kg of dissolved salt. A solution of 0.2 kg/L enters at 5 L/min, and the well-mixed solution leaves at 3 L/min. How many kilograms of salt are in the tank after 50 minutes?
- 37.05 kg
- 50.61 kg
- 58.8 kg
- 29.39 kg
Answer
B. 50.61 kg
Solution
The volume is V=100+2t, so dA/dt=1-3A/100+2t. The integrating factor is (100+2t)3/2, giving A(100+2t)3/2= (100+2t)5/25+C. With A(0)=50: C=30000. At t=50 (V=200 L): A=200/5+ 300002003/2 50.61 kg.
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