Project ForgeProcess Calculations
Material Balance
GATE 2020
Hard
A well-mixed tank (volume 20 m³, constant T,P, constant molar density 40 mol/m³) initially has 21 mol% O2, 79 mol% N2. Pure N2 enters and mixture exits, both at 8 mol/s. The time (s) for the tank's O2 content to fall to 1 mol% is
- A100.45
- 304.45
- C3.445
- D10
Explanation
Total moles in tank=20×40=800 (constant). dy_O2/dt=−(8/800)y_O2=−0.01y_O2. y_O2(t)=0.21e^(−0.01t). Setting =0.01: e^(−0.01t)=0.04762 ⟹ t=−ln(0.04762)/0.01=304.45 s.
Source: GATE CH 2020 (2020)
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