GATE 2020 CH – Question 42

Process Calculations · Steady and unsteady state mass and energy balances · 2 marks · Multiple choice

A well-mixed tank initially contains ideal gas with 21 mol% O₂ and 79 mol% N₂. Pure N₂ enters and gas exits, both at 8 mol/s. Temperature and pressure are constant, molar density is 40 mol/m³ and volume 20 m³. Find time for O₂ to decrease to 1 mol%.

100.45 s
304.45 s
3.445 s
10 s

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Correct answer: (B) 304.45 s

Explanation

The tank holds $N=40(20)=800$ mol. Oxygen has no inlet, and leaves at rate 8y mol/s, so $800dy/dt=-8y$. Thus $y=0.21e^{-0.01t}$. At y = 0.01, $t=100\ln(0.21/0.01)=100\ln21=304.45$ s, B. Constant total inflow and outflow preserve the molar holdup.

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