GATE AG 2021 • Q47 MCQ • 2 Marks

Section 6: Agricultural Process Engineering

Size Reduction and Material Handling

Subtopic: Filtration and membrane separation

Question Statement:

A 30 μm thick membrane having 3 m² surface area is used to separate NaCl from a solution at steady state condition. The mass transfer coefficient of NaCl at the solution side is 1×10⁻⁶ m·s⁻¹ and that at the other side of the membrane is 3×10⁻⁷ m·s⁻¹. Concentration of NaCl in the solution is 0.03 g·(100 mL)⁻¹ and, that on the other side of the membrane is assumed to be zero. Permeability of the membrane is 9×10⁻⁶ m·s⁻¹. The rate of removal of the NaCl by the membrane in g·h⁻¹ is

Options:

  • (A) 0.73
  • (B) 0.81
  • (C) 0.86
  • (D) 0.93

Official Answer Key:

A

Step-by-Step Solution & Explanation

Three mass-transfer resistances act in series (feed-side film, membrane, permeate-side film): 1/K_overall = 1/k₁ + 1/P_m + 1/k₂ = 1/(1×10⁻⁶) + 1/(9×10⁻⁶) + 1/(3×10⁻⁷) = 1,000,000 + 111,111 + 3,333,333 = 4,444,444 s/m. K_overall = 2.25×10⁻⁷ m/s. Concentration: 0.03 g/100 mL = 0.3 g/L = 300 g/m³. Rate = K_overall×A×ΔC = 2.25×10⁻⁷×3×300 = 2.025×10⁻⁴ g/s = 2.025×10⁻⁴×3600 = 0.73 g/h, matching (A).

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