GATE AG 2025 • Q61 NAT • 2 Marks

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

Subtopic: Steady state heat transfer in conduction, convection and radiation

Question Statement:

N₂ and He mixture in a pipe at 1.0 atm, 298 K. Partial pressure of N₂ = 60.80 kPa at one point and 20.31 kPa at a point 0.22 m away. Diffusion coefficient = 0.612×10⁻⁴ m²/s. R = 8314 m³·Pa/(kgmol·K). Steady-state flux of N₂ = n×10⁻⁶ kgmol/(s·m²). Find n. (Rounded to 2 decimal places)

Official Answer Key:

4.50 to 4.60

Step-by-Step Solution & Explanation

For steady-state equimolar counter-diffusion (Fick's law, ideal gas): N_A = D/(RTz)·(pA1−pA2) = (0.612×10⁻⁴)/(8314×298×0.22)×(60800−20310) = (0.612×10⁻⁴/545,220)×40490 = 4.55×10⁻⁶ kgmol/(s·m²).

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