Subtopic: Psychrometry – properties of air-water vapour mixture
Question Statement:
In a tray drying experiment of mango pulp, the constant rate of drying was found to be 6.18 × 10⁻⁵ kg water m⁻² s⁻¹. The humidity ratio and saturation humidity ratio of the air were 0.02 kg water vapour (kg dry air)⁻¹ and 0.075 kg water vapour (kg dry air)⁻¹ respectively at 1 atm pressure and 65 °C temperature. Assuming the distance of travel for water vapour in drying air to be 10 mm, the mass diffusivity of water in m² s⁻¹ is
Options:
(A) 10⁻⁴
(B) 10⁻⁵
(C) 10⁻⁶
(D) 10⁻⁷
Official Answer Key:
B
Step-by-Step Solution & Explanation
Constant-rate drying flux through a stagnant air film: N = D·(Cs − C)/x, where Cs, C are vapour concentrations (kg/m³) corresponding to Ws and W, and x is the diffusion distance. Humid air density at 65 °C, 1 atm ≈ 1.044 kg/m³ (using ideal-gas estimate). Cs = Ws·ρ = 0.075×1.044 = 0.0783 kg/m³; C = W·ρ = 0.02×1.044 = 0.0209 kg/m³. D = N·x/(Cs−C) = 6.18×10⁻⁵ × 0.010/(0.0783−0.0209) = 6.18×10⁻⁷/0.0574 = 1.08×10⁻⁵ m²/s ≈ 10⁻⁵ m²/s, matching option (B) (order of magnitude).
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