Question Statement:
Preservation of Food: Kinetics of microbial death – pasteurization and sterilization of milk and other liquid foods; preservation of food by cooling and freezing; refrigeration and cold storage basics and applications.
In an air blast freezing operation, a flat tray of 1.0 m×1.0 m×0.02 m is used to freeze filled depodded peas. Bulk density and moisture content of peas are 550 kg/m³ and 85% (w.b.) respectively. Latent heat of freezing from water to ice at -1°C is 335 kJ/kg and heat transfer occurs identically from the top and bottom surfaces of the tray. Convective film heat transfer coefficient on the heat transfer surfaces of the tray is 30 W/m²K and the thermal conductivity of frozen peas is 0.54 W/m·K. Assuming the tray to be a semi-infinite slab, the freezing time (minutes) to completely freeze the product (rounded to 1 decimal) is ______.
Step-by-Step Solution & Explanation
Plank's equation for freezing time of an infinite slab, cooled symmetrically from both faces (half-thickness a = 0.02/2 = 0.01 m):
t = (ρ·L)/(T_f − T_a) × [ (P·a/h) + (R·a²/k) ], with the standard slab shape factors P = 1/2, R = 1/8.
All physical quantities needed are given EXCEPT the air (medium/blast) temperature, T_a — the problem statement supplies the latent-heat reference temperature (−1°C, the freezing point) but not the temperature of the circulating freezing air, so the driving temperature difference (T_f − T_a) cannot be evaluated from the data as given.
For reference, with a = 0.01 m, h = 30 W/m²K, k = 0.54 W/m·K, ρ = 550 kg/m³, L = 335 kJ/kg = 335,000 J/kg:
Geometric term = (0.5×0.01/30) + (0.125×0.01²/0.54) = 1.667×10⁻⁴ + 2.315×10⁻⁵ = 1.898×10⁻⁴ (units: m²K/W)
t × (T_f − T_a) = ρL × [geometric term] = 550×335,000 × 1.898×10⁻⁴ = 34,960 (units: s·K)
Without T_a this cannot be converted to a numeric freezing time. This missing input is precisely why the official GATE key awarded marks to all candidates for this question. If a typical blast-freezing air temperature (e.g., T_a = −35°C, giving T_f−T_a ≈ 34 K with T_f ≈ −1°C) is assumed, t ≈ 34,960/34 ≈ 1028 s ≈ 17.1 minutes — shown only as an illustrative estimate, since T_a is not stated in the paper.
Appendix A — Consolidated Answer Table
Appendix B — Section-wise Weightage & Preparation Observations
Preparation observations:
• General Aptitude (15%) and Section 4 — Soil and Water Conservation Engineering (15%) carry the single largest shares of the paper; SWC Engineering alone spans Fluid Mechanics, Soil Mechanics, Hydrology, Surveying, and Soil & Water Erosion — build a dedicated handbook for each of these five sub-areas rather than treating SWC Engineering as one topic.
• Section 6 — Agricultural Process Engineering (14%) and Sections 1 & 3 (13% each) are close behind. Process Engineering questions in this paper were calculation-heavy (mass balances, psychrometry, Henderson's drying equation, size-reduction geometry) — prioritise numerical fluency here, not just definitions.
• Hydrology (Section 4) alone contributed 5 of this paper's questions (Q9, 21, 22, 34, 49) — it is worth isolating as its own high-yield sub-topic across multiple past papers, not lumped generically under 'SWC Engineering'.
• Two questions in this paper (Q37, Q55) were awarded marks to all candidates due to unit/data ambiguity in the original question — a reminder to always state units explicitly and double-check given data completeness while attempting NAT questions under exam pressure.
• Farm Power (Section 3) questions leaned heavily on tractor mechanics (traction, overturning, rolling resistance, seat vibration) rather than pure IC-engine theory — revise Wismer-Luth/Brixius traction formulas and tractor stability derivations specifically, since these are frequently tested via numerical problems rather than conceptual MCQs.
• Across the paper, roughly 60% of AG-section marks came from NAT (numerical answer type) questions — sustained calculation speed and unit discipline (kPa vs Pa, cm/h vs mm/day, g vs kg) matter as much as conceptual recall for a top rank.