Subtopic: Controlled and modified atmosphere storage
Question Statement:
Cheese is packed in a bilayer plastic package made up of LDPE and PET. The thickness of LDPE and PET in the package are 1.5 mm and 1.3 mm, respectively. The surface area of the plastic package is 6.25 cm². The partial pressure difference of oxygen across the package wall is 0.30 atm. The permeability coefficient of oxygen in LDPE and PET are 4.18×10⁻⁸ and 1.67×10⁻¹⁰ cm³ cm cm⁻²s⁻¹atm⁻¹, respectively. If the food gets spoiled when it absorbs 0.025 ml of oxygen, then the shelf life of food in days is
Options:
(A) 121
(B) 103
(C) 73
(D) 61
Official Answer Key:
A
Step-by-Step Solution & Explanation
For a bilayer (series) barrier, the layer resistances (thickness/permeability) add: R_total = L₁/P₁ + L₂/P₂ = (0.15 cm)/(4.18×10⁻⁸) + (0.13 cm)/(1.67×10⁻¹⁰) = 3.589×10⁶ + 7.784×10⁵ = 4.166×10⁶ (cm·s·atm/cm³, effectively).
Oxygen transmission rate, Q = A×ΔP/R_total = (6.25×0.30)/(4.166×10⁶) = 1.875/(4.166×10⁶) ≈ 2.398×10⁻⁹ cm³/s.
Time to absorb 0.025 ml (=0.025 cm³) = 0.025/2.398×10⁻⁹ = 1.0425×10⁷ s = 120.7 days ≈ 121 days. Answer: (A).
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