Cheese packaging has LDPE1.5 mm and PET1.3 mm layers, area 6.25 cm²,and oxygen pressure difference.30 atm. Oxygen permeabilities are4.18×10⁻⁸ and 1.67×10⁻¹⁰ cm³·cm/(cm²·s·atm). Spoilage occurs after .025 mL oxygen uptake. Find shelf life in days.
Treat layers as diffusion resistances in series, with thicknesses.15 and .13 cm. Oxygen entry rate is $\dot V=A\Delta p/(l_1/P_1+l_2/P_2)=6.25(.30)/[.15/(4.18\times10^{-8})+.13/(1.67\times10^{-10})]$ cm³/s. Shelf time is $.025/\dot V=120.6839$ days after dividing seconds by 86400. Hence **121 days, A**.
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