Chapter 14, Problem 14.49P

Consider a DVD similar to that of Problem 5.99. To protect sensitive information within the storage medium, a very thin film of reactive polymer is embedded within the polycarbonate at a distance d = 0.5 mm from the surface. The thin film can undergo a chemical reaction with oxygen during which it is converted from a transparent material to an opaque material, rendering the information unreadable. The chemical reaction begins when the oxygen concentration at the reactive polymer reaches ${\bar{C}}_{\text{crit}}=5\times {10}^{-5}kmol/m^3$ . The DVD is shipped in an oxygen-proof pouch: determine the elapsed time after removal from the pouch before the DVD self- destructs. The solubility and diffusivity of oxygen in polycarbonate are $S=8.9\times {10}^{-3}kmol/m^3$ bar and $D_{\text{AB}}=6.5\times {10}^{-12}{m}^2/s$ . respectively.