Adapted from problem $5\mathrm{.}14(30$ marks$)$ An FCC iron$-$carbon alloy initially containing $0\mathrm{.}35wt\%$

C is exposed to an oxygen$-$rich and virtually carbon$-$free atmosphere at $1400$ K $.$ Under these circumstances

the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is$,$ the

carbon concentration at the surface position is maintained essentially at $0wt\%C.($This process of carbon

depletion is termed decarburization.$)$ At what position will the carbon concentration be $0\mathrm{.}15wt\%$ after a

$10-$h treatment? Take $D_0$ as $9\mathrm{.}1{10}^{-5}\frac{m^2}{s}$ and $Q_d=168k\frac{J}{m}ol.$