An iron$-$carbon alloy initially containing $0\mathrm{.}307wt\%C$ is exposed to an oxygen$-$rich and virtually carbon$-$free atmosphere at $1180C.$ 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 $0\mathrm{.}0wt\%C.$ At what position will the carbon concentration be $0\mathrm{.}230$ wt$\%$ after a $5h$ treatment? The value of $D$ at $1180C$ is $5\mathrm{.}2{10}^{-11}\frac{m^2}{s}.$

$\backslash$table$[[z,$erf$(z),z,$erf$(z),z,$erf$(z)$