In a carburizing process, consider an

iron$-$carbon alloy that initially has auniform

carbon concentration of $0\mathrm{.}3wt\%$ and

is to be treated at $950C.$ To achieve a

carbon content of $0\mathrm{.}75wt\%$ at a position

$0\mathrm{.}5$ mm below the surfacewith H hour

of carburizing process, calculate the

concentration of carbon thatshould be

maintained at the surface. The diffusion

coefficient for carbon in iron at this

temperature is $1\mathrm{.}61011\frac{m^2}{s}$; assume that

the steel piece is semi$-$infinite.