An FCC iron$-$carbon alloy initially containing $\backslash (0\mathrm{.}22\backslash$mathrm$\{$wt$\}\backslash \%\backslash )$ carbon is carburized at an elevated temperature and in an atmosphere wherein the surface carbon concentration is maintained at $\backslash (1\mathrm{.}1\backslash$mathrm$\{$wt$\}\backslash \%\backslash )$ carbon. If after $50\mathrm{.}0$ hours the concentration of carbon is $\backslash (0\mathrm{.}47\backslash$mathrm$\{$wt$\}\backslash \%\backslash )$ at a position $2\mathrm{.}2$ mm below the surface, determine the temperature $($in K $)$ at which the treatment was carried out.

Make a $3$D plot of $\backslash ($ C$($x$,$ t$)\backslash )$ for the problem in part $($d$)$