The surface of $0\mathrm{.}10$ wt$\%$ carbon steel is to be strengthened by carburizing. The steel is placed in an atmosphere that provides a maximum of $1\mathrm{.}2$ wt$\%$ carbon at the surface of the steel at a high temperature. Carbon then diffuses $0\mathrm{.}83$ cm into the surface of the steel giving a carbon concentration of $0\mathrm{.}45$ wt$\%$ carbon at that depth. How long $($in hours$)$ will the process of carburizing take if the diffusion coefficient is $2107$ cm$2/$s$?$ Use the table below for error function values as needed.