Steel is carburized in a high-temperature process that depends on the transfer of carbon by diffusion. The value of the diffusion coefficient is strongly temperature dependent and may be approximated as \(D_{\mathrm{C}-\mathrm{S}}\left(\mathrm{m}^{2} / \mathrm{s}\right) \approx\) \(2 \times 10^{-5} \exp [-17,000 / T(\mathrm{~K})]\). If the process is effected at \(950^{\circ} \mathrm{C}\) and a carbon mole fraction of 0.025 is maintained at the surface of the steel, how much time is required to elevate the carbon content of the steel from an initial value of \(0.1 \%\) to a value of \(1.0 \%\) at a depth of \(1 \mathrm{~mm}\) ?