(Solved): Problem 2: The wear resistance of a steel shaft is to be improved by hardening its surface by incr ...

Problem 2: The wear resistance of a steel shaft is to be improved by hardening its surface by increasing the nitrogen content within an outer surface layer as a result of nitrogen diffusion into the steel; the nitrogen is to be supplied from an external nitrogen-rich gas at an elevated and constant temperature. The initial nitrogen content of the steel is $0.002\mathrm{wt}\%$, whereas the surface concentration is to be maintained at $0.50\mathrm{wt}\%$. For this treatment to be effective, a nitrogen content of $0.10\mathrm{wt}\%$ must be established at a position $0.40\mathrm{mm}$ below the surface. Specify appropriate heat treatments in terms of temperature and time for temperatures between $475^{?}\mathrm{C}$ and $625^{?}\mathrm{C}$. The preexponential and activation energy for the diffusion of nitrogen in iron are $3\times 10^{?7}{\mathrm{m}}^2/\mathrm{s}$ and $76,150\mathrm{J}/\mathrm{mol}$, respectively, over this temperature range.