A sheet of steel $3\mathrm{.}0mm$ thick has nitrogen atmospheres on both sides at $900C$ and is permitted to achieve a steady$-$state condition. The diffusion coefficient for nitrogen in steel at this temperature is $1\mathrm{.}85{10}^{-10}\frac{m^2}{s},$ and the diffusion flux is $1\mathrm{.}0{10}^{-7}k\frac{g}{m^2}-s.$ The concentration of nitrogen in the steel at the high$-$pressure surface is $2k\frac{g}{m^3}.$ How far into the sheet from the high$-$pressure side will the concentration be $0\mathrm{.}5k\frac{g}{m^3}?$ Assume a linear concentration profile.

An FCC iron$-$carbon alloy initially containing $0\mathrm{.}55wt\%C$ is exposed to an oxygen$-$rich and virtually carbon$-$free atmosphere at $1325K(1052C).$ Under these conditions, the carbon diffuses from the alloy and reacts at the surface with oxygen in the atmosphere such that the carbon concentration at the surface position is maintained at essentially

$0wt\%C($decarburization process $-$ carbon depletion$).$ At what position will the carbon concentration be $0\mathrm{.}25wt\%$ after a $10-$hr treatment? D at $1325K$ is $3\mathrm{.}3{10}^{-11}\frac{m^2}{s}.$

The outer surface of a steel gear is to be hardened by increasing its carbon content; the carbon is to be supplied from an external carbon$-$rich atmosphere maintained at an elevated temperature. A diffusion heat treatment at $600C(873K)$ for $100$ minutes increases the carbon concentration to $0\mathrm{.}75\%$ at a position $0\mathrm{.}5mm$ below the surface.

Determine the diffusion time required to achieve this same concentration at the $0\mathrm{.}5mm$ position at $900C(1173K).$

Assume that the surface carbon content is the same for both heat treatments, which is maintained constant. Use the diffusion data in Table $5\mathrm{.}2$ for $C$ diffusion in a$-$Fe$.$