Question $3$

$1$ pts

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