A sheet of steel $1\mathrm{.}5mm$ thick has nitrogen atmospheres on both sides at $1200C$ and is

permitted to achieve a steady$-$state diffusion condition. The diffusion coefficient for

nitrogen in steel at this temperature is $6{10}^{-11}\frac{m^2}{s},$ and the diffusion flux is found to be $1\mathrm{.}2$

${10}^{-7}k\frac{g}{m^2}\frac{?}{s}.$ Also, it is known that the concentration of nitrogen in the steel at the high$-$

pressure surface is $4k\frac{g}{m^3}.$ How far into the sheet from this high$-$pressure side will the

concentration be $2\mathrm{.}0k\frac{g}{m^3}?$ Assume a linear concentration profile.

a$.$ Write the relevant equation.

b$.$ Rearrange the equation to solve for the desired variable.

c$.$ Define the terms in the equation using numbers $(2$ points$).$

d$.$ How far into the sheet from this high$-$pressure side will the concentration be $2\mathrm{.}0$

$k\frac{g}{m^3}?$