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

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

nitrogen in steel at this temperature is $6\backslash$times $10-11$ m$2$

$/$s$,$ and the diffusion flux is found to be $1\mathrm{.}2$

$\backslash$times $10-7$ kg$/$m$2/$s$.$ Also, it is known that the concentration of nitrogen in the steel at the highpressure surface is $4$ kg$/$m$3$

$.$ How far into the sheet from this high$-$pressure side will the

concentration be $2\mathrm{.}0$ kg$/$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 $2\mathrm{.}0$

kg$/$m$3?$