Nitrogen from a gaseous phase is to be diffused into pure iron at $675C.$ If the

surface concentration is maintained at $0\mathrm{.}3wt.\%N,$ what will be the concentration at $2\mathrm{.}5$

$mm$ from the surface after $20$ hours? Pure iron has a BCC structure at this temperature and

the diffusivity data are given in the table below.

$($Hint$)$ Assume that the situation is similar to diffusion in a semi$-$infinite solid, in which the

surface concentration is held constant. In this case, the solution for the diffusion equation

is:

$\frac{C_x-C_0}{C_s-C_0}=1-$erf$(\frac{x}{2\sqrt[\phantom{2}]{Dt}}),$

where $C_x$ represents the concentration at depth $x$ after time $t.$ The error function values are

also given in the table below. PLEASE PROVIDE DETAILED EXPALANTIONS FOR EACH STEP.