An iron$-$carbon alloy initially containing $0\mathrm{.}220$ wt$\%$ C is exposed to an oxygen$-$rich and virtually An iron$-$carbon alloy initially containing $0\mathrm{.}220wt\%C$ is exposed to an oxygen$-$rich and virtually carbon$-$free atmosphere at $1190C.$

Under these circumstances the carbon diffuses from the alloy and reacts at the surface with the oxygen in the atmosphere; that is$,$ the

carbon concentration at the surface position is maintained essentially at $0\mathrm{.}0wt\%C.$ At what position will the carbon concentration

be $0\mathrm{.}165wt\%$ after a $6$ h treatment? The value of $D$ at $1190C$ is $6\mathrm{.}0{10}^{-11}\frac{m^2}{s}.$

carbon$-$free atmosphere at $1190\backslash$deg C$.$ Under these circumstances the carbon diffuses from the alloy

and reacts at the surface with the oxygen in the atmosphere; that is$,$ the carbon concentration at

the surface position is maintained essentially at $0\mathrm{.}0$ wt$\%$ C$.$ At what position will the carbon

concentration be $0\mathrm{.}165$ wt$\%$ after a $6$ h treatment? The value of D at $1190\backslash$deg C is $6\mathrm{.}0\backslash$times $10$ m $/$s$.$

z erf$($z$)$ z erf$($z$)$ z erf$($z$)$

$0\mathrm{.}000\mathrm{.}00000\mathrm{.}550\mathrm{.}56331\mathrm{.}30\mathrm{.}9340$

$0\mathrm{.}0250\mathrm{.}02820\mathrm{.}600\mathrm{.}60391\mathrm{.}40\mathrm{.}9523$

$0\mathrm{.}050\mathrm{.}05640\mathrm{.}650\mathrm{.}64201\mathrm{.}50\mathrm{.}9661$

$0\mathrm{.}100\mathrm{.}11250\mathrm{.}700\mathrm{.}67781\mathrm{.}60\mathrm{.}9763$

$0\mathrm{.}150\mathrm{.}16800\mathrm{.}750\mathrm{.}71121\mathrm{.}70\mathrm{.}9838$

$0\mathrm{.}200\mathrm{.}22270\mathrm{.}800\mathrm{.}74211\mathrm{.}80\mathrm{.}9891$

$0\mathrm{.}250\mathrm{.}27630\mathrm{.}850\mathrm{.}77071\mathrm{.}90\mathrm{.}9928$

$0\mathrm{.}300\mathrm{.}32860\mathrm{.}900\mathrm{.}79702\mathrm{.}00\mathrm{.}9953$

$0\mathrm{.}350\mathrm{.}37940\mathrm{.}950\mathrm{.}82092\mathrm{.}20\mathrm{.}9981$

$0\mathrm{.}400\mathrm{.}42841\mathrm{.}00\mathrm{.}84272\mathrm{.}40\mathrm{.}9993$

$0\mathrm{.}450\mathrm{.}47551\mathrm{.}10\mathrm{.}88022\mathrm{.}60\mathrm{.}9998$

$0\mathrm{.}500\mathrm{.}52051\mathrm{.}20\mathrm{.}91032\mathrm{.}80\mathrm{.}9999$