An fcc iron–carbon alloy initially containing 0.35 wt% c is exposed to an oxygen-rich and virtually carbon-free atmosphere at 1400 k (1127 °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 wt% c. (this process of carbon depletion is termed decarburization.) at what position will the carbon concentration be 0.15 wt% after a 10-h treatment? the value of d at 1400 k is 6.9 x 10-11 m2 /s. g

3.99 mm

Explanation:

To treat a diffusive process in function of time and distance we need to solve  2nd Ficks Law. This a partial differential equation, with certain condition the solution looks like this:

Where Cs is the concentration in the surface of the solid

Cx is the concentration at certain deep X

Co is the initial concentration of solute in the solid

and erf is the error function

First we need to solve the Cs-Cx/Cs-Co on the left to search the corresponding value later on a table.

We look on a table and we see for erf(z)=0.4284 z=0.40

Then we solve for x

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