QIESTION FOUR

$(2)$ Defining all the terms, show that FICK's second law for non $-$steady state diffusion is given by the expression

$\frac{\text{d}\text{e}\text{l}\text{C}}{\text{d}\text{e}\text{l}\text{t}}=D(\frac{de{l}^{2}C}{del{x}^2})$

$[10$ marks$]$

$($b$)$ A diffusion couple was formed between pure copper and a Copper:Nickel alloy. After heating the couple to $1000C$ for $30$ days, the concentration of nickel in the pure copper was found to be $10\mathrm{.}0wt\%$ at a position $0\mathrm{.}5$ mm from the pure copper$-$Copper:Nickel interface. What is the original composition of nickel in the Copper:Nickel alloy? The preexponential, $D_0,$ is $2\mathrm{.}7{10}^{-4}\frac{m^2}{s}$ and the activation energy for the diffusion of Nickel in Copper is $236,000\frac{J}{m}ol.$ Take the Universal gas constant, R $,$ to be $8\mathrm{.}314\frac{J}{m}o\frac{l}{K}$ and the Avogadro's constant, N $,$ to be $6\mathrm{.}022\frac{{10}^{23}}{m}ol.$ Use the error function values below.

Table $1.$ Tabulation of Error Function values.

$[$Total $20$ Marks$]$

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