$($a$)$ Calculate the diffusion coefficient for magnesium in aluminum at $400C.$

$($b$)$ If a magnesium$/$aluminum diffusion couple is heated at $400C$ for $15$ hours, a certain concentration profile is achieved. What time would be required at $525C$ to achieve the same concentration profile? Do NOT assume steady$-$state diffusion.

$($c$)$ State assumptions required to solve this problem.

Some information:

$Q_d=131k\frac{J}{m}ol$

$D_0=1\mathrm{.}2{10}^{-4}\frac{m^2}{s}$

$Mg$ has the HCP structure

Al has the FCC structure