(Solved): Problem 4. Thin-film solution Imagine that a film with thickness of b with so ...

???????

Problem 4. Thin-film solution Imagine that a film with thickness of $$b$$ with solution concentration $$C_0$$ is plated on one end of a long rod of solute-free material. If a similar solute-free rod is welded to the plated end of the rod (without any diffusion occurring) and the rod is then annealed at for a time $$t$$ so that diffusion can occur, the concentration of solute along the bar will be given by the equation, $$C(x,t)=\frac{b{c}_0}{2\sqrt{?Dt}}\exp \left(\frac{?x^2}{4Dt}\right)$$ in those regions where $$\sqrt{Dt}>b$$. Here $$x$$ is the distance in either direction normal to the initial solute film. 2. Extra Credit: Solving partial differential equation Derive Eq. 4 from the Fick's 2nd Law. Use the relation: $${?}_{??}^{+?}C(x,t)dx=b{C}_0$$ Show all steps.