Equilibrium Solidification of Alloy: Consider the equilibrium solidification of an alloy bar discussed in. In particular, the original composition of the homogeneous liquid phase is $X_0$, at temperature T, the equilibrium composition of the solid and liquid phases are respectively $X_S$ and $X_L$. The length of solid part and liquid part in the bar are respectively $L_S$ and $L_L$
(a) Show a schematic plot of the alloy bar, indicate the liquid and solid regions, and label the current compositions of both liquid and solid phases, as well as the original composition $X_0$
(b) Derive the ration of $L_S/L_L$ in terms of $X_0$, $X_S$ and $X_L$, using conversion of solutes. How this relation is related to lever rule that we discussed for phase diagrams?
