To the right is the iron$-$iron carbide

phase diagram, which we have

examined in class. As a reminder,

this phase diagram extends from $0$

wt $\%$ C to $6\mathrm{.}70$ wt $\%$ C$,$ with an

intermetallic compound $($cementite$,$

$F{e}_{3}C)$ existing at $6\mathrm{.}70wt\%C.$ Though

we have mostly used the lever rule

in simpler phase diagrams, but we

can also employ it to determine

mass$/$weight fractions for more

complex systems. Consider a $0\mathrm{.}25$

wt$\%$ C $-95\mathrm{.}75$ wt$\%$ Fe alloy.

a$.$ Using the lever rule, what

are the mass fractions of the

$$ and $$ phases at $750C?$

Show all work.

b$.$ What are the mass fractions at $600C?$ Show all work. $($Hint: remember that below the

eutectic isotherm, the compositions of each phase are determined by the compositions at the

eutectic isotherm$)$