$(25$ points$)($a$)$ Considering the binary regular solution of $Cu-Fe$ shown in Figure $1,$ any small negative composition deviation from $x_{Cu}=0\mathrm{.}5$ will spontaneously drive $\frac{}{b}ar(G{)}_{Cu}=RTln{a}_{Cu}$ to $-,$ i$.$e$.$ drive $a_{Cu}$ to $0.$ We know this won't happen. Please use G$-$D eqn to explain why not. $(5$ points$)($b$)$ Please use the G$-$H eqn to discuss how activity coefficient ${}_{Fe}$ changes with rising temperature for the $Cu-Fe$ system? Is this mixing an endothermic or exothermic $($ or $)$ process? HINT: Thinking how a rising $T$ changes the system toward an ideal behavior. $(5$ points$)($c$)$ If you measure the $G^M$ of $Cu-Fe(1$:$1)$ melt at $T=1540C$ and $($:$T_m^{Cu}=1322C$