$(25$ 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 $($:$T_m^{Cu}=1322C\}$ and found that $G_{\text{m}\text{i}\text{n}}^M$ is not at $x_{Cu}=0\mathrm{.}5,$ please draw the deviated $G^M$ and the ideal $G_{id}^M$ on Figure $2.(5$ points$)($d$)$ If you keep the Cu$-$Fe system at a particular $T$ and $x_{Cu}$ and find $a_{se}$ is smaller than the expected value, what experiment operations can you do to make $a_{Fe}$ toward the expected value? $(5$ points$)$ Explain why it is not regular and why your operation can make it "more regular". $(5$ points$)$ HINT: Thinking G$-$H eqn and how much $G^M$ deviated from Raoultian behavior.