Compounds A and B mix uniformly over their entire composition range, both in a solid phase and in a liquid phase. $-$ The free energy of pure, solid A varies with temperature according to G$\_$m$,$ A$,($s$)=5$kJ $/$ mol$-$T$(1$J $/$ mol$$K$)-$ The free energy of pure, solid B varies with temperature according to G$\_$m$,$ B$,($s$)=10$kJ $/$ mol$-$T$(5$J $/$ mol$$K$)-$ The free energy of pure, liquid A varies with temperature according to G$\_$m$,$ A$,($l$)=10$kJ $/$ mol$-$T$(5$J $/$ mol$$K$)-$ The free energy of pure, liquid B varies with temperature according to G$\_$m$,$ B$,(1)=15$kJ $/$ mol$-$T$(15$J $/$ mol$$K$)$ The free energy of mixing vs$.$ composition of the both the liquid phase and solid phases of alloy A$\_1-$x B$\_$x is ideal. NOTE: Ignore all slopes$/$tangents at x$\_$B$=1,$ x$\_$B$=0.$ You are allowed to solve the problem numerically. a$.$ Make a graph of the free energy of the solid phase vs$.$ composition x$\_$B at $1000$K$.$ b$.$ Make a graph of the free energy of the liquid phase vs$.$ composition x$\_$B at $1000$K$.$ c$.$ Draw, quantitatively, the phase diagram of the alloy. Label the solid phase, liquid phase, and any coexistence region. Label the liquidus and the solidus. What is the melting point of pure A and pure B $?$ d$.$ Consider that you have $10$ moles of component A and $5$ moles of component B$.$ What are the chemical potentials of A and B in the mixture at T $=800$ K$?$