In the $A-B$ binary phase diagram, assume A and $B$ form ideal solutions in the liquid and the

solid state. Given the melting temperature of B $(1500K)$ is lower than that of $A(1800K),$

$($a$)$ What is the critical temperature of the system? $(5\%)$

$($b$)$ Sketch the binary phase diagram of the system $(T$ vs $x_B).(5\%)$

$($c$)$ Sketch the Gibbs free energy of mixing of liquid solution $G(l)$ and solid solution $G(s)$ at

$1600$ K$.(5\%)$

$($d$)$ Sketch the activity of $A(a_A)$ vs composition of $B(x_B)$ specify the standard state you use.

$(5\%)$In the A$$B binary phase diagram, assume A and B form ideal solutions in the liquid and the

solid state. Given the melting temperature of B $(1500$ K$)$ is lower than that of A $(1800$ K$),$

$($a$)$ What is the critical temperature of the system? $(5\%)$

$($b$)$ Sketch the binary phase diagram of the system $($T vs Xb$).(5\%)$

$($c$)$ Sketch the Gibbs free energy of mixing of liquid solution G$($l$)$ and solid solution G$($s$)$ at

$1600$ K$.(5\%)$

$($d$)$ Sketch the activity of A $($aA$)$ vs composition of B $($XB$)$ specify the standard state you use.

$(5\%)$