Construct the phase diagram, temperature $(C)$ vs composition $($mole $\%$B$),$ of a binary A$-$B system from the following information and$\_$label the fields.

i$)$ A melts at $1100C$ and $B$ melts at $1000C.$

ii$)$ There are two intermetallic compounds in the system. The compound $A_3{B}_2$ melts incongruently at $700C$ and the compound $A{B}_4$ melts congruently at $900C.$

iii$)$ A has an $harr$ polymorphism at $550C.$

iv$)$ The maximum solubility of $B$ in the $$ phase is $2\%.$

v$)$ There is no solubility of A in B in solid state at all temperatures.

vi$)$ A monotectic reaction occurs at $900C.$

$L_1(15\%B)harr(10\%B)+L_2(??\%B)$

The amount of the solid phase $()$ just below the monotectic temperature is $80\%$ for the monetectic alloy.

vii$)$ A peritectic transition occurs at $700C.$

$A_3{B}_2$harr$(7\%B)+L(50\%B)$

viii$)$ A eutectic reaction occurs at $600C.$

$L(??\%B)harr{A}_3{B}_2+A{B}_4$

The amount of $A{B}_4$ just below the eutectic temperature is $50\%$ for the eutectic alloy.

ix$)$ A second eutectic reaction occurs at $800C.$

$L(86\%B)harrB+A{B}_4$

x$)$ A eutectoid reaction occurs at $500C.$

$(4\%B)harr+A_3{B}_2$

xi$)$ B undergoes an allotropic change at $400C.$

a$)$ What is the solubility limit of $B$ in $A$ in solid state?

b$)$ Draw the free energy$-$composition diagram for the room temperature. Show the curves of the stable phases only.

b$)$ Estimate the enthalpy of melting for component B$.($Take $R=2ca\frac{l}{m}ol.K)$