$10\mathrm{.}11*$ The phase diagram of an alloy that has a eutectoid transformation is shown in

Figure $10\mathrm{.}33.$

a$.$ Sketch the Gibbs free energy curves for this alloy at $T=T^{\text{'}}.$

b$.$ Show that the $\frac{}{}$ solvus must enter the $\frac{}{}$ two$-$phase field $($as shown by the

arrow$).$

c$.$ Besides $T=T^{\text{'}},$ sketch the Gibbs free energy curves for $T_1,T_2,T_3,$ and show

how taut string method can be used to construct the phase diagram.

Sketch problem b$.$