$4.$ A specimen of hypoeutectoid $($meaning composition is below the eutectoid$)$ steel having a

composition of $0\mathrm{.}5\%$ C and a mass of $1$ kg is slowly cooled from a temperature $850$ o

C$.$

a$.$ If we stop cooling at a temperature just above the eutectoid isotherm, determine the

fractions of the two phases and the total weight of the ferrite $\backslash$alpha phase in the specimen.

This phase is called proeutectoid $($meaning pre$-$ or before eutectoid$)$ ferrite.

b$.$ Next, the specimen is further cooled slowly to room temperature, which transforms

the rest of the austenite into pearlite. Determine the total weight fraction of ferrite and

the total mass of ferrite in the specimen at room temperature.

c$.$ The weight fraction of protoeutectoid ferrite $($part a$)$ is not affected by the additional

cooling to room temperature. Calculate the weight fraction of the total specimen that

is eutectoid ferrite at room temperature