Based on the IRON$-$CARBON SYSTEM $($Fe$-$Fe $3$ C$)$ solve the following questions

Instructions: Solve each problem or exercise based on the iron$-$carbon system. There is no

need to copy the entire problem statement; simply indicate the number and subsection.

Each subsection must be supported with arguments or by showing the lever rule, and

the phase diagram used must be attached.

The activity will be evaluated based on the number of correct answers obtained $($the

procedure will be considered if the lever rule is applied correctly for phase selection$).$

Each subsection has the same weight.

It is important that handwriting and$/$or operations are legible, otherwise the item will be

void.

A ferritic cast iron containing $2\mathrm{.}5\%C$ is in equilibrium at room temperature.

Determine:

a$)$ The phases present and their relative amounts.

b$)$ Repeat the above for a temperature of $1130C.$ Is there a difference in the results?

Explain.

c$)$ Sketch the microstructures resulting from the previous subsections.

A hypoeutectoid steel $(0\mathrm{.}6\%C)$ is slowly cooled from $850C$ to room temperature.

Using the Iron$-$Carbon diagram, calculate:

a$)$ The fractions of proeutectoid Austenite $($ y $)$ and Ferrite $()$ present just above the

eutectoid temperature $(727+T).$

b$)$ The fractions of Ferrite $($ a $)$ and Cementite $($ Fe$3$C $)$ present just below the eutectoid

temperature $(727-T).$

c$)$ The amount of eutectoid ferrite $($secondary$)$ in the pearlite just below the eutectoid

temperature $(727-T).$

Analyze the solidification process of a $70kg$ iron piece containing $750g$ of carbon.

Determine:

a$)$ The temperature at which solidification begins.

b$)$ The final temperature of solidification.

c$)$ The composition of the phases at room temperature.