Question

Is it possible to have an iron-carbon alloy for which the mass fractions of total ferrite and proeutectoid cementite are 0.846 and 0.049, respectively? Why or why not?

Answer 1

Answer:

Yes it is possible.

Explanation:

This problem is about to possibility to have alloy of iron-carbon for which mass fraction of ferrite, $W_{\alpha} = 0.846$  and proeutectoid cementite, $W_{Fe_3C}=0.049$

An alloy formation is possible when the composition values of the two alloy are equal.

Now writing the expression for the mass fraction of total ferrite, we have

$W_{\alpha}=\frac{C_{Fe_3C}-C_0}{C_{Fe_3C}-C_{\alpha}}$

$0.846}=\frac{6.70-C_0}{6.70-0.022}$

$5.649588 = 6.70 - C_0$

$\therefore C_0 = 1.05$ wt. % of C

Now write the expression for the mass fraction of the proeutectoid cementite :

$W_{Fe_3C}=\frac{C_1-0.76}{5.94}$

$0.049=\frac{C_1-0.76}{5.94}$

$C_1 = 1.05$ % wt. C

Since, $C_0 =C_1$, it is possible to have an alloy of iron - carbon.