Answer:
Yes it is possible.
Explanation:
This problem is about to possibility to have alloy of iron-carbon for which mass fraction of ferrite, [tex]$W_{\alpha} = 0.846$[/tex] and proeutectoid cementite, [tex]$W_{Fe_3C}=0.049$[/tex]
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
[tex]$W_{\alpha}=\frac{C_{Fe_3C}-C_0}{C_{Fe_3C}-C_{\alpha}}$[/tex]
[tex]$0.846}=\frac{6.70-C_0}{6.70-0.022}$[/tex]
[tex]$5.649588 = 6.70 - C_0$[/tex]
[tex]$\therefore C_0 = 1.05 $[/tex] wt. % of C
Now write the expression for the mass fraction of the proeutectoid cementite :
[tex]$W_{Fe_3C}=\frac{C_1-0.76}{5.94}$[/tex]
[tex]$0.049=\frac{C_1-0.76}{5.94}$[/tex]
[tex]$C_1 = 1.05$[/tex] % wt. C
Since, [tex]$C_0 =C_1$[/tex], it is possible to have an alloy of iron - carbon.
