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

Yes it is possible.

Step-by-step 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

`$W_(\alpha)=(C_(Fe_3C)-C_0)/(C_(Fe_3C)-C_(\alpha))$`

`$0.846}=(6.70-C_0)/(6.70-0.022)$`

`$5.649588 = 6.70 - C_0$`

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

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

`$W_(Fe_3C)=(C_1-0.76)/(5.94)$`

`$0.049=(C_1-0.76)/(5.94)$`

`$C_1 = 1.05$` % wt. C

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