Question

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

Answer 1

Answer:

okkkk please mark me as braineliest

Explanation:

yes it's possible

This problem is about to possibility to have alloy of iron-carbon for which mass fraction of ferrite, W_{\alpha} = 0.846W

α

=0.846 and proeutectoid cementite, W_{Fe_3C}=0.049W

Fe

3

C

=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}}W

α

=

C

Fe

3

C

−C

α

C

Fe

3

C

−C

0

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

5.649588 = 6.70 - C_05.649588=6.70−C

0

\therefore C_0 = 1.05∴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}W

Fe

3

C

=

5.94

C

1

−0.76

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

5.94

C

1

−0.76

C_1 = 1.05C

1

=1.05 % wt. C

Since, C_0 =C_1C

0

=C

1

, it is possible to have an alloy of iron - carbon.