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Chapter 9: Problem 73

Is it possible to have an iron-carbon alloy for which the mass fractions of total ferrite and pearlite are \(0.860\) and \(0.969\), respectively? Why or why not?

Short Answer

Expert verified
Answer: No, it is not possible because the sum of mass fractions (1.829) exceeds the maximum allowable value of 1 (or 100%).

Step by step solution

01

Check the given mass fractions

First, we need to verify whether an iron-carbon alloy can have mass fractions of total ferrite and pearlite at \(0.860\) and \(0.969\), respectively.
02

Compute the sum of mass fractions

Now let's add the mass fractions of both ferrite and pearlite: \(\textrm{Total mass fractions} = \textrm{Mass fraction of Ferrite} + \textrm{Mass fraction of Pearlite}\) \(\textrm{Total mass fractions} = 0.860 + 0.969 = 1.829\)
03

Determine if the sum is valid

We see that the sum of mass fractions is \(1.829\), which is greater than \(1\). Since the mass fractions cannot add up to more than 100% (or a total mass fraction of \(1\)), it is not possible to have an iron-carbon alloy with mass fractions of total ferrite and pearlite at \(0.860\) and \(0.969\), respectively.

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Most popular questions from this chapter

Plot the mass fraction of phases present versus temperature for a \(40 \mathrm{wt} \% \mathrm{Sn}-60 \mathrm{wt} \% \mathrm{~Pb}\) alloy as it is slowly cooled from \(250^{\circ} \mathrm{C}\) to \(150^{\circ} \mathrm{C}\).

The mass fraction of eutectoid cementite in an iron-carbon alloy is \(0.109\). On the basis of this information, is it possible to determine the composition of the alloy? If so, what is its composition? If this is not possible, explain why.

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Given here are the solidus and liquidus temperatures for the copper-gold system. Construct the phase diagram for this system and label each region. $$ \begin{array}{ccc} \hline \begin{array}{c} \text { Composition } \\ \text { (wt\% Au) } \end{array} & \begin{array}{c} \text { Solidus } \\ \text { Temperature }\left({ }^{\circ} \mathrm{C}\right) \end{array} & \begin{array}{c} \text { Liquidus } \\ \text { Temperature }\left({ }^{\circ} \boldsymbol{C}\right) \\ \hline 0 \end{array} & 1085 & 1085 \\ \hline 20 & 1019 & 1042 \\ \hline 40 & 972 & 996 \\ \hline 60 & 934 & 946 \\ \hline 80 & 911 & 911 \\ \hline 90 & 928 & 942 \\ \hline 95 & 974 & 984 \\ \hline 100 & 1064 & 1064 \\ \hline \end{array} $$
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