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Chapter 9: Problem 35

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 \(150^{\circ} \mathrm{C}\).

Short Answer

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Question: Calculate and plot the mass fractions of phases present for a 40 wt% Sn - 60 wt% Pb alloy as it cools from 250°C to 150°C. Indicate the mass fractions for liquid, α-Pb, and eutectic phases at each temperature point.

Step by step solution

01

Find the phase transition temperatures

Consult a Sn-Pb phase diagram to find the phase boundaries (i.e., temperatures where phase transitions occur) for the given alloy composition. Note the solidus and liquidus temperatures, as well as the eutectic temperature and composition.
02

Identify the phases present at each stage of cooling

Analyze the phase diagram to determine which phases are present at each stage of cooling: - From the beginning of cooling (\(250^\circ C\)) to solidus temperature - Between the solidus and eutectic temperatures - From the eutectic temperature to the end of cooling (\(150^\circ C\))
03

Calculate the mass fractions using the lever rule

Use the lever rule to calculate the mass fractions of the phases present at each stage of cooling. The lever rule states that the mass fraction of a phase is proportional to the length of the tie-line arm opposite to that phase. Formula for the Lever Rule: \(\frac{W_{phase}}{W_{total}} = \frac{C_{opposite} - C_{alloy}}{C_{opposite} - C_{adjacent}}\) Apply the lever rule for each phase present in the three stages of cooling.
04

Plot the mass fractions versus temperature

Using the mass fractions calculated in Step 3, plot the mass fraction of each phase versus temperature for the entire cooling process of the alloy, ranging from \(250^\circ C\) to \(150^\circ C\). Make sure to label the graph and indicate the mass fractions for liquid, \(\alpha\)-Pb, and eutectic phases at each temperature point. Following the above steps, you'll be able to plot the mass fraction of phases present for the \(40 wt\% Sn - 60 wt\% Pb\) alloy as it cools from \(250^\circ C\) to \(150^\circ C\).

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Most popular questions from this chapter

For a series of \(\mathrm{Fe}-\mathrm{Fe}_{3} \mathrm{C}\) alloys with compositions ranging between \(0.022\) and \(0.76 \mathrm{wt} \% \mathrm{C}\) that have been cooled slowly from \(1000^{\circ} \mathrm{C}\), plot the following: (a) mass fractions of proeutectoid ferrite and pearlite versus carbon concentration at \(725^{\circ} \mathrm{C}\) (b) mass fractions of ferrite and cementite versus carbon concentration at \(725^{\circ} \mathrm{C}\).

Is it possible to have a copper-silver alloy that, at equilibrium, consists of a \(\beta\) phase of composition \(92 \mathrm{wt} \%\) Ag-8 \(\mathrm{wt} \% \mathrm{Cu}\) and also a liquid phase of composition \(76 \mathrm{wt} \%\) Ag-24 wt \(\% \mathrm{Cu}\) ? If so, what will be the approximate temperature of the alloy? If this is not possible, explain why.

For a lead-tin alloy of composition \(80 \mathrm{wt} \% \mathrm{Sn}-\) \(20 \mathrm{wt} \% \mathrm{~Pb}\) and at \(180^{\circ} \mathrm{C}\left(355^{\circ} \mathrm{F}\right)\), do the following: (a) Determine the mass fractions of the \(\alpha\) and \(\beta\) phases. (b) Determine the mass fractions of primary \(\beta\) and eutectic microconstituents. (c) Determine the mass fraction of eutectic \(\beta\).

For alloys of two hypothetical metals \(\mathrm{A}\) and \(\mathrm{B}\), there exist an \(\alpha\), A-rich phase and a \(\beta\), B-rich phase. From the mass fractions of both phases for two different alloys provided in the following table (which are at the same temperature), determine the composition of the phase boundary (or solubility limit) for both \(\alpha\) and \(\beta\) phases at this temperature. $$ \begin{array}{lcc} \hline \begin{array}{c} \text { Alloy } \\ \text { Composition } \end{array} & \begin{array}{c} \text { Fraction } \\ \boldsymbol{\alpha} \text { Phase } \end{array} & \text { Fraction } \\ \hline 70 \mathrm{wt} \% \mathrm{~A}-30 \mathrm{wt} \% \mathrm{~B} & 0.78 & 0.22 \\ \hline 35 \mathrm{wt} \% \mathrm{~A}-65 \mathrm{wt} \% \mathrm{~B} & 0.36 & 0.64 \\ \hline \end{array} $$

What thermodynamic condition must be met for a state of equilibrium to exist?
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