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Chapter 9: Problem 16

A magnesium-lead alloy of mass \(7.5 \mathrm{kg}\) consists of a solid \(\alpha\) phase that has a composition just slightly below the solubility limit at \(300^{\circ} \mathrm{C}\) \(\left(570^{\circ} \mathrm{F}\right)\) (a) What mass of lead is in the alloy? (b) If the alloy is heated to \(400^{\circ} \mathrm{C}\left(750^{\circ} \mathrm{F}\right)\) how much more lead may be dissolved in the \(\alpha\) phase without exceeding the solubility limit of this phase?

Short Answer

Expert verified
Answer: An additional 60 g of lead can be dissolved in the α-phase when the alloy is heated from 300°C to 400°C.

Step by step solution

01

Find the composition of the α-phase at 300°C

First, we need to find the composition of the α-phase at 300°C. For this, we'll consult the magnesium-lead phase diagram. From the phase diagram, the composition of the α-phase at 300°C is approximately 1.4 wt% lead (Pb) and 98.6 wt% magnesium (Mg).
02

Calculate the mass of lead at 300°C

Now we can calculate the mass of lead in the alloy at 300°C, using the given total mass of the alloy and its composition. Total mass of the alloy = 7.5 kg wt% of Pb at 300°C = 1.4% wt% of Mg = 98.6% So, Mass of Pb = (wt% of Pb / 100) × Total mass of the alloy Mass of Pb = (1.4 / 100) × 7.5 kg Mass of Pb = 0.105 kg = 105 g At 300°C, the mass of lead in the alloy is 105 g.
03

Find the composition of the α-phase at 400°C

Next, we need to find the composition of the α-phase at 400°C. From the phase diagram, the solubility limit of lead in the α-phase is approximately 2.2 wt% at 400°C.
04

Calculate the increased mass of lead at 400°C

Now we can calculate the mass of lead in the alloy at 400°C when the alloy is heated. wt% of Pb at 400°C = 2.2% So, Mass of Pb at 400°C = (wt% of Pb at 400°C / 100) × Total mass of the alloy Mass of Pb = (2.2 / 100) × 7.5 kg Mass of Pb = 0.165 kg = 165 g At 400°C, the mass of lead in the alloy is 165 g.
05

Find the difference in mass of lead at 300°C and 400°C

Finally, we can determine how much more lead can be dissolved in the α-phase as the temperature is increased from 300°C to 400°C. Difference in mass of Pb = Mass of Pb at 400°C - Mass of Pb at 300°C Difference in mass of Pb = 165 g - 105 g Difference in mass of Pb = 60 g When the alloy is heated to 400°C, an additional 60 g of lead can be dissolved in the α-phase without exceeding the solubility limit.

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Most popular questions from this chapter

Is it possible to have a copper-silver alloy that, at equilibrium, consists of an \(\alpha\) phase of composition 4 wt \(\%\) Ag- 96 wt \(\%\) Cu, and also a \(\beta\) phase of composition 95 wt \(\%\) Ag-5 wt \(\%\) Cu? If so, what will be the approximate temperature of the alloy? If this is not possible, explain why.

Is it possible to have a copper-silver alloy of composition 20 wt \(\%\) Ag -80 wt \(\%\) Cu that, at equilibrium, consists of \(\alpha\) and liquid phases having mass fractions \(W_{\alpha}=0.80\) and \(W_{L}=\) \(0.20 ?\) If \(\mathrm{so},\) what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.

A \(2.0-\mathrm{kg}\) specimen of an \(85 \mathrm{wt} \% \mathrm{Pb}-15 \mathrm{wt} \%\) Sn alloy is heated to \(200^{\circ} \mathrm{C}\left(390^{\circ} \mathrm{F}\right)\); at this temperature it is entirely an \(\alpha\) -phase solid solution (Figure 9.8 ). The alloy is to be melted to the extent that \(50 \%\) of the specimen is liquid, the remainder being the \(\alpha\) phase. This may be accomplished by heating the alloy or changing its composition while holding the temperature constant. (a) To what temperature must the specimen be heated? (b) How much tin must be added to the \(2.0-\mathrm{kg}\) specimen at \(200^{\circ} \mathrm{C}\) to achieve this state?

It is desirable to produce a copper-nickel alloy that has a minimum noncold- worked tensile strength of \(380 \mathrm{MPa}(55,000 \mathrm{psi})\) and a ductility of at least \(45 \%\) EL. Is such an alloy possible? If so, what must be its composition? If this is not possible, then explain why.A 60 wt\(\% $$\mathrm{Pb}-40\) wt\(\%\) \(\mathrm{Mg}\) alloy is rapidly quenched to room temperature from an elevated temperature in such a way that the hightemperature microstructure is preserved. This microstructure is found to consist of the \(\alpha\) phase and \(\mathrm{Mg}_{2} \mathrm{Pb},\) having respective mass fractions of 0.42 and \(0.58 .\) Determine the approximate temperature from which the alloy was quenched.

Is it possible to have a magnesium-lead alloy in which the mass fractions of primary \(\alpha\) and total \(\alpha\) are 0.60 and \(0.85,\) respectively, at \(460^{\circ} \mathrm{C}\) \(\left(860^{\circ} \mathrm{F}\right) ?\) Why or why not?
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