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Chapter 9: Problem 20

A hypothetical A-B alloy of composition \(55 \mathrm{wt} \%\) B-45 \(\mathrm{wt} \% \mathrm{~A}\) at some temperature is found to consist of mass fractions of \(0.5\) for both \(\alpha\) and \(\beta\) phases. If the composition of the \(\beta\) phase is \(90 \mathrm{wt} \%\) B-10 \(\mathrm{wt} \% \mathrm{~A}\), what is the composition of the \(\alpha\) phase?

Short Answer

Expert verified
Answer: The composition of the α phase is 20 wt% B and 80 wt% A.

Step by step solution

01

Set up the equation using the lever rule

Let x be the wt% of B in the α phase. Then, the wt% of A in the α phase will be (100-x). According to the lever rule principle, we can set up the following equation: 0.5 * x + 0.5 * 90 = 55.
02

Solve for x

Solve the equation for x: 0.5 * x + 45 = 55. Now, subtract 45 from both sides: 0.5 * x = 10. Divide by 0.5: x = 20. So, the composition of the α phase is 20 wt% B and 80 wt% A.

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Most popular questions from this chapter

Consider \(2.5 \mathrm{~kg}\) of austenite containing \(0.65\) wt \(\%\) C, cooled to below \(727^{\circ} \mathrm{C}\left(1341^{\circ} \mathrm{F}\right)\). (a) What is the proeutectoid phase? (b) How many kilograms each of total ferrite and cementite form? (c) How many kilograms each of pearlite and the proeutectoid phase form? (d) Schematically sketch and label the resulting microstructure.

For \(11.20 \mathrm{~kg}\) of a magnesium-lead alloy of composition \(30 \mathrm{wt} \% \mathrm{~Pb}-70 \mathrm{wt} \% \mathrm{Mg}\), is it possible, at equilibrium, to have \(\alpha\) and \(\mathrm{Mg}_{2} \mathrm{~Pb}\) phases having respective masses of \(7.39 \mathrm{~kg}\) and \(3.81 \mathrm{~kg}\) ? If so, what will be the approximate temperature of the alloy? If such an alloy is not possible, explain why.

The mass fractions of total ferrite and total cementite in an iron-carbon alloy are \(0.88\) and \(0.12\), respectively. Is this a hypoeutectoid or hypereutectoid alloy? Why?

For an iron-carbon alloy of composition 5 wt \% C-95 wt \(\%\) Fe, make schematic sketches of the microstructure that would be observed for conditions of very slow cooling at the following temperatures: \(1175^{\circ} \mathrm{C}\left(2150^{\circ} \mathrm{F}\right), 1145^{\circ} \mathrm{C}\) \(\left(2095^{\circ} \mathrm{F}\right)\), and \(700^{\circ} \mathrm{C}\left(1290^{\circ} \mathrm{F}\right)\). Label the phases and indicate their compositions (approximate).

Consider \(2.0 \mathrm{~kg}\) of a \(99.6 \mathrm{wt} \% \mathrm{Fe}-0.4 \mathrm{wt} \% \mathrm{C}\) alloy that is cooled to a temperature just below the eutectoid. (a) How many kilograms of proeutectoid ferrite form? (b) How many kilograms of eutectoid ferrite form? (c) How many kilograms of cementite form?
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