Foundations of Materials Science and Engineering
Foundations of Materials Science and Engineering
6th Edition
ISBN: 9781259696558
Author: SMITH
Publisher: MCG
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Textbook Question
Chapter 8.15, Problem 24AAP

If 500 g of a 40 wt% Ag–60 wt% Cu alloy is slowly cooled from 1000°C to just below 780°C (see Fig. P8.23):

  1. a. How many grams of liquid and proeutectic alpha are present at 850°C?
  2. b. How many grams of liquid and proeutectic alpha are present at 780°C + ΔT?
  3. c. How many grams of alpha are present in the eutectic structure at 780°C − ΔT?
  4. d. How many grams of beta are present in the eutectic structure at 780°C − ΔT?

(a)

Expert Solution
Check Mark
To determine

Refer Fig P8.23, if 500g of a 40 wt%Ag-60wt%Cu alloy is cooled slowly from temperature of 1000°C to just below 780°C.

Determine the grams of liquid and proeutectic alpha present at 850°C.

Answer to Problem 24AAP

The weight of liquid and proeutectic alpha phase is 364gand136g respectively.

Explanation of Solution

Express wt% of liquid.

wt%liquid=407.9527.9×100%=72.8%=0.728

Express wt% of proeutectic α.

wt%proeutecticα=5240527.9×100%=27.2%=0.272

Express the weight of liquid phase.

wtliquidphase=(500g)(0.728)=364g

Express the weight of proeutectic α.

wtproeutecticα=(500g)(0.272)=136g

Hence, the weight of liquid and proeutectic alpha phase is 364gand136g respectively.

(b)

Expert Solution
Check Mark
To determine

Refer Fig P8.23, if 500g of a 40 wt%Ag-60wt%Cu alloy is cooled slowly from temperature of 1000°C to just below 780°C.

Determine the grams of liquid and proeutectic alpha present at 780°C+ΔT.

Answer to Problem 24AAP

The weight of liquid and proeutectic alpha phase is 251gand249g respectively.

Explanation of Solution

Express wt% of liquid.

wt%liquid=407.971.97.9×100%=50.2%=0.502

Express wt% of proeutectic α.

wt%proeutecticα=71.94071.97.9×100%=49.8%=0.498

Express the weight of liquid phase.

wtliquidphase=500g(0.502)=251g

Express the weight of proeutectic α.

wtproeutecticα=(500g)(0.498)=249g

Hence, the weight of liquid and proeutectic alpha phase is 251gand249g respectively.

(c)

Expert Solution
Check Mark
To determine

Refer Fig P8.23, if 500g of a 40 wt%Ag-60wt%Cu alloy is cooled slowly from temperature of 1000°C to just below 780°C.

Determine the grams of alpha present in the eutectic structure at 780°CΔT.

Answer to Problem 24AAP

The weight of alpha is 307.5g.

Explanation of Solution

Express wt% of total α.

wt%totalα=91.24091.27.9×100%=61.5%=0.615

Express the weight of alpha.

wttotalα=(500g)(0.615)=307.5g

Hence, the weight of alpha is 307.5g.

(d)

Expert Solution
Check Mark
To determine

Refer Fig P8.23, if 500g of a 40 wt%Ag-60wt%Cu alloy is cooled slowly from temperature of 1000°C to just below 780°C.

Determine the grams of beta present in the eutectic structure at 780°CΔT.

Answer to Problem 24AAP

The weight of beta is 192.5g.

Explanation of Solution

Express wt% of total β.

wt%totalβ=407.991.27.9×100%=38.5%=0.385

Express the weight of beta.

wttotalβ=(500g)(0.385)=192.5g

Hence, the weight of beta is 192.5g.

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Chapter 8 Solutions

Foundations of Materials Science and Engineering

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