Question
Asked Mar 8, 2020
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Considering an alloy of the two soluble components A and B described by a phase diagram Figure P2.31, determine the masses of the alloy that are in the liquid and solid phases at a given temperature if the total mass of the alloy is 100 g, component B represents 60% of the alloy, 25% of the liquid is component B, and 70% of solid is component B.

Percent weight of material A
100
75
50
25
Melting temperature
of material A
Liquid
Liquid and solid
Melting temperature
of material B
Solid
25
50
75
100
Percent weight of material B
FIGURE P2.31
Temperature
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Percent weight of material A 100 75 50 25 Melting temperature of material A Liquid Liquid and solid Melting temperature of material B Solid 25 50 75 100 Percent weight of material B FIGURE P2.31 Temperature

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Expert Answer

Step 1

Given:

Total mass of the alloy, M = 100 gm

Percentage of component B, PB = 60%

Percentage of component B in liquid, PL = 25%

Percentage of component B in solid, PS = 70%

Step 2

The total mass of the alloy is the sum of the masses of the alloy that are in liquid and solid phase.

Civil Engineering homework question answer, step 2, image 1

Here,

ML = mass of alloy in liquid phase

MS = mass of alloy in solid phase

 

Substitute the value of total mass in the above equation,

Civil Engineering homework question answer, step 2, image 2

 

The mass of alloy in liquid and solid phase is calculated by the percentages of component B in each phase using the following equation:

Civil Engineering homework question answer, step 2, image 3

Substitute the respective percentages of component B and the total mass of the alloy in the above equation,

Civil Engineering homework question answer, step 2, image 4

From equation (1) and (2),

Civil Engineering homework question answer, step 2, image 5

...

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