7/30/2019 MSE 308 Problem Set 12 Solutions

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MSE 308 Dept. of Materials Science & Engineering

Thermodynamics of Materials Spring 2005/Bill Knowlton

Problem Set 12 Solutions

1. For a regular solution, it is known for a two component system, that:

1 2 1 1 2 2( ln ln )

mix oG a X X RT X X X X = + + .

Consider a system in which ao is -13,500 J/mole.a. Derive .xsmixG

b. Derive 1xs

G .

c. Derive 2xs

G .

d. Derive the activity coefficient for component 1.e. Derive the activity coefficient for component 2.

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7/30/2019 MSE 308 Problem Set 12 Solutions

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MSE 308 Dept. of Materials Science & Engineering

Thermodynamics of Materials Spring 2005/Bill Knowlton

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7/30/2019 MSE 308 Problem Set 12 Solutions

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MSE 308 Dept. of Materials Science & Engineering

Thermodynamics of Materials Spring 2005/Bill Knowlton

f. Plot the activity coefficient for component 1 as a function of X2 over atemperature range from 300K to 1000K on one graph using a mathematical

program that is not Excel.

0 0.2 0.4 0.6 0.8 1

X2

0

0.2

0.4

0.6

0.8

1

1

300 1000 K HBlack to Blue L

inc. temp.

g. Plot the activity coefficient for component 2 as a function of X2 over atemperature range from 300K to 1000K on one graph using a mathematical

program that is not Excel.

0 0.2 0.4 0.6 0.8 1

X2

0

0.2

0.4

0.6

0.8

1

1

300 1000 K HBrown to RedL

inc. temp.

h. Plot as a function of XmixG 2 over a temperature range from 300K to 1000K on

one graph using a mathematical program that is not Excel.

0 0.2 0.4 0.6 0.8 1

X2

-8000

-6000

-4000

-2000

0

1

300 1000 K HBrown to RedL

inc. temp.

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7/30/2019 MSE 308 Problem Set 12 Solutions

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MSE 308 Dept. of Materials Science & Engineering

Thermodynamics of Materials Spring 2005/Bill Knowlton

2. For an nonregular (subregular) solution, a two parameter solution model is given by:

1 2 1 1 2 2(1 ) ( ln ln )

mix o

TG a X X RT X X X X

c = + + + .

a. Determine .xsmix

G

b. Determine and show whether or not

matches your answer in part a.

andxs xs

mix mix

H Sxs xs xs

mix mix mix

G H T S =

c. Find 1xs

G and 2xs

G and use your answers to determine . Show whether

or not your answer for agrees with your answer in part a.

xs

mixG

xs

mixG

d. Determine a1 and a2 (activities)

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7/30/2019 MSE 308 Problem Set 12 Solutions

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MSE 308 Dept. of Materials Science & Engineering

Thermodynamics of Materials Spring 2005/Bill Knowlton

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MSE 308 Dept. of Materials Science & Engineering

Thermodynamics of Materials Spring 2005/Bill Knowlton

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MSE 308 Dept. of Materials Science & Engineering

Thermodynamics of Materials Spring 2005/Bill Knowlton

3. In the paper handed out in class:J. H. Hildebrand, Solubility. XII. Regular Solutions, Journal of the AmericanChemical Society, Vo. 51 (1929) p. 66-88Describe five aspects of the paper that you can relate to what you have learned in this

course. This is an open ended question.

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