MSE 308
Thermodynamics of Materials
Dept. of Materials Science & Engineering
Spring 2005/Bill Knowlton
Problem Set 12 Solutions
1. For a regular solution, it is known for a two component system, that:
∆Gmix = ao X 1 X 2 + RT ( X 1 ln X 1 + X 2 ln X 2 ) .
Consider a system in which ao is -13,500 J/mole.
xs
.
a. Derive ∆Gmix
xs
b. Derive ∆G1 .
xs
c. Derive ∆G 2 .
d. Derive the activity coefficient for component 1.
e. Derive the activity coefficient for component 2.
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MSE 308
Thermodynamics of Materials
Dept. of Materials Science & Engineering
Spring 2005/Bill Knowlton
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MSE 308
Thermodynamics of Materials
Dept. of Materials Science & Engineering
Spring 2005/Bill Knowlton
f. Plot the activity coefficient for component 1 as a function of X2 over a
temperature range from 300K to 1000K on one graph using a mathematical
program that is not Excel.
300 − 1000 K HBlack to Blue L
1
0.8
inc. temp.
γ1
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
X2
g. Plot the activity coefficient for component 2 as a function of X2 over a
temperature range from 300K to 1000K on one graph using a mathematical
program that is not Excel.
300 − 1000 K HBrown to Red L
1
inc. temp.
0.8
γ1
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
X2
h. Plot ∆Gmix as a function of X2 over a temperature range from 300K to 1000K on
one graph using a mathematical program that is not Excel.
300 − 1000 K HBrown to Red L
0
-2000
γ1
inc. temp.
-4000
-6000
-8000
0
0.2
0.4
0.6
X2
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0.8
1
MSE 308
Thermodynamics of Materials
Dept. of Materials Science & Engineering
Spring 2005/Bill Knowlton
2. For an nonregular (subregular) solution, a two parameter solution model is given by:
T
∆Gmix = ao X 1 X 2 (1 + ) + RT ( X 1 ln X 1 + X 2 ln X 2 ) .
c
xs
a. Determine ∆Gmix .
xs
xs
xs
xs
xs
and ∆Smix
and show whether or not ∆Gmix
= ∆H mix
− T ∆Smix
b. Determine ∆H mix
matches your answer in part a.
xs
xs
xs
. Show whether
c. Find ∆G1 and ∆G 2 and use your answers to determine ∆Gmix
xs
agrees with your answer in part a.
or not your answer for ∆Gmix
d. Determine a1 and a2 (activities)
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MSE 308
Thermodynamics of Materials
Dept. of Materials Science & Engineering
Spring 2005/Bill Knowlton
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MSE 308
Thermodynamics of Materials
Dept. of Materials Science & Engineering
Spring 2005/Bill Knowlton
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MSE 308
Thermodynamics of Materials
Dept. of Materials Science & Engineering
Spring 2005/Bill Knowlton
3. In the paper handed out in class:
J. H. Hildebrand, Solubility. XII. Regular Solutions, Journal of the American
Chemical Society, Vo. 51 (1929) p. 66-88
Describe 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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