MSE 308 Dept. of Materials Science & Engineering
Thermodynamics of Materials Spring 2005/Bill Knowlton
Problem Set 10
1. We derived Einstein’s famous crystal model in class. Repeat the exercise explaining all
assumptions and steps.
2. For each Einstein temperature,
θ
E, of 100K, 200K, 300K, and 500K, use a computer
program other than Excel to calculate and plot the:
a. partition function
b. Cv
for the Einstein model as a function of given E
hv
Tk
θ
=. Consider the system as a simple
cubic Einstein crystal. Of interest is the range of temperatures from 0-500K. Your plot
should be similar to figure 6.1 in Gaskell. Use a mathematical program that is NOT
Excel. Your plots should be labeled thoroughly.
3. Comment on the similarities and differences between statistical thermodynamics and
classical thermodynamics.
4. Comment on the partition function.
5. Derive the equation that we obtained for the Tangent method. Explain any assumptions
and your steps.
6. The change in volume of each component for a particular solution two component system
are given by
2
12
2
212
(1 2 )
2
o
o
VaX X
VaXX
∆= −
∆=
1
Strictly using the following form of the Gibb’s-Duhem equation:
2
1
0
kk
i
Xd B
=
∆
=
∑
prove the Gibb’s-Duhem equation is zero using the volumes given.
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