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A problem set from the materials science and engineering (mse) 308 course focused on thermodynamics of materials. Students are required to repeat the derivation of einstein's crystal model, calculate and plot partition function and specific heat for various temperatures using a non-excel mathematical program, comment on the similarities and differences between statistical and classical thermodynamics, derive the tangent method equation, and prove the gibbs free energy equation is zero using given volumes.
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MSE 308 Dept. of Materials Science & Engineering Thermodynamics of Materials Spring 2005/Bill Knowlton
Problem Set 10
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 T k
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.
o o
V a X X V a X X
1
Strictly using the following form of the Gibb’s-Duhem equation: 2
1
k k^0 i
prove the Gibb’s-Duhem equation is zero using the volumes given.
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