MSE 308 Problem Set 9 Solutions

MSE 308 Problem Set 9 Solutions - MSE 308 Thermodynamics of...

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MSE 308 Dept. of Materials Science & Engineering Thermodynamics of Materials Spring 2005/Bill Knowlton Problem Set 9 Solutions 1. Given the partition function of a monatomic gas equation: 3/2 2 kT V m π ⎡⎤ ℘= ⎢⎥ ⎣⎦ use the partition function and your knowledge of statistical thermodynamics to derive the following in terms of n (or N o , the total number of particles in the system) AND R : a. ln[ ] b. ln[ ] v d dT ⎛⎞ ⎜⎟ ⎝⎠ c. 2 2 ln[ ] v d dT d. Helmholtz free energy, F e. Entropy, S f. Internal free energy, U g. Heat capacity, C v h. Comment on your findings in part g relative to the value obtained for C v using classical thermodynamics 1 of 4
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MSE 308 Dept. of Materials Science & Engineering Thermodynamics of Materials Spring 2005/Bill Knowlton h. Comment on your findings in part g relative to the value obtained for C v using classical thermodynamics: Cp – Cv = R Where Cp = 5/2R and Cv = 3/2 R. Thus, both Classical and Statistical thermodynamics give the same answer!
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MSE 308 Problem Set 9 Solutions - MSE 308 Thermodynamics of...

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