Answer to Question #234122 in Physics for NANA

Question

(a) Classical Einstein Solid (or “Boltzmann” Solid): Consider a single harmonic oscillator in three dimensions with Hamiltonian H = p 2 2m + k 2 x 2 ⊲ Calculate the classical partition function Z = Z dp (2π~) 3 Z dx e −βH(p,x) Note: in this problem p and x are three dimensional vectors (they should appear bold to indicate this unless your printer is defective). ⊲ Using the partition function, calculate the heat capacity 3kB. ⊲ Conclude that if you can consider a solid to consist of N atoms all in harmonic wells, then the heat capacity should be 3N kB = 3R, in agreement with the law of Dulong and Peti

Answer 1

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