Debye's Assumptions For Heat Capacity

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SUMMARY

The discussion centers on the assumptions of the Debye model for heat capacity, which expands upon the Einstein model. While the Einstein model assumes N oscillators of a single frequency in one dimension, the Debye model incorporates a distribution of frequencies from phase space, allowing for a more accurate representation of heat capacity in solids. Key references include the original work by Debye and a derivation of the Einstein model's specific heat. The conversation also touches on the mathematical resolution of average energy equations using geometric progression.

PREREQUISITES
  • Understanding of the Debye model for heat capacity
  • Familiarity with the Einstein model of specific heat
  • Knowledge of statistical mechanics and density of states
  • Basic proficiency in solving geometric progressions
NEXT STEPS
  • Study the derivation of the Debye model for specific heat
  • Explore the mathematical foundations of density of states in solids
  • Learn about the implications of frequency distribution in thermal properties
  • Investigate applications of the Debye model in modern materials science
USEFUL FOR

Physicists, materials scientists, and students studying thermodynamics and statistical mechanics will benefit from this discussion, particularly those interested in heat capacity models and their derivations.

yasef
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What are the Debye model`s assumptions for heat capacity or density of states? According to the einstein model we assume that N oscillators of the same frequency [ω][/o] and in one dimension. In three dimension N is replaced by 3N, there being three modes per oscillator.
 
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the Deybe model assumes the same as Einstein's except that the frequency of oscillations is not a single w but a distribution from phase space.
 
Debye expounded the assumptions in quite some detail:
http://onlinelibrary.wiley.com/doi/10.1002/andp.19123441404/abstract
 
Thanks for help.
 
hello, i would like to as about the derivation of einstein model of specific heat.. this is the derivation that i copied from a book
http://i38.photobucket.com/albums/e122/asifadio/EP8.jpg

how the average energy equation(the summation on both numerator and denominator) can be solve to be like the one in the below of the picture?(below the statement 'solve to get')
 
using a geometric progression
 

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