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THERMAL PROPERTIES II - Coggle Diagram
THERMAL PROPERTIES II
Derivation for Specific Heat
In the Debye approximation, the velocity of sound vs is taken as constant for each polarization type, as it would be for a classical elastic continuum
Density of states
heat capacity
Specific Heat of Lead, Silver, Aluminium and Diamond
At high temperature limit T>>TD
At low temperature limit, T<<TD
General results for an oscillator
Thermal energy = total energy of the phonons in a equilibrium state
By using statistical mechanics, the average energy of the phonons with frequency q and in q mode is
Einstein’s model
assumed that the atoms are vibrating as harmonic oscillators
assumed Planck’s (1990) quantization rule for each oscillator
Debye's Model
Atoms are considered as harmonic oscillators that produce elastic waves with varying frequencies
3N normal modes (patterns) of oscillations
Why does Debye model work better at low T than Einstein model?
The Debye model gives a better representation for the very low energy vibrations
At low temperatures, these vibrations matter most
Limit of the Debye model
