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thermal properties, image - Coggle Diagram

- - - - It resulting that Cv calculated through classical approach is only suittable for monoatom only
- - - - and then substitute with the eisntein formula, we get
        U=
        
        then by using the Cv formula, we get
        
        This formula is qualitatively correct as we able to get Cv=3R for large T and Cv approach to 0 as T approach 0
- - - - the volume for the wave vector, q = and since there is cut off wave vector, qd where
        
        it give the number of modes and the Debye temperature are
        
        the vs is taken as constant, then with the density, thermal energy for each polarization, the Cv obtain is
        
        satisfy both at low temperature and high temperature
        
        Debye model work better than eisntein model because Debye model gives a better representation for the very low energy vibrations.