Question

regarding the contributions of phonons to the specific heat of a solid

when is there a contribution of optical modes? if you want to determine this contribution as an insulator ,would you measure the specific heat at a low or high temperature and why

Answer 1

Solution

Answer to the first part : As name suggest that optical modes i.e they are of very high frequency , which must generate at high temperature . So we can state that optical modes generally contribute to the specific heat of solid at high temperature .i.e at T > where is the De-bye temperature , which act as cut off for the phonon

Now come to second part, since optical modes are generated at higher temperature, so it is better to measure the specific heat at high temperature. But is the material dependent , it may be low as 5-10K or high as a few hundred K. So one has to calculate the De-bye temperature