Question

Using the Debye approximation, calculate the temperature dependence of the heat capacity for the limit where T is much smaller than the Debye temperature (in 1 and 2 dimensions). Then, the sound velocity of diamond is 12000 m/s whereas lead has 2000 m/s. For a finite fixed temperature in the limit T<<TD, which of the two materials will have the highest heat capacity? From knowledge of the phonon dispersion of a mono-atomic 1D chain, why does diamond have a higher sound velocity?

Answer 1

The speed of sound is given by Laplace equation

where is the density and is the coefficient of stiffness .

Thus the speed of sound increases with the stiffness of the material. Diamond has higer coefficient of stiffness thant lead, hence speed of sound is higher in diamond.

#Please give thumbs up. Thank you.