solve this

4. Phonon mean free path and relaxation time. Given the thermal conductivity of Si at 300 K as 145 Wm K", the speed of sound as 6400 m s", the volumetric specific heat 1.66 x 10' J m' K-], (a) Estimate the phonon mean free path in Si at 300 K from the kinetic theory. Note that in reality, this estimation usually leads to a much shorter mean free path (about a factor of 10 shorter) than with more sophisticated modeling. (b) Estimate the relaxation time of phonons in silicon