What factors affect the mean free path of phonons in Germanium at 300K?

[poojagbn]

Homework Statement

If all the heat transport is by phonons, estimate the mean free path of phonons in Germanium at 300K using the following data. Thermal conductivity=80W/K m; Debye temperature=360K; atomic weight=72.6; sound velocity=4500m/s; density=5500kg m−3

Homework Equations

K=C_Vv_sl

l is the mean free path
C_V is the heat capacity at constant volume

The Attempt at a Solution

Rearrange the first equation to find l.

CV can be found using some long equation that involves 'N'

But how is N, the number of atoms supposed to be found when the question does not even tell you the mass of the sample, or what the volume of the sample is?

To calculate the heat capacity, is the Einstein model or the Debye model supposed to be used? The Einstein model, my notes say is only for optical frequencies, so can't be used in this case? But the Debye model just seems too complicated.

 

[PietKuip]

This type of questions always includes all you need to know. Real life is not like that. So it would have been more realistic if the problem had started with: Consider a sample of germanium of 20 x 5 x 1 mm.

The problem mentions the Debye temperature, not the Einstein temperature. That might give you a hint, but feel free to make approximations: "make an estimate".