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

• poojagbn
In summary, using the given data of thermal conductivity, Debye temperature, atomic weight, sound velocity, and density, an estimate for the mean free path of phonons in Germanium at 300K can be found by rearranging the given equation and using the Debye model for heat capacity. However, the problem does not provide information about the sample's mass or volume, making the calculation less realistic.
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=CVvsl

l is the mean free path
CV 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.

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".

What is the mean free path of phonons?

The mean free path of phonons is the average distance a phonon (a quantum of lattice vibration) can travel through a material before colliding with another particle or defect.

Why is the mean free path of phonons important?

The mean free path of phonons is important because it affects the thermal conductivity of a material. A longer mean free path means phonons can travel further and transfer heat more efficiently, leading to higher thermal conductivity.

How is the mean free path of phonons calculated?

The mean free path of phonons can be calculated using the phonon mean free path formula, which takes into account the material's thermal conductivity, specific heat, and phonon velocity.

What factors can affect the mean free path of phonons?

The mean free path of phonons can be affected by factors such as the material's crystal structure, temperature, impurities, and defects. A material with a more ordered crystal structure and fewer defects will have a longer mean free path for phonons.

Can the mean free path of phonons be manipulated?

Yes, the mean free path of phonons can be manipulated by altering the material's structure, composition, or temperature. For example, adding impurities or defects can decrease the mean free path, while increasing temperature can increase it.

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