Mean free path at low temperatures

[Armandito]

Homework Statement

Hi, It's not a homework question, but as i am a beginner in physics, I prefer to post here first :

I try to evaluate thermal resistance at low temperature. I need to compute the mean free path of both electron and phonon in metals, but I do not find any formulas. Can anybody tell me where I could find that?

By the way, Is there two different mean free path : far from the wall and near the wall?

Best thanks!

Homework Equations

The Attempt at a Solution

 

[kNYsJakE]

Homework Statement

Hi, It's not a homework question, but as i am a beginner in physics, I prefer to post here first :

I try to evaluate thermal resistance at low temperature. I need to compute the mean free path of both electron and phonon in metals, but I do not find any formulas. Can anybody tell me where I could find that?

By the way, Is there two different mean free path : far from the wall and near the wall?

Best thanks!

Homework Equations

The Attempt at a Solution

I assume that you know what mean free path is so here is the basic formula for the mean free path:

$$l=\left(\sigma n\right)^{-1}$$

where $$l$$ is the mean free path, $$n$$ is the number of target particles per unit volume, and $$\sigma$$ is the effective cross sectional area for collision.

From this I guess you can derive whatever you want to get about mean free path.

If you are doing the particle physics, then the mean free path is replaced by the similar concept called 'attenuation length' or 'absorption length.' It is the distance $$\lambda$$ into a material when the probability (that particle has not been absorbed) has dropped to $$1/e$$.

Hope it helped.

 

[tomcue]

Hello! The mean free path at low temperatures can be calculated using the following formula:

λ = (1/√2πnσ²) * (kT/m)

Where λ is the mean free path, n is the number density of particles, σ is the collision cross section, k is the Boltzmann constant, T is the temperature, and m is the mass of the particles. This equation can be used for both electrons and phonons in metals.

There are two different mean free paths: one for particles far from the wall and one for particles near the wall. The mean free path for particles near the wall is shorter due to increased collisions with the surface.

I hope this helps! You can find more information on mean free path and thermal resistance in textbooks or online resources on thermodynamics and statistical mechanics. Best of luck with your studies!

 

[nlightner]

Hi there,

Thank you for reaching out. The mean free path at low temperatures is an important concept in the study of thermal resistance. The mean free path is defined as the average distance traveled by a particle between collisions. In metals, both electrons and phonons contribute to thermal conductivity, and their mean free paths can be calculated using different formulas.

For electrons in metals, the mean free path can be calculated using the Drude model, which assumes that electrons behave like a gas of free particles. The formula for mean free path in this model is l = vτ, where l is the mean free path, v is the average velocity of electrons, and τ is the relaxation time between collisions. This formula can be modified for low temperatures by taking into account the temperature dependence of the relaxation time.

For phonons in metals, the mean free path can be calculated using the Debye model, which assumes that phonons behave like a gas of quasiparticles. The formula for mean free path in this model is l = vτ, where l is the mean free path, v is the average velocity of phonons, and τ is the relaxation time between collisions. The Debye model also takes into account the temperature dependence of the relaxation time.

Regarding your question about mean free paths near and far from the wall, the mean free path is generally shorter near the wall due to increased scattering from surface imperfections and impurities. However, this difference is negligible at low temperatures.

I hope this helps answer your questions. Best of luck with your studies!