# Thermal Conductivity

1. May 28, 2007

### Brewer

1. The problem statement, all variables and given/known data
The bulk phonon mean free path between phonon collisions for Umklapp process of a crystal is 30nm. If the crystal is of size 70nm, what is the effective mean free path that should be used in the equation for thermal conductivity?

2. Relevant equations
$$\kappa = \frac{1}{3}C_v\rho vl$$

3. The attempt at a solution
I haven't got the foggiest clue for this one. My notes tell me that at low temperatures the mean free path is limited by the size of the sample, and that it is independent of temperature. However it doesn't mention anything about the effective mean free path. I know that l is the mean free path in the equation, and I would be tempted to say that l=30nm, but I'm pretty sure thats incorrect (even for a 1 mark example exam question that seems far too obvious).

Any help on this would be appreciated.

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