When we teach about thermal physics at the macroscopic scale, we talk in terms of the thermal conductivity, k. For the 1d problem of a homogeneous rod of cross sectional area A and length L, the rate that energy flows from one end of the rod to the other is given by (kA/L)(Th-Tc), where Th and Tc are the temperatures of the hot and cold ends of the rod, respectively. Built into this approach is the tacit assumption that the phonons, the quantized vibrational modes of the lattice that carry what we consider to be the thermal energy of the atoms in the solid, move in a diffusive way. That is, if a phonon is launched, it bounces many times in a random walk sort of motion before it traverses across our region of interest. Phonons can scatter off disorder in the lattice, or mobile charge carriers (or even each other, if the vibrations aren't perfectly harmonic).
Wednesday, April 25, 2012
Heat flow at the mesoscale
Posted by Douglas Natelson at 9:01 PM