| MadSci Network: Physics |
Hello, Ian!
The free electrons have both a kinetic energy and a charge, so when they are
moving through the lattice, they both conduct heat (carry their kinetic
energy with them) and current (carry their charge with them). This is why a
conductor strapped across a thermal gradient will acquire a voltage along
its length. Electrons at the hot end will move more rapidly toward the cold
end than electrons at the cold end will move toward the hot end, just
because the hot electrons have more kinetic energy than the cold ones. This
then carries some charge along, and an electric field builds up.
There are two "differences" between thermal conduction and electrical
conduction that I can think of. One, the driving force (potential
difference, or thermal gradient) is different. Two, electrons are
not the only method of heat transfer; one can have lattice vibrations (i.e.
phonons) do this as well.
Perhaps you can recast your approach to this subject to consider the drift
and diffusion currents of the electrons. The former is written
j = q m n E q is charge
m is the mobility of the electrons
in the lattice
n is the volume density of electrons
E is the electric field value
and the latter is written
j = q (kTm/q) (dn/dx) T is the temperature
k is Boltzman's constant
(dn/dx) is the gradient of electron
concentration
q, m as above
The quantity (kTm/q) is known at the Diffusivity of the electrons in the
lattice, D. I wrote it this way to show the relationship between diffusivity
and mobility...one is a constant multiple of the other for any given
temperature, due to the fact that both are related to electrons moving in
the lattice. You should note that E and n are both functions of position
in the lattice, and m is a function of the temperature.
In general, the drift equation tells how the electrons respond to the
electric field, and the diffusion equation tells how the electrons respond
to thermal effects (as well as concentration gradients from such things
as charge injection across a junction, etc, but that needn't be considered
here).
Try working with these two equations to understand what's going on. I find
it a more natural way to envision what the electrons are doing in response
to applied external influences, be they thermal or electrical.
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