electricity - Drift velocity of electrons in a conductor

How does the drift velocity of electrons in a conductor depend on the temperature?

I have two contradicting views for this.

• First, we can say that increasing the temperature of the conductor will increase the kinetic energy of the electrons. Hence, their drift velocity should increase with increase in temperature.


• Or, from the relation $v_d = \frac{eE}{m}T$ ($T$ is the relaxation time) we can say that the drift velocity is directly proportional to the relaxation time. Increasing the temperature will obviously decrease the relaxation time - as collisions will become more frequent - and thus decrease the drift velocity. Hence, an increase in the temperature will cause a decrease in the drift velocity.

So which view is correct?

Answer

You can think of it in simple terms.
The average kinetic energy of the lattice ions increases as the temperature increases.
Between "collisions" with the metal lattice ions the free electrons are accelerated by the electric field and so increase their velocity along the electric field direction.
However because the lattice ions are vibrating more, that increase in velocity will not be as great, so the drift velocity is less.

In the macroscopic world that decrease in the drift velocity would manifest itself as an increase in the resistance of the (metal) conductor.

Note that the free electrons also increase their kinetic energy due to the increase in temperature but that is an increase in their root mean square velocity which a measure of their random movement throughout the conductor.