Question

The thermal conductivity of solid metals increases with rise in temperature

Answer 1

Thermal conductivity of any material is dependent on two things:
i. Motion of free electrons
ii. Molecular vibrations

For metals, the thermal conductivity is mainly a function of the motion of free electrons. As the temperature increases, the molecular vibrations increase (in turn decreasing the mean free path of molecules). So, they obstruct the flow of free electrons, thus reducing the conductivity.

In case of non metals, there are no free electrons. So, only the molecular vibrations are responsible for conduction of heat and hence for non metals the conductivity increases with increase in temperature.