Here Q is the thermal energy conducted through a cross-sectional area A
in time t between two planes with a temperature gradient of T/x. Since
good electrical conductors are also good conductors of thermal energy, it is
natural to assume that the highly mobile electron gas is responsible for transporting
charge as well as thermal energy through the metal via random collision
processes. A remarkable triumph of the classical free electron model was
to show that if free electrons were responsible for both electrical and thermal
conduction in metals, then the ratio of K/ should be a universal constant, the
same for all metals, and dependent only on the absolute temperature. Since such an
unusually simple connection between K and had already been observed
experimentally (the Wiedemann–Franz law), this prediction confirmed that
the motion of the electron gas was basically responsible for both electrical and
thermal conductivity