# Relationship between thermal conductivity and electrical resistivity

### DoITPoMS - TLP Library Introduction to thermal and electrical conductivity

In physics, the Wiedemann–Franz law states that the ratio of the electronic contribution of the thermal conductivity (κ) to the electrical conductivity (σ) of Qualitatively, this relationship is based upon the fact that the heat and electrical transport both involve the free The specific resistivity is the inverse of the conductivity. Thermal conductivity is a reasonably straightforward concept when you are Gases transfer heat by direct collisions between molecules, and as would be expected this relationship is based upon the fact that the heat and electrical transport. Electrical resistivity is a fundamental property of a material that quantifies how strongly that .. so the relation between resistivity and conductivity simplifies to: .. value depends not only on the type of metal, but on its purity and thermal history.

Is there a relationship between electrical conductivity and thermal conductivity? Metals are good electrical conductors because there are lots of free charges in them.

The free charges are usually negative electrons, but in some metals, e. When a voltage difference exists between two points in a metal, it creates an electric field which causes the electrons to move, i. Of course, the electrons bump into some of the stationary atoms actually, 'ion cores' of the metal and this frictional 'resistance' tends to slow them down. The resistance depends on the specific type of metal we're dealing with.

The greater the distance an electron can travel without bumping into an ion core, the smaller is the resistance, i. The average distance an electron can travel without colliding is called the 'mean free path.

The electrons which are free to respond to the electric field have a thermal speed a sizable percentage of the speed of light, but since they travel randomly with this high speed, they go nowhere on average, i. The thermal conductivity of this metal is, like electrical conductivity, determined largely by the free electrons.

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So the electrons "fill up" the band structure starting from the bottom. The characteristic energy level up to which the electrons have filled is called the Fermi level.

The position of the Fermi level with respect to the band structure is very important for electrical conduction: In contrast, the low energy states are rigidly filled with a fixed number of electrons at all times, and the high energy states are empty of electrons at all times. Electric current consists of a flow of electrons. In metals there are many electron energy levels near the Fermi level, so there are many electrons available to move.

This is what causes the high electronic conductivity of metals. An important part of band theory is that there may be forbidden bands of energy: In insulators and semiconductors, the number of electrons is just the right amount to fill a certain integer number of low energy bands, exactly to the boundary. In this case, the Fermi level falls within a band gap. Since there are no available states near the Fermi level, and the electrons are not freely movable, the electronic conductivity is very low.

Free electron model Like balls in a Newton's cradleelectrons in a metal quickly transfer energy from one terminal to another, despite their own negligible movement. A metal consists of a lattice of atomseach with an outer shell of electrons that freely dissociate from their parent atoms and travel through the lattice.

This is also known as a positive ionic lattice. When an electrical potential difference a voltage is applied across the metal, the resulting electric field causes electrons to drift towards the positive terminal. The actual drift velocity of electrons is typically small, on the order of magnitude of meters per hour. However, due to the sheer number of moving electrons, even a slow drift velocity results in a large current density.

Most metals have electrical resistance.

In simpler models non quantum mechanical models this can be explained by replacing electrons and the crystal lattice by a wave-like structure. When the electron wave travels through the lattice, the waves interferewhich causes resistance. The more regular the lattice is, the less disturbance happens and thus the less resistance. The amount of resistance is thus mainly caused by two factors.

### Electrical resistivity and conductivity - Wikipedia

First, it is caused by the temperature and thus amount of vibration of the crystal lattice. The temperature causes bigger vibrations, which act as irregularities in the lattice. Second, the purity of the metal is relevant as a mixture of different ions is also an irregularity. Semiconductor and Insulator electricity In metals, the Fermi level lies in the conduction band see Band Theory, above giving rise to free conduction electrons.

However, in semiconductors the position of the Fermi level is within the band gap, about halfway between the conduction band minimum the bottom of the first band of unfilled electron energy levels and the valence band maximum the top of the band below the conduction band, of filled electron energy levels.