Wiedemann-Franz Law

Definition

The Wiedemann-Franz law is a fundamental principle in condensed matter physics that describes the relationship between the thermal and electrical conductivities of metals. It states that the ratio of the thermal conductivity to the electrical conductivity of a metal is proportional to the absolute temperature.

5 Must Know Facts For Your Next Test

1. The Wiedemann-Franz law is a consequence of the free electron model of metals, which assumes that the conduction electrons in a metal behave like a gas of free electrons.
2. The law states that the ratio of the thermal conductivity (κ) to the electrical conductivity (σ) of a metal is proportional to the absolute temperature (T), and this proportionality is given by the Lorenz number (L).
3. The Wiedemann-Franz law can be expressed mathematically as: κ/σ = LT, where L is the Lorenz number, a constant with a value of approximately $2.44 \times 10^{-8}$ W⋅Ω/K^2.
4. The Wiedemann-Franz law is valid for pure metals at temperatures above the Debye temperature, where the dominant heat carriers are the conduction electrons.
5. The Wiedemann-Franz law provides a useful tool for understanding the transport properties of metals and has applications in the design of thermoelectric materials and the characterization of metal samples.

Review Questions

• Explain the relationship between thermal conductivity and electrical conductivity as described by the Wiedemann-Franz law.
  • The Wiedemann-Franz law states that the ratio of the thermal conductivity (κ) to the electrical conductivity (σ) of a metal is proportional to the absolute temperature (T). This relationship is expressed as κ/σ = LT, where L is the Lorenz number, a constant with a value of approximately $2.44 \times 10^{-8}$ W⋅Ω/K^2. This means that metals with high electrical conductivity also tend to have high thermal conductivity, and vice versa. The law is a consequence of the free electron model of metals, which assumes that the conduction electrons in a metal behave like a gas of free electrons and are responsible for both the electrical and thermal transport properties.
• Describe the conditions under which the Wiedemann-Franz law is valid and discuss its importance in the study of metal properties.
  • The Wiedemann-Franz law is valid for pure metals at temperatures above the Debye temperature, where the dominant heat carriers are the conduction electrons. In this regime, the law provides a useful tool for understanding the transport properties of metals and has applications in the design of thermoelectric materials and the characterization of metal samples. By measuring either the thermal or electrical conductivity of a metal, the Wiedemann-Franz law allows for the estimation of the other transport property, which is important for understanding the fundamental behavior of metals and their potential applications. The law also helps to differentiate between the contributions of electrons and phonons to the overall thermal conductivity of a material.
• Analyze how the Wiedemann-Franz law can be used to gain insights into the electronic structure and scattering mechanisms in metals.
  • The Wiedemann-Franz law provides a direct link between the thermal and electrical transport properties of metals, which are intimately related to the electronic structure and scattering mechanisms within the material. By measuring the ratio of thermal to electrical conductivity and comparing it to the theoretical Lorenz number, researchers can gain insights into the dominant scattering processes affecting the conduction electrons. Deviations from the expected Lorenz number can indicate the presence of electron-electron scattering, electron-phonon scattering, or other complex many-body effects that alter the electronic transport. Additionally, the Wiedemann-Franz law can be used to probe the density of states at the Fermi level, which is a fundamental property of the electronic structure. Overall, the Wiedemann-Franz law is a powerful tool for elucidating the underlying physics governing the behavior of metals and other conductive materials.

Related terms

Thermal Conductivity: The ability of a material to conduct heat, measured by the rate at which heat flows through the material per unit area per unit temperature gradient.

Electrical Conductivity: The measure of a material's ability to allow the flow of electric current, which is the rate of movement of electric charge through a material.

Lorenz Number: A constant that represents the proportionality between the thermal and electrical conductivities of a metal, as described by the Wiedemann-Franz law.