Wiedemann-Franz Law: Linking Electrical and Thermal Conductivity

by Yuvi K - January 7, 2024

Introduction to Wiedemann-Franz Law

There is a phenomenon in physics which states that the ratio of thermal and electrical conductivity is always the same for an electrically-conducting metal, regardless of changes in pressure, temperature, or other conditions. This phenomenon is known as Wiedemann-Franz Law.

Wiedemann-Franz Law, also known as the Lorenz Number, was developed by German physicists Gustav Wiedemann and Robert Franz in the 19th century and is widely used in research involving electrical conductivity.
The law is considered to be an example of universal behavior in nature, as it applies to a variety of metals and conditions, and is also used in engineering and electronics.

Understanding the Basics of Wiedemann-Franz Law

The core of Wiedemann-Franz Law is that the electrical conductivity (σ) and thermal conductivity (λ) of a metal are directly proportional to each other. In other words, they can be expressed in terms of a proportionality constant – the Lorenz number (L) – with the following equation:

L = λ/σT

The proportionality constant is found to be approximately 2.44 x 10-8 W/(K2 m). The thermal conductivity (λ) is the transfer of energy due to a temperature gradient, while the electrical conductivity (σ) is determined by the electrons that are moving in the material. The temperature (T) is measured in Kelvin.

The ratio of thermal conductivity to electrical conductivity is the same for all metals, regardless of their temperature or other conditions.
This ratio remains the same even in non-conductors such as semiconductors.

History of Wiedemann-Franz Law

The principle of Wiedemann-Franz Law was proposed by German physicists Gustav Wiedemann and Robert Franz in their 1853 book, “Statics of Metals.”
In the book, the two scientists hypothesized that the thermal and electrical conductivities of metals could be related by a constant.

However, at the time, the law was considered to be a hypothesis as the technology of the time was not advanced enough to measure the values of electrical and thermal conductivity accurately.
The law was not verified until 1864, when the French physicist Matthieu Charles Edouard Crouzet was able to measure the electrical and thermal conductivities of several metals with a higher degree of accuracy.

Applications of Wiedemann-Franz Law

Wiedemann-Franz Law is an important phenomenon in the understanding of transport phenomena in metals. It is used to design thermal management systems such as heatsinks to regulate heat distributions in electronics and explains why metals conduct heat so well.

In addition, the law is used to measure the thermal conductivity of thermoelectric materials and also provides a quick way to calculate the thermal conductivities of metals. It can also be used to calculate the band gap of a semiconductor, which is an important material property for devices such as transistors.

The law is also used to explain the behavior of heat transported through a medium, such as air or water, which is governed by the laws of thermodynamics and electrical conduction.

Conclusion

In conclusion, Wiedemann-Franz Law states that the ratio of thermal and electrical conductivity is always constant for a given material. It is an important principle in understanding the behavior of metals and other materials, and has a wide range of applications such as electronics, engineering, and thermal management systems.