# Why does the Wiedemann-Franz law relate electrical and thermal conductivities

This article explains the Wiedemann-Franz law and its relationship between electrical and thermal conductivities. Learn about its applications and limitations.

# Why does the Wiedemann-Franz law relate electrical and thermal conductivities?

The Wiedemann-Franz law is an empirical relationship between electrical conductivity and thermal conductivity of a metal. It states that the ratio of the thermal conductivity to the electrical conductivity is proportional to the temperature. This law was discovered independently by Gustav Wiedemann and Rudolf Franz in 1853. The law holds true for most metals at low temperatures.

## The Wiedemann-Franz law

The Wiedemann-Franz law is a fundamental principle in the study of condensed matter physics. It is an expression of the fact that the flow of heat and the flow of charge are both carried by the same electrons in a metal. The law is expressed mathematically as:

K/σT = L

Where K is the thermal conductivity, σ is the electrical conductivity, T is the temperature, and L is the Lorenz number. The Lorenz number is a fundamental constant of nature and has a value of 2.45 x 10^-8 WΩ/K^2.

## Explanation of the law

The Wiedemann-Franz law is a consequence of the behavior of electrons in metals. Metals are characterized by the presence of a sea of free electrons that can move throughout the metal. When a metal is heated, the temperature causes the free electrons to move faster,

## Applications of the Wiedemann-Franz law

The Wiedemann-Franz law has many important applications in condensed matter physics and materials science. It is used to study the transport properties of metals and to design new materials with specific properties.

One important application of the law is in the study of thermoelectric materials. Thermoelectric materials are materials that can convert heat into electrical energy and vice versa. They are used in devices such as thermocouples and thermoelectric generators. The Wiedemann-Franz law plays a key role in the design and optimization of thermoelectric materials.

Another application of the law is in the study of superconductivity. Superconductivity is a phenomenon in which the electrical resistance of a material drops to zero at very low temperatures. The Wiedemann-Franz law provides important insights into the behavior of electrons in superconducting materials.

The Wiedemann-Franz law also has practical applications in the design of electronic devices. For example, it is used to optimize the thermal management of electronic devices such as computer processors. By controlling the flow of heat and charge, designers can improve the efficiency and reliability of electronic devices.

## Limitations of the Wiedemann-Franz law

While the Wiedemann-Franz law is a useful empirical relationship, it has some limitations. The law assumes that the motion of electrons is the primary mechanism for heat transfer in a metal. This is true at low temperatures, but at higher temperatures, other mechanisms such as phonon transport may become important.

The law also assumes that the metal is in a state of thermal equilibrium. In practice, this is not always the case, especially in materials with strong electronic correlations. In these materials, the Wiedemann-Franz law may not hold.

Finally, the law is only applicable to metals and does not apply to other types of materials such as insulators and semiconductors.

## Conclusion

In conclusion, the Wiedemann-Franz law is a fundamental principle that relates the electrical conductivity and thermal conductivity of a metal. The law is based on the idea that the same electrons that carry electrical current also carry heat in a metal. The law has important applications in condensed matter physics, materials science, and electronic device design. While the law has some limitations, it remains a useful empirical relationship that provides important insights into the behavior of electrons in metals.