Wiedemann-Franz law

The Wiedemann-Franz law says that in many metals, thermal conductivity and electrical conductivity are proportional to absolute temperature. In College Physics I, it connects heat flow and charge flow through the same electrons.

What is the Wiedemann-Franz law?

The Wiedemann-Franz law is the rule that, for many metals in College Physics I, heat conduction and electrical conduction are tied together by the same mobile electrons. If a metal is a good electrical conductor, it is usually also a good thermal conductor, and the ratio of those conductivities scales with temperature.

The usual way to write it is k/σ = L T, where k is thermal conductivity, σ is electrical conductivity, T is absolute temperature, and L is the Lorenz number. You may also see it written as k = LσT. The Lorenz number is close to a constant for simple metals, which makes the law useful for quick estimates and for checking whether real data looks metal-like.

The physics behind the law is simpler than it first looks. Free electrons move through a metal and can carry both electric charge and thermal energy. When an electric field is applied, electrons drift and make current. When one side of a metal is hotter than the other, the more energetic electrons spread energy from the hot region to the cold region. Because the same particles do both jobs, the two conductivities are linked.

This link is not exact for every material or every temperature. At ordinary temperatures, electron scattering from the lattice and impurities still allows the law to work fairly well for many metals. At low temperatures, the details of scattering change, and the simple proportionality can break down. That is why the law is a model for metallic conduction, not a universal rule for all solids.

In a typical intro physics setting, you do not usually derive the law from quantum theory. Instead, you use it to connect ideas from conduction, conductivity, and temperature. If a problem gives you electrical conductivity, you can estimate thermal conductivity, or vice versa, as long as the material is a metal and the conditions are reasonable. The point is to see that heat flow in metals is strongly tied to electron motion, not just to the atoms vibrating in the lattice.

Why the Wiedemann-Franz law matters in College Physics I – Introduction

The Wiedemann-Franz law shows up right inside the heat conduction unit because it explains why metals behave so differently from insulators. A copper wire, for example, does not just carry electric current well, it also transfers heat efficiently. That connection helps you predict which materials make good heat sinks, which metals warm up quickly, and why some everyday objects feel cold when you touch them even at room temperature.

It also gives you a way to interpret the meaning of conductivity, instead of treating thermal conductivity as just another formula symbol. In a problem, you may need to decide whether a material is a good conductor because of electrons or because of the lattice. For metals, the law points you toward electron transport. For nonmetals, that connection usually fails, which is a useful clue in conceptual questions.

The law is a good checkpoint for lab data too. If a metal sample has conductivities that do not fit the expected pattern, that can point to impurities, unusual scattering, or a material that is not behaving like a simple metal. That makes the law useful both for solving textbook questions and for reading real measurement results with more care.

How the Wiedemann-Franz law connects across the course

Thermal Conductivity

This is the heat-transfer side of the relationship. Wiedemann-Franz tells you that in metals, thermal conductivity is not separate from electrical behavior, because the same electrons help move heat. When you compare two materials, a high thermal conductivity often goes with a high electrical conductivity if the material is metallic.

Electrical Conductivity

Electrical conductivity measures how easily charge flows through a material. The law links that charge flow to heat flow in metals, so a change in electrical conductivity usually signals a change in thermal conductivity too. That is why one conductivity can sometimes stand in for the other in simple metal problems.

Lorenz Number

The Lorenz number is the constant that sets the scale in the Wiedemann-Franz law. In an intro physics problem, it is the bridge between conductivity and temperature, and it tells you how close a metal is to the standard electron-transport model. If the number is far off, the material may not behave like a simple metal.

mean free path

Mean free path affects how far electrons travel between collisions. If electrons scatter more often, both electrical and thermal conductivity usually drop. That is why this idea sits behind the law: the same scattering processes that hinder current also reduce heat transport.

Is the Wiedemann-Franz law on the College Physics I – Introduction exam?

A quiz or problem set may give you a metal’s electrical conductivity and ask you to estimate its thermal conductivity using k = LσT. You may also be asked to explain why two metals with similar conductivity values should behave similarly in heat transfer, or why the relation breaks down outside simple metallic behavior.

On a conceptual question, the move is to identify electrons as the common carrier of charge and heat. If the question mentions a nonmetal, very low temperature, or unusual scattering, you should be ready to say the law may not fit well. In a lab or data-analysis task, you might compare measured conductivities against the expected proportionality and discuss whether the sample looks like a normal metal.

The Wiedemann-Franz law vs Fourier's Law

Fourier's law tells you how heat flows through a material from a temperature gradient. The Wiedemann-Franz law does something different, it links thermal conductivity to electrical conductivity in metals. Fourier's law is the heat-transfer equation you use directly in conduction problems, while Wiedemann-Franz helps explain why a metal’s thermal conductivity has the value it does.

Key things to remember about the Wiedemann-Franz law

• The Wiedemann-Franz law connects thermal conductivity and electrical conductivity in many metals.

• It works because the same electrons carry both heat and electric charge.

• The Lorenz number and temperature set the scale of the relationship.

• The law is useful for estimating one conductivity from the other in intro physics problems.

• It can break down when the metal is very cold or when scattering is not simple.

Frequently asked questions about the Wiedemann-Franz law

What is Wiedemann-Franz law in College Physics I?

It is the rule that links a metal’s thermal conductivity to its electrical conductivity through temperature. In simple metals, the same free electrons move both heat and charge, so the two conductivities are proportional. You usually see it written as k = LσT.

Why do thermal conductivity and electrical conductivity go together in metals?

Because electrons are doing both jobs. When electrons drift under an electric field, they carry current, and when they move from hot to cold regions, they carry thermal energy. If scattering slows them down, both kinds of transport tend to drop together.

How is Wiedemann-Franz law different from Fourier's law?

Fourier's law is the basic heat-conduction equation that tells you how fast heat flows when there is a temperature difference. Wiedemann-Franz is a material relation that connects thermal conductivity to electrical conductivity in metals. One is a heat-flow law, the other is a transport connection between two conductivities.

When does the Wiedemann-Franz law stop working well?

It can fail when the scattering behavior of electrons changes a lot, especially at low temperatures or in materials that are not simple metals. That is why it is a useful model, not a universal rule for every solid. If a problem hints at unusual low-temperature behavior, check the assumptions carefully.