CND-02

Wiedemann–Franz law

κ/σ = L T. The Lorenz number L links electronic heat and charge transport.

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Electrons in solidsWiedemann–Franz

Governing equation

\kappa/\sigma=L T

$T \in \left[20, 800\right]$

where

\sigma: Conductivity (MS/m)
T: Temperature (K)
L: Lorenz number (nW Ω K⁻²)
\kappa: Thermal conductivity (W/m/K)

The figure, part by part

Each numbered marker wears the color of its card. Hover a card to light the marker. Tap a marker to jump to that card. The slider walks a red point along the curve; Animate drawing traces it like a pen.

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①

Governing law — red

\kappa/\sigma=L T

$T \in \left[20, 800\right]$

$T = 20$ $\kappa = 4.88$

Along the curve

②

Domain of the variable — blue

T_{\min} = 20,\quad T_{\max} = 800

$T \in \left[20, 800\right]$

$T = 20$ $T = 20$

Along the curve

③

Response curve — green

\kappa/\sigma=L T

$T \in \left[20, 800\right]$

$T = 20$ $\kappa = 4.88$

Along the curve

④

Rate of change — amber

\frac{\mathrm{d}\kappa}{\mathrm{d}T}

$T \in \left[20, 800\right]$

$T = 24.91$ $\kappa^{\prime} = 0.244$

Along the curve

Lecture brief

Historical brief

Drude electrons, Bloch waves, BCS pairing (1957) and Wiedemann–Franz heat are the first solids-and-metals laws. The lab is conductivity, gap and phonon heat in closed form. This sheet (CND-02 — Wiedemann–Franz law) is the form associated with Wiedemann–Franz. Working symbols: $\sigma$ , $T$ , $L$ $\rightarrow$ $\kappa$ . Sommerfeld L = (π²/3)(k_B/e)² ≈ 2.44×10⁻⁸ W Ω K⁻². Phonons add extra κ.

Purpose

Purpose: compute

\kappa

from

\sigma

T

L

in Condensed matter via

\kappa/\sigma=L T

κ/σ = L T. The Lorenz number L links electronic heat and charge transport. Use it when a real condensed matter question must be answered in SI before a code check.

Live realistic example

In symbols

Live case. Given

\sigma = 10.000\,\mathrm{MS/m}

T = 300.000\,\mathrm{K}

L = 24.400\,\mathrm{nW Ω K⁻^{2}}

, the governing relation

\kappa/\sigma=L T

yields

\kappa = 73.2\,\mathrm{W/m/K}

. A metal bar, a heat current and an electric current. Move a slider: the numbers are this situation, not a canned story.

Calculator

Inputs

Conductivity \sigma10 MS/mTemperature T300 KLorenz number L24.4 nW Ω K⁻²

Outputs

Thermal conductivity \kappa73.2 W/m/K

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Narration of this film

A metal bar, a heat current and an electric current.

Sommerfeld L = (π²/3)(k_B/e)² ≈ 2.44×10⁻⁸ W Ω K⁻². Phonons add extra κ.

Reading speed

Watch on YouTube