Right off the bat I should say: thermal conductivity and electrical conductivity are definitely correlated in metals.
image source: https://www.doitpoms.ac.uk/tlplib/thermal_electrical/printall.php
But my question: is thermal conductivity correlated with speed of sound in metals? It seemed to me like it should be because– according to highly rated answers to another question— the speed of sound is like the "speed of information" about macroscopic deformations. So intuitively I expected faster speed of sound in a metal = faster conduction of heat in that same metal.
I used data from Engineering Toolbox's pages Speed of Sound in common Solids and Thermal Conductivity of Metals. The speed of sound dataset was the limiting set, so I was only able to get data on both for 11 metals Aluminum, Beryllium, Brass, Copper, Gold, Iron, Lead, Silver, Steel (low carbon steel), Stainless Steel, and Titanium:
Initially looks like there is no trend. However– there are two outlier points. Lead and Beryllium are the metals marked in orange instead of blue. The other 9 metals had sound speeds between 3 and 7 thousand m/s. I removed those two from the data:
Here's where I get confused. My assumption was: faster speed of "information" through the metal equals higher thermal conductivity. It looks (to me) like there is a trend and the trend shows the opposite of what I assumed. What am I missing?
Best Answer
In metals, there is the Wiedemann-Franz law because in metals heat is carried mostly by electrons.
Alloying reduces the electron mean free path, but it does not affect the speed of sound that much. For example compare copper and brass (a Cu-Zn alloy) or iron and different steel alloys.
In insulators, thermal conductivity is mediated by phonons. Both speed of sound and mean free path are important there. But that was not what the question was about.