# Does good electrical conductivity imply good thermal conductivity?

Typically materials which are good conductor of electricity are also good conductor of heat, and vice versa. Are there notable exceptions?

Beryllium oxide is a very good electrical insulator but at the same time the best non-metal (except diamond) thermal conductor.

So to summarize. In general, good thermal conductivity is correlated with good electrical conductivity, but it is not a strict relationship.

For example, there is the empirical Wiedemann-Franz law for metals which states that the ratio of thermal conductivity $k$ and electrical conductivity $\sigma$ is proportional to temperature $T$.

$$\frac{k}{\sigma} =c_0T$$

The proportionality constant is $c_0$. But as the wiki article points out there are exceptions to this empirical relationship.

For metals, good electrical conductivity does indeed imply good thermal conductivity. This is known from the Wiedemann–Franz law, which gives the ratio between electronic contribution of thermal conductivity ($\lambda$) and electrical conductivity ($\sigma$) and is proportional to the temperature ($T$).

$$\frac{\lambda}{\sigma} = LT$$

This gives the empirical constant $L$ known as the Lorenz number.

$$L = \frac{\lambda}{\sigma T} = \frac{\pi^2}{3}(\frac{\lambda_B}{e})^2 = 2.44 \times 10^{-8} W\Omega K^{-2}$$

As stated, this law applies to metals. Diamond, for example, is an excellent thermal conductor because of its structure, but at the same time it has a very high resistance to electrical current.

• And, naturally, it gets a little more interesting when playing with semimetals :-) . By which I just mean complicated. Electrons are pretty good at carrying energy. May 14 '17 at 11:29

As alluded to in the other answers, a most notable exception is diamond. Diamond is an excellent thermal conductor. The thermal conductivity of natural diamond is around 22 W/(cm·K), which makes diamond five times better than copper at conducting heat. At the same time, the electrical resistivity of most diamonds is on the order of 10E11 to 10E18 Ω·m.