Thermal Diffusivity

Two materials with the same conductivity can behave completely differently in a temperature swing, and the quantity that tells them apart is diffusivity: $\alpha = k/(\rho c)$. Conductivity is on top because it carries heat forward. Volumetric heat capacity $\rho c$ is underneath because it soaks heat up along the way — every joule the material absorbs to raise its own temperature is a joule that does not continue inward. Conductivity answers "how much gets through in the end". Diffusivity answers "how fast does the news travel", and for anything periodic or transient it is the only property that matters.

Confusing the two is the classic mistake on this subject, and it runs in a direction that surprises people. Concrete conducts heat about twelve times better than softwood, so intuition says it must pass a temperature swing along twelve times faster. It does not: it is roughly four times denser, so its $\rho c$ is about four times larger and its diffusivity is only about five times higher. A dense material can conduct well and still delay heat well, because being dense is exactly what puts a large number in the denominator. This is also why "thermal mass" is a slightly misleading name for the effect — it is not the mass that delays the heat, it is the low diffusivity, and mass is only one of the two ways to get there.

The numbers cluster in bands worth memorising. Earth, brick, stone and ordinary concrete nearly all land between about 0.4 and 1.0 mm²/s, which is why they behave so similarly and why traditional thick walls converge on roughly the same thickness on four continents. Softwood is near 0.15, straw and mineral wool lower still. Water is 0.14. Steel is about 12 and copper about 110 — a thousand times faster than brick, which is why a copper pan responds to the burner instantly and a masonry oven takes half a day. Note that insulation is at the slow end not because it stores much heat (it stores almost none) but because $k$ is tiny; a thin sheet of it has a low diffusivity and negligible capacity at once.

Two cautions on getting a value. Diffusivity is very sensitive to moisture, and in the wrong direction from most guesses: wetting a porous material raises $k$ far more than it raises $\rho c$, so damp earth diffuses heat faster than dry earth and lags less. And measuring $c$ by backing it out of a diffusivity is the least reliable of the four ways to use this equation, because $\rho$ and $c$ enter only as a product — any error in the density lands entirely on the specific heat.

Finally, what diffusivity does not tell you: how much heat leaks through your wall on an average winter day. That is conductivity and R-value, a different question with a different answer. A wall can be superb at one and poor at the other, and an earth wall usually is.