# Why some materials expand linearly on heating while others have areal and volumetric expansion for the same temperature difference?

Why some materials expand linearly on heating while others have areal and volumetric expansion for the same temperature difference? What actually cause materials to expand?

• Commented Apr 12 at 14:10

When it is heated an unconstrained solid object will expand in all three dimensions by the same proportional amount. However, if the object is long and thin (e.g. a metal rod or bar or wire) then the absolute amount of expansion in its length will be much greater than the absolute amount of expansion in the other two dimensions, so we are typically only interested in how its length changes. Therefore when calculating the expansion of a rod or bar or wire we will use the linear coefficient of expansion, which is (roughly) one third of the volumetric coefficient of expansion (see this Wikipedia article).

A gas or liquid, however, is often constrained in two dimensions (e.g. it is constrained within a cylinder or a pipe). When calculating the expansion of a liquid or gas, we will often use the volumetric coefficient of expansion, and then implicitly use the fact that all of this expansion needs to take place along one dimension.

What actually cause materials to expand ?

The Wikipedia article linked above gives this explanation: "When a substance is heated, molecules begin to vibrate and move more, usually creating more distance between themselves."

Another important consideration is the solid-state 3-D lattice structure (called the "unit cell") of the material as a function of temperature. Different unit cells have different densities in the bulk, and in some materials the unit cell transitions from one structure to another reversibly upon heating and cooling, at a certain critical temperature.

Iron does this; an iron wire subjected to heat will elongate up to the point where it switches unit cells (this is called a phase change) at which point it suddenly shrinks instead of elongating. More heat will then cause the new phase to elongate.