What Happens in Thermal Expansion?

Most materials expand when heated. As long as the temperature change is sufficiently small, each dimension of an object expands according to:

ΔL = LoαΔT   or   L = Lo (1+αΔT)

where Lo is the original length.

Basic features:
The length change is proportional to the temperature change.
Here α is the coefficient of linear expansion.

Correspondingly, the volume expands according to:

V = [Lo (1+αΔT) ]3
= Lo3(1 + αΔT)3
≈ Vo (1 + 3αΔT)
≡ Vo [1 + βΔT]

where β = 3 α is the coefficient of volume expansion.

An important counterexample: water!! Water is denser than ice! This effect: