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

ΔL = L_oαΔT   or   L = L_o (1+αΔT)

where L_o 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 = [L_o (1+αΔT) ]³
= L_o³(1 + αΔT)³
≈ V_o (1 + 3αΔT)
≡ V_o [1 + βΔT]

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

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

• allows pond life to live through winter.
• causes icebergs to float.
• underlies the icebomb.