Definitions and qualifiers


This section provides concise explanations of the definitions and the various qualifiers (or 'variations on the theme') relevant to thermal expansion and density. If you need more information please read the other sections or consider having a look at the Literature list.

Thermal expansion, definition:

Thermal expansion is defined as the change in dimensions of a material due to an increase in temperature. In most cases this means an increase in size or expansion of the material. Less commonly, some materials shrink on heating.

Thermal expansion, qualifiers:

  • coefficient of thermal expansion (CTE)
  • mean CTE (averaged over a specified temperature interval)
  • linear expansion coefficient (one-dimensional expansion)
  • volumetric expansion coefficient (in all three dimensions)
  • expansivity (fractional length increase per unit temperature rise)


Qualifiers: See the pictures below to get an idea of the qualifiers for thermal expansion.
These pictures with further explanation can be found by following this link.


Density, definition:

Density ρ is the mass (m) per unit volume (V) of a medium, whether solid, liquid or gas, and it is expressed as ρ = m / V.


Understanding density: Take a look at the two boxes below. Each box has the same volume. If each ball has the same mass, which box would weigh more? Why?

Answer: The box that has more balls has more mass per unit of volume. This property of matter is called density.

Density, qualifiers:

  • bulk density (including pores and cracks)
  • apparent solid density (with pores and cracks inaccessible from the exterior)
  • true solid density (excluding all pores and cracks)
  • theoretical density, for an ideal solid, is the density at zero kelvin

For liquids and gases usually no such qualifiers are used.