# Thermal Expansion

## Summary

- Thermal expansion refers to a fractional change in size of a material in response to a change in temperature.
- This includes…
- changes in length compared to original length (Δℓ/ℓ
_{0}) called linear expansion - changes in area compared to original area (Δ
*A*/*A*_{0}) called areal expansion or superficial expansion - changes in volume compared to original volume (Δ
*V*/*V*_{0}) called volumetric expansion or cubical expansion

- changes in length compared to original length (Δℓ/ℓ
- For most materials, over small temperature ranges, these fractional changes…
- are directly proportional to temperature change (Δ
*T*) and - have the same sign (i.e., materials usually expand when heated and contract when cooled)
- are larger for liquids than solids

- are directly proportional to temperature change (Δ
- A coefficient of thermal expansion…
- is the ratio of the fractional change in size of a material to its change in temperature
- is represented by the symbol α (alpha) for solids and β (beta) for liquids
- uses the SI unit inverse kelvin (K
^{−1}or 1/K) or the equivalent acceptable non SI unit inverse degree Celsius (°C^{−1}or 1/°C).

- Solids…
- tend to retain their shape when not constrained and so are best described by a linear coefficient of thermal expansion, α (alpha).
- have an areal expansion that is very nearly twice their linear expansion, 2α (since two perpendicular linear measurements describe an area)
- have a volumetric expansion that is very nearly three times their linear expansion, 3α (since three perpendicular linear measurements describe a volume)

- Liquids…
- tend to take on the shape of their container and so are best described by a volumetric coefficient of thermal expansion, β (beta).

- Gases…
- have a thermal expansion that is best described using the ideal gas law described later in this book.

equation | solids | |||
---|---|---|---|---|

Δℓ | = | ℓ_{0} |
αΔT |
linear expansion |

ΔA |
= | A_{0} |
2αΔT |
areal (or superficial) expansion |

ΔV |
= | V_{0} |
3αΔT |
volumetric (or cubical) expansion |

equation | liquids | |||

ΔV |
= | V_{0} |
βΔT |
volumetric (or cubical) expansion |

equation | gases | |||

PV |
= | nRT |
ideal gas law |