The Physics
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Opus in profectus

# 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 (∆ℓ/ℓ0) called linear expansion
• changes in area compared to original area (A/A0) called areal expansion or superficial expansion
• changes in volume compared to original volume (V/V0) called volumetric expansion or cubical expansion
• For most materials, over small temperature ranges, these fractional changes…
• are directly proportional to temperature change (T) and
• have the same sign (i.e., materials usually expand when heated and contract when cooled)
• are larger for liquids than solids
• 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, (since two perpendicular linear measurements describe an area)
• have a volumetric expansion that is very nearly three times their linear expansion, (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.
Equations of thermal expansion
equation solids
∆ℓ  =  0 α∆T linear expansion
A  =  A0 2α∆T areal (or superficial) expansion
V  =  V0 3α∆T volumetric (or cubical) expansion
equation liquids
V  =  V0 β∆T volumetric (or cubical) expansion
equation gases
PV  =  nRT ideal gas law