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, 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.