Relation Between Expansion Coefficients (αv = 3αl and αa = 2αl)

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αv = 3αl and αa = 2αl

What each symbol means

SymbolWhat it stands for
αaCoefficient of area (superficial) expansion (K⁻¹)
αlCoefficient of linear expansion (K⁻¹)
αvCoefficient of volume (cubical) expansion (K⁻¹)

When to use this

Derived for isotropic materials from (1+αl ΔT)³ ≈ 1+3αl ΔT for small αl ΔT. ΔA/A = αa ΔT, ΔV/V = αv ΔT. For ideal gas at constant pressure, αv = 1/T. Water shows anomalous expansion: contracts from 0°C to 4°C, then expands normally.