Coefficient of Lineal Thermal Expansion
Definition and meaning of Coefficient of Lineal Thermal Expansion in chemistry.
Coefficient of lineal thermal expansion is the fractional increase in the length of a solid per unit rise in temperature, measured at constant pressure. It is defined as α = (1/L)(dL/dT), where L is the original length, and is usually expressed per degree Celsius or per kelvin.
In more detail
As a solid is heated, increased thermal vibration of its atoms raises their average interatomic separation because the bonding potential energy curve is asymmetric (anharmonic), so the material lengthens rather than merely vibrating more without net expansion. Because the effect is small, α is normally reported in units of per degree Celsius (or per kelvin), often on the order of 10⁻⁶ to 10⁻⁵. It is a directional (linear) counterpart to the coefficient of cubical (volume) expansion, and for an isotropic solid the volume coefficient is approximately three times the linear coefficient. Engineers use α to size expansion joints in bridges, railroad track gaps, and bimetallic strips in thermostats.
Key facts
| Symbol | α (alpha) |
|---|---|
| Defining equation | α = (1/L)(dL/dT), constant pressure |
| SI Units | K⁻¹ (or °C⁻¹) |
| Field | Physical Chemistry |
Steel has a lineal expansion coefficient of about 12 × 10⁻⁶ per °C. A 1-meter steel rail heated by 20°C therefore lengthens by roughly 1 × 12 × 10⁻⁶ × 20 = 2.4 × 10⁻⁴ m, or about 0.24 mm.
Frequently asked questions
How does the lineal expansion coefficient relate to the cubical (volume) expansion coefficient?
For an isotropic solid, the volume expansion coefficient β is approximately three times the lineal expansion coefficient, β ≈ 3α, since volume expands along all three dimensions.
Why do most solids expand when heated?
Heating increases the amplitude of atomic vibrations, and because the interatomic potential energy curve is anharmonic (steeper on the repulsive side than the attractive side), the average atomic spacing, and thus the material's length, increases.