Linear Expansion

Most solids EXPAND when heated. Linear expansion: ΔL = α·L₀·ΔT, where α is the coefficient of linear expansion (K⁻¹).

Typical α values: steel ~12×10⁻⁶/K, aluminum ~23×10⁻⁶/K, copper ~17×10⁻⁶/K, glass ~9×10⁻⁶/K, invar ~1×10⁻⁶/K.

Larger α ⇒ more expansion per unit temperature rise.

Bimetallic strips: two metals with different α bonded together bend on heating — used in thermostats.

Railway tracks have gaps between rails to accommodate expansion in summer heat.

Bridges have expansion joints — accommodate thermal length changes.

Invar (Fe-Ni alloy) has very low α ⇒ used in precision instruments where dimensional stability matters.

Thermal expansion arises from anharmonic potential at atomic level — atoms vibrate more on heating and move slightly apart.