Linear Expansion
ΔL = L₀αΔT — see metals lengthen with temperature.
Key Notes
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.
Formulas
Linear expansion
Linear approximation valid for moderate ΔT.
New length
L₀ = original length at reference temperature.
Strain due to expansion
Fractional change in length per unit ΔT.
Thermal stress (constrained)
If body can't expand freely, stress builds up.
Important Points
α is SMALL (~10⁻⁵ /K) — but at large scales (km bridges) gives meters of expansion.
Heating a metal ring with hole INCREASES the hole size (same fractional expansion as solid).
Bimetallic strips bend toward the metal with LOWER α — used as thermostat switches.
Constrained body cannot expand ⇒ huge thermal stress; can damage bridges, rails.
Linear expansion is FIRST-ORDER in ΔT; valid for moderate ranges. At extreme temperatures, nonlinearity matters.
Invar (α ≈ 1×10⁻⁶/K) is used in pendulum clocks, surveying tapes, anywhere stability matters.
Linear Expansion notes from sciphylab (also known as SciPhy, SciPhy Lab, SciPhy Labs, Physics Lab). Class 11 physics revision for JEE Mains, JEE Advanced, NEET UG, AP Physics 1/2/C, SAT, and CUET-UG.