Area Expansion
β ≈ 2α — square sheet expanding in 2D.
Key Notes
Area expansion: ΔA = β·A₀·ΔT, where β = 2α is the area expansion coefficient.
Holds for isotropic materials (same α in all directions).
Twice the linear coefficient because A ∝ L².
Useful for thin plates, sheet metals, surface areas of objects.
Hole in a plate: increases in area same as solid plate (β·A·ΔT).
Differential expansion can warp thin plates if heated asymmetrically.
Most metals: β ~ 20-50 × 10⁻⁶/K. Glass: ~18 × 10⁻⁶/K.
Bimetallic plates curl into spherical caps when heated uniformly.
Formulas
Area expansion
Twice the linear coefficient.
New area
Used for plates and sheets.
Fractional area change
Twice fractional linear change.
Important Points
β = 2α for ISOTROPIC materials — area expands twice as fast as length (since A = L²).
Hole in a plate behaves like solid plate of same area — both expand at the same rate.
Thin metal plates can warp if heated unevenly (one side expands more).
Bimetallic plate ⇒ spherical curve on uniform heating.
Important for thermometer scales, pressure gauges, scientific instruments.
Differential expansion is a key concern in chip-fabrication and aerospace.
Area 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.