Explain the three types of thermal expansion of solids with formulas and examples.

1. 1 · Open in one line. Solids expand on heating because their particles vibrate more and move farther apart.
2. 2 · Linear expansion. Increase in length: ΔL/L₀ = αL ΔT. Example: gaps between railway rails.
3. 3 · Superficial expansion. Increase in area: ΔA/A₀ = αA ΔT. Example: a metal roof sheet expands in sunlight.
4. 4 · Cubical expansion. Increase in volume: ΔV/V₀ = αV ΔT. Example: a heated ball no longer passes through a ring.
5. 5 · Symbols and unit. L₀, A₀, V₀: original size; ΔT: rise in temperature; each coefficient has the unit K⁻¹.
6. 6 · Real-life link. Expansion joints on flyovers and sagging power lines in summer.
7. 7 · Close in one line. So a solid expands in length, area and volume when it is heated.

Scoring tip: Write the three formulas one below the other and say what each symbol means. Add one example for each type.