Volume Expansion

Volume expansion: ΔV = γ·V₀·ΔT, where γ = 3α is the volume expansion coefficient (for isotropic solids).

Liquids and gases have their OWN γ — usually much larger than solids.

γ (water) at 20°C: ~2×10⁻⁴/K. γ (mercury): ~1.8×10⁻⁴/K. γ (air at constant P): 1/273 = 3.66×10⁻³/K.

Gases follow ideal gas law: V/T = const at constant P ⇒ γ_gas = 1/T ≈ 3.66×10⁻³/K at 273 K.

Liquid expansion is used in mercury and alcohol thermometers.

Solid container with liquid: APPARENT expansion of liquid = γ_liquid − γ_container (the difference shows up).

Anomalous behavior of water: density MAX at 4°C; expands when COOLING from 4°C to 0°C.

Thermal expansion of pavement and concrete is why expansion joints exist in roads and bridges.