Volume Expansion
γ — liquid level rises in a bulb.
Key Notes
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.
Formulas
Volume expansion (solid)
For isotropic solid: γ ≈ 3α.
New volume
Linear approximation.
Ideal gas (constant P)
Charles's law: V₂/V₁ = T₂/T₁ at constant P.
Apparent vs real (liquid in container)
What you observe vs. true expansion.
Important Points
γ = 3α for isotropic solids (volume scales as L³).
Liquids have γ much larger than solids; gases even more (γ ≈ 1/T at constant P).
When measuring liquid expansion in a container, must subtract container's expansion.
Hot air rises because heated air expands and becomes less dense.
Anomalous water: γ NEGATIVE between 0°C and 4°C. Density peaks at 4°C ⇒ lakes freeze top-down.
Real-world: bridges, pipes, and railways must accommodate γ·V·ΔT volumetric changes.
Volume 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.