Describe some of the everyday applications and consequences of thermal expansion

2.2.1 Thermal Expansion of Solids, Liquids and Gases

What is thermal expansion? (constant‑pressure assumption)

When the temperature of a material changes, the kinetic energy of its particles changes. The particles vibrate more vigorously and, on average, move farther apart. Consequently the size of the material changes – it expands when heated and contracts when cooled. In the syllabus the discussion of gases is explicitly at **constant pressure** (Charles’s law); for solids and liquids the pressure effect is negligible.

Qualitative behaviour for the three states of matter

• Solids: Particles are fixed in a lattice but can vibrate about their equilibrium positions. Heating increases the vibration amplitude, so the average separation between neighbouring atoms increases and the solid expands.
• Liquids: Particles are already free to slide past one another. A rise in temperature increases the average distance between particles, giving a larger expansion than in a solid.
• Gases (constant pressure): Gas particles move independently and fill the whole container. Heating increases both the speed of the particles and the average separation, producing the greatest expansion of the three states.

Why does the magnitude of expansion differ?

Because the freedom of motion of the particles increases from solid → liquid → gas, a given temperature change (ΔT) produces a larger change in average separation, and therefore a larger change in volume. Hence, in order of increasing expansion:

solids < liquids < gases

This directly follows the syllabus wording: “particles in gases are free to move the most, so a given ΔT produces the largest volume change, followed by liquids, then solids.”

Mathematical description (small ΔT)

• Linear expansion of a solid: ΔL = α L₀ ΔT
• Area expansion of a thin plate: ΔA = 2α A₀ ΔT
• Volume expansion of a solid or liquid: ΔV = β V₀ ΔT where β ≈ 3α for isotropic solids.
• Ideal gas at constant pressure (Charles’s law): V/T = constant or V₂/V₁ = T₂/T₁ (temperatures in kelvin).

Remember:

• α – linear coefficient of thermal expansion, units × 10⁻⁶ °C⁻¹ (or K⁻¹).
• β – volume coefficient of thermal expansion, units × 10⁻⁶ °C⁻¹ (or K⁻¹).

Coefficients of thermal expansion (typical values)

Everyday applications

Applications involving solids

• Expansion joints in bridges and railway tracks: Small gaps allow metal members to expand in summer without buckling.
• Bimetallic strip thermostats: Two metals with different α are bonded; heating causes the strip to bend and operate a switch.
• Metal lids on glass jars: The lid is heated to expand, placed on the jar, then cools to create a tight seal.
• Railway‑track spacing: Regular gaps (≈ 10 mm per 20 m of rail) prevent buckling in hot weather.

Applications involving liquids

• Mercury or alcohol thermometers: The liquid expands linearly with temperature, moving up a calibrated tube.
• Hot‑water heating systems: Expansion tanks give the water room to expand when heated.
• Fuel‑level gauges in cars: The gauge is calibrated to account for the volume change of fuel with temperature.
• Thermal‑expansion compensators in hydraulic systems: Small chambers absorb the extra fluid volume when the system warms.

Applications involving gases

• Hot‑air balloons: Heating the air inside reduces its density, providing lift.
• Internal‑combustion engines: Rapid expansion of combustion gases pushes the pistons.
• Air‑conditioners and refrigerators: Controlled compression and expansion of refrigerant gases absorb and release heat.
• Gas‑pipeline flow‑rate compensation: Pipelines are laid with expansion loops or temperature‑compensating flow meters.

Consequences of uncontrolled expansion

1. Structural damage: If expansion is restrained, compressive stresses develop, leading to cracks or buckling (e.g., cracked railway tracks in summer).
2. Mis‑alignment of precision instruments: Optical benches, laser interferometers and measuring devices must be built from low‑expansion materials (e.g., Invar) to retain accuracy.
3. Failure of sealed containers: Pressure rise in a closed vessel can cause rupture unless a safety valve or expansion space is provided.
4. Variation of flow rates in pipelines: Changes in liquid or gas volume alter velocity and pressure, so temperature compensation is required.

Design strategies to manage expansion (essential points)

• Use materials with very low coefficients of expansion (e.g., Invar, fused silica, certain ceramics) for high‑precision parts.
• Incorporate expansion joints, sliding bearings or flexible couplings in large structures such as bridges, railways and pipelines.
• Provide clearance gaps or “free‑expansion” spaces in assemblies (e.g., between rails, bridge decks and supports).
• Fit pressure‑relief or safety valves on sealed containers and include expansion tanks in heating/cooling circuits.

Summary table – key points