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?

When the temperature of a material changes, its particles move more vigorously and the average separation between them changes.

This results in a change of size – an increase when heated and a decrease when cooled.

Mathematical Description

For small temperature changes the expansion can be approximated by linear relationships:

• Linear expansion of a solid: \$\Delta L = \alpha L_0 \Delta T\$
• Area expansion of a thin plate: \$\Delta A = 2\alpha A_0 \Delta T\$
• Volume expansion of a solid or liquid: \$\Delta V = \beta V_0 \Delta T\$ where \$\beta \approx 3\alpha\$ for isotropic solids.
• For an ideal gas the volume change with temperature at constant pressure is given by Charles’s law: \$\frac{V}{T}= \text{constant}\$ or \$\frac{V2}{V1}= \frac{T2}{T1}\$ (temperatures in kelvin).

Coefficients of Thermal Expansion

Typical coefficients (α for linear, β for volume) for common materials are shown below.

Everyday Applications

Applications Involving Solids

• Expansion joints in bridges and railway tracks: Small gaps allow the structure to expand without buckling.
• Thermostats (bimetallic strips): Two metals with different α are bonded; heating causes the strip to bend and operate a switch.
• Fit of metal lids on glass jars: The lid is heated to expand, placed on the jar, and then cools to create a tight seal.

Applications Involving Liquids

• Thermometers (mercury or alcohol): The liquid expands linearly with temperature, moving up a calibrated tube.
• Hot‑water heating systems: Expansion tanks accommodate the increase in water volume when heated.
• Fuel‑level gauges in cars: The fuel expands with temperature; the gauge is calibrated to account for this.

Applications Involving Gases

• Hot‑air balloons: Heating the air inside reduces its density, providing lift.
• Internal combustion engines: The rapid expansion of gases pushes pistons, producing work.
• Air‑conditioners and refrigerators: Compression and expansion of refrigerant gases absorb and release heat.

Consequences of Thermal Expansion

1. Structural damage: If expansion is restrained, compressive stresses develop, leading to cracks (e.g., cracked railway tracks in summer).
2. Misalignment of precision instruments: Optical benches, laser interferometers, and measuring devices must be mounted on low‑expansion materials (e.g., Invar) to maintain accuracy.
3. Failure of sealed containers: Pressure build‑up in a closed vessel can cause rupture unless a safety valve or expansion space is provided.
4. Changes in volume of liquids and gases affect flow rates: Pipelines transporting oil or gas need temperature compensation to maintain constant flow.

Design Strategies to Manage Expansion

• Use materials with low coefficients of expansion (e.g., Invar, fused silica) for precision parts.
• Incorporate expansion joints, sliding bearings, or flexible couplings in large structures.
• Provide clearance gaps in assemblies (e.g., between rails, bridge decks, and supports).
• Install pressure relief valves on sealed containers.

Summary Table – Key Points