Describe, qualitatively, the thermal expansion of solids, liquids and gases at constant pressure

2.2.1 Thermal Expansion of Solids, Liquids and Gases

When the temperature of a material is increased while the external pressure is kept constant, its particles gain kinetic energy, move more vigorously and tend to occupy a larger volume. This phenomenon is called thermal expansion. The amount of expansion depends on the state of matter and on the intrinsic properties of the material.

1. Qualitative Description (Constant‑Pressure)

• All three states – solids, liquids and gases – expand when heated at constant pressure.
• Why the magnitude differs: the average distance between particles increases most where the particles are already far apart (gases), less where they are close together (liquids), and least where they are fixed in a lattice (solids).

Solids – Linear Expansion

• Particles vibrate about fixed lattice points. Heating increases the average separation slightly, so the dimensions of the solid increase.
• Change in length:
  \[ \Delta L = \alpha L_{0}\,\Delta T \]
  • \(\Delta L\) – change in length
  • \(\alpha\) – coefficient of linear expansion (≈ 10⁻⁶ – 10⁻⁵ K⁻¹ for metals)
  • \(L_{0}\) – original length
  • \(\Delta T\) – temperature change (°C or K)
• For an isotropic solid the volume‑expansion coefficient \(\beta\) is roughly three times the linear coefficient: \(\beta \approx 3\alpha\).

Liquids – Volume Expansion

• Particles are free to slide past one another; the intermolecular forces are weaker than in solids. Heating increases the average intermolecular distance, giving a noticeable rise in volume.
• Change in volume:
  \[ \Delta V = \beta V_{0}\,\Delta T \]
  • \(\Delta V\) – change in volume
  • \(\beta\) – coefficient of volume expansion (typically 10⁻⁴ – 10⁻³ K⁻¹)
  • \(V_{0}\) – original volume
  • \(\Delta T\) – temperature change

Gases – Volume Expansion (Charles’s Law)

• Gas particles are far apart and experience negligible attractive forces. Heating raises their average speed, so they strike the container walls more forcefully, expanding the gas.
• For an ideal gas at constant pressure: \[ \frac{V}{T}= \text{constant}\qquad\text{or}\qquad\frac{\Delta V}{V_{0}}=\frac{\Delta T}{T_{0}} \]
• Thus the coefficient of volume expansion for an ideal gas is \[ \beta = \frac{1}{T} \] where \(T\) is the absolute temperature (K).

2. Typical Coefficients of Expansion

3. Everyday Applications & Consequences (IGCSE‑relevant examples)

• Expansion joints in bridges and railway tracks – metal expands in summer; joints allow movement and prevent buckling.
• Concrete sidewalks and pavement – laid with regular joints; without them the concrete would crack as it expands.
• Bimetallic strips in thermostats – two metals with different \(\alpha\) values bend when heated, operating a switch.
• Glass laboratory containers – borosilicate or lead‑glass has a low \(\beta\) to resist cracking on heating.
• Thermometers – mercury or coloured alcohol expands uniformly with temperature, giving a reliable scale.
• Engine pistons and cylinder heads – designed with clearance gaps so the hot gases can expand without seizing the moving parts.
• Metallic pipelines – fitted with expansion loops or flexible couplings to accommodate temperature‑induced length changes.
• Railway tracks – continuous welded rail includes expansion gaps or is laid at a temperature that minimises stress throughout the year.

4. Experimental Demonstration (Practical Box)

5. Summary

• All matter expands when heated at constant pressure.
• Solids: small, linear expansion; \(\Delta L = αL_{0}\Delta T\).
• Liquids: moderate, volume expansion; \(\Delta V = βV_{0}\Delta T\).
• Gases: large, volume expansion; obey Charles’s Law \(\displaystyle\frac{V}{T}= \text{constant}\) and \(\beta = 1/T\).
• The order of magnitude (gases > liquids > solids) follows directly from how far apart the particles are in each state.
• Coefficients \(α\) and \(β\) are material‑specific; engineers must provide space (expansion joints, clearances, flexible components) to accommodate the change and avoid stress or failure.