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

Published by Patrick Mutisya · 14 days ago

Thermal Expansion of Solids, Liquids and Gases

2.2.1 Thermal Expansion of Solids, Liquids and Gases

When the temperature of a material is increased at constant pressure, its particles 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 material’s intrinsic properties.

Key Concepts

  • Expansion occurs at constant pressure.

  • Particles gain kinetic energy as temperature rises.

  • Solids, liquids and gases all expand, but to different extents.

  • Expansion is described using linear or volume coefficients.

1. Solids

In a solid the particles are held in fixed positions by strong intermolecular forces. When heated, the average separation between particles increases slightly, causing the solid to expand.

The linear expansion of a solid is given by

\$\Delta L = \alpha L_0 \Delta T\$

where

  • \$\Delta L\$ = change in length

  • \$\alpha\$ = coefficient of linear expansion (≈ 10⁻⁶ K⁻¹ for many metals)

  • \$L_0\$ = original length

  • \$\Delta T\$ = change in temperature (°C or K)

For isotropic solids the volume expansion coefficient \$\beta\$ is approximately three times the linear coefficient:

\$\beta \approx 3\alpha\$

2. Liquids

Liquids have weaker intermolecular forces than solids, so their particles can move past one another more easily. Heating a liquid increases the average distance between particles, leading to a noticeable increase in volume.

The volume change of a liquid is expressed as

\$\Delta V = \beta V_0 \Delta T\$

where \$\beta\$ is the coefficient of volume expansion for the liquid (typically 10⁻⁴ K⁻¹ to 10⁻³ K⁻¹).

3. Gases

Gases consist of particles far apart with negligible attractive forces. At constant pressure, heating a gas causes a large increase in volume because the particles move faster and collide more forcefully with the container walls.

For an ideal gas at constant pressure, the volume expansion follows Charles’s Law:

\$\frac{V}{T} = \text{constant} \quad \text{or} \quad \frac{\Delta V}{V0} = \frac{\Delta T}{T0}\$

Thus the coefficient of volume expansion for an ideal gas is

\$\beta = \frac{1}{T}\$

where \$T\$ is the absolute temperature in kelvin.

Typical Coefficients of Expansion

MaterialStateCoefficient of Linear Expansion \$α\$ (K⁻¹)Coefficient of \cdot olume Expansion \$β\$ (K⁻¹)
AluminiumSolid2.4 × 10⁻⁵≈ 7.2 × 10⁻⁵
Glass (typical)Solid9 × 10⁻⁶≈ 2.7 × 10⁻⁵
WaterLiquid–2.1 × 10⁻⁴ (20 °C → 30 °C)
Air (ideal gas)Gas–≈ 1/T (≈ 3.6 × 10⁻³ at 300 K)

Practical Implications

  1. Metal bridges and railway tracks are provided with expansion joints to accommodate length changes.

  2. Glass containers are made with a small amount of lead oxide to reduce expansion and prevent cracking.

  3. Thermometers use liquids (e.g., mercury) that expand uniformly with temperature.

  4. Engines and pistons are designed with clearance gaps to allow for gas expansion during combustion.

Suggested diagram: Schematic showing linear expansion of a metal rod, volume expansion of a liquid in a bulb, and a gas-filled piston moving outward when heated.

Summary

  • All matter expands when heated at constant pressure.

  • Solids: small linear expansion, described by \$ΔL = αL_0ΔT\$.

  • Liquids: moderate volume expansion, described by \$ΔV = βV_0ΔT\$.

  • Gases: large volume expansion, obeying \$V/T = \text{constant}\$ (Charles’s Law).

  • Coefficients \$α\$ and \$β\$ are material‑specific and determine the magnitude of expansion.

  • Engineering designs must allow for thermal expansion to avoid stress and failure.