Explain, in terms of the motion and arrangement of particles, the relative order of magnitudes of the expansion of solids, liquids and gases as their temperatures rise

2.2.1 Thermal Expansion of Solids, Liquids and Gases

What is Thermal Expansion?

When a material is heated, its particles (atoms or molecules) vibrate more vigorously.

Because the particles push against each other, the material’s size changes.

This change is called thermal expansion.

How Particles Move and Arrange

• Solids: particles are tightly packed in a fixed lattice. They can only vibrate around their positions. 🔒
• Liquids: particles are close but can slide past one another. They have more freedom to move. 💃
• Gases: particles are far apart and move freely in all directions. They hardly feel each other. 🚀

Relative Magnitudes of Expansion

1. Solids – Very small expansion because the lattice keeps particles close.

   Typical linear coefficient: \$\alpha \approx 10^{-6}\,\text{K}^{-1}\$.

2. Liquids – Larger expansion because particles can move past each other.

   Typical linear coefficient: \$\alpha \approx 10^{-4}\,\text{K}^{-1}\$.

3. Gases – Huge expansion because particles are far apart and hardly interact.

   For an ideal gas, the volume change follows \$V \propto T\$ (Charles’ law).

   Linear coefficient is effectively much larger, \$\alpha \approx 10^{-2}\,\text{K}^{-1}\$ or more.

Illustrative Example

Imagine a metal ruler, a plastic bottle of water, and a helium balloon all heated by the sun:

• Ruler: only a few micrometres longer – almost invisible. 🏃‍♂️
• Bottle: a few millimetres longer – you can see it. 💧
• Balloon: expands dramatically, maybe doubling its volume. 🎈

Formula for Linear Expansion

The change in length is given by:

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

where \$L_0\$ is the original length, \$\Delta T\$ is the temperature change, and \$\alpha\$ is the coefficient of linear expansion.

Coefficients of Linear Expansion (Typical Values)