IGCSE Physics - 2.2.1 Thermal Expansion of Solids, Liquids and Gases

This section describes the thermal expansion of solids, liquids, and gases at constant pressure. We will explore how temperature changes affect the volume of these states of matter.

2.2.1.1 Thermal Expansion - Introduction

When a substance is heated, its particles move more vigorously. This increased movement causes the average separation between the particles to increase, resulting in an expansion of the substance. This phenomenon is known as thermal expansion.

At constant pressure, the change in volume of a substance is directly proportional to the change in temperature. This relationship is described by the coefficient of thermal expansion.

2.2.1.2 Thermal Expansion of Solids

Mechanism

In solids, the particles are held in fixed positions by strong intermolecular forces. When heated, the particles vibrate with greater amplitude. This increased vibration leads to a slight increase in the average distance between the particles, causing the solid to expand. The effect is generally small.

Coefficient of Thermal Expansion (α)

The coefficient of thermal expansion (α) is a material property that quantifies how much a material expands for each degree Celsius (or Kelvin) change in temperature. It is defined as:

$$ \alpha = \frac{\Delta L}{L_0 \Delta T} $$ where:

• $\Delta L$ is the change in length
• $L_0$ is the original length
• $\Delta T$ is the change in temperature

The units of α are per degree Celsius (°C) or per Kelvin (K).

Qualitative Description

When a solid is heated, it will generally increase in length, width, and height. The extent of this change depends on the material's coefficient of thermal expansion and the amount of temperature change.

Solid	Coefficient of Thermal Expansion (approximate)
Steel	$11 \times 10^{-6} \, ^\circ\text{C}^{-1}$
Aluminum	$23 \times 10^{-6} \, ^\circ\text{C}^{-1}$
Glass	$9 \times 10^{-6} \, ^\circ\text{C}^{-1}$

Note that different materials have different coefficients of thermal expansion. For example, steel expands less than aluminum for the same temperature change.

2.2.1.3 Thermal Expansion of Liquids

Mechanism

In liquids, the intermolecular forces are weaker than in solids, allowing for greater movement of the particles. When heated, the particles gain kinetic energy and move further apart, resulting in a more significant expansion compared to solids.

Coefficient of Thermal Expansion (α)

The coefficient of thermal expansion for liquids is generally higher than for solids because the intermolecular forces are weaker.

Qualitative Description

When a liquid is heated, it will increase in volume. The amount of expansion depends on the liquid's coefficient of thermal expansion and the temperature change. Liquids expand more than solids for the same temperature change.

2.2.1.4 Thermal Expansion of Gases

Mechanism

In gases, the particles are widely separated and move randomly. When heated, the particles gain kinetic energy and move faster and collide with the walls of the container more frequently. This increased molecular motion leads to a significant increase in volume.

Coefficient of Thermal Expansion (α)

The coefficient of thermal expansion for gases is generally higher than for both solids and liquids because the particles are far apart and have less intermolecular attraction.

Qualitative Description

When a gas is heated, it expands significantly. The volume of the gas is directly proportional to the temperature change (at constant pressure). This relationship is described by Charles's Law.

$$ \frac{V_1}{T_1} = \frac{V_2}{T_2} $$

where:

• $V_1$ is the initial volume
• $T_1$ is the initial temperature (in Kelvin)
• $V_2$ is the final volume
• $T_2$ is the final temperature (in Kelvin)

2.2.1.5 Applications of Thermal Expansion

The thermal expansion of materials has several practical applications:

• Bimetallic Strips: Used in thermostats and other temperature-sensitive devices. A bimetallic strip consists of two different metals with different coefficients of thermal expansion. When heated, the strip bends.
• Expansion Joints in Bridges and Roads: These joints allow for expansion and contraction of bridges and roads due to temperature changes, preventing stress and cracking.
• Thermos Flasks: The vacuum between the inner and outer walls of a thermos flask reduces heat transfer by conduction and convection, minimizing the effect of thermal expansion.
• Expansion in Railways: Railway tracks are laid with small gaps (expansion joints) to accommodate expansion in hot weather.