Thermal Expansion: Understanding the Effects of Heat in A-Level Science

What Is Thermal Expansion?

Thermal expansion refers to the increase in size of a material when its temperature rises due to the increase in the kinetic energy of its particles.

Types of Thermal Expansion

Linear Expansion

Change in length of solids:

\[ \Delta L = \alpha L_0 \Delta T \]

Where:

• \( \Delta L \): Change in length (m)
• \( \alpha \): Coefficient of linear expansion (1/°C)
• \( L_0 \): Original length (m)
• \( \Delta T \): Temperature change (°C)

Areal Expansion

Change in surface area:

\[ \Delta A = 2\alpha A_0 \Delta T \]

Where \( A_0 \) is the original area (m²).

Volume Expansion

Change in volume of solids and liquids:

\[ \Delta V = \beta V_0 \Delta T \]

Where:

• \( \Delta V \): Change in volume (m³)
• \( \beta = 3\alpha \): Coefficient of volume expansion (1/°C)
• \( V_0 \): Original volume (m³)

Real-Life Applications of Thermal Expansion

Bridges and Railroads

Expansion joints are used to prevent buckling due to temperature changes.

Thermometers

Thermal expansion of liquids is used to measure temperature.

Bimetallic Strips

Used in thermostats to control heating and cooling systems.

Example Problem

A steel rod of length \( 2 \, \text{m} \) expands when heated from \( 20^\circ \text{C} \) to \( 100^\circ \text{C} \). The coefficient of linear expansion for steel is \( 12 \times 10^{-6} \, \text{/°C} \). Find the change in length.

1. Formula:
   \[ \Delta L = \alpha L_0 \Delta T \]
2. Substitute Values:
   \[ \Delta L = 12 \times 10^{-6} \times 2 \times (100 – 20) = 0.00192 \, \text{m} \, \text{or} \, 1.92 \, \text{mm} \]

Common Mistakes in Thermal Expansion Problems

1. Forgetting to convert units (e.g., mm to m)
2. Mixing up coefficients of linear and volume expansion
3. Using the wrong formula for specific expansion types

Practice Questions

1. A copper rod expands \( 1.2 \, \text{mm} \) when heated. If its original length is \( 1 \, \text{m} \) and \( \Delta T = 50^\circ \text{C} \), find \( \alpha \).
2. Explain the purpose of expansion joints in bridges.
3. Describe one application of volume expansion in liquids.