1. What Is Expansion of Solids?
When a solid is heated, its particles vibrate faster and need slightly more space. This causes the solid to expand. The amount of expansion is usually small but important in practical situations like building bridges, laying railway tracks, or fixing metal lids.
Expansion in solids can occur in length, area, or volume depending on the shape of the object.
2. Why Solids Expand on Heating
In solids, particles are held tightly in fixed positions but still vibrate. Heating increases their vibration. Since they cannot move freely, the extra motion pushes particles apart very slightly, leading to expansion.
2.1. Nature of Bonding
Particles in solids are bound by strong forces, so expansion is less compared to liquids and gases. The amount of expansion depends on the material and how its particles are arranged.
2.2. Effect of Temperature
The higher the temperature rise, the greater the expansion. For small temperature changes, expansion is proportional to the temperature change.
3. Types of Expansion in Solids
Depending on the dimension considered, solids can show three types of expansion: linear expansion, area expansion and volume expansion.
3.1. Linear Expansion
Linear expansion refers to the change in length of a solid rod or wire when its temperature changes.
\( \Delta L = \alpha L \Delta T \)
Here, α is the coefficient of linear expansion.
3.2. Area Expansion
When a solid sheet is heated, its surface area increases. This is called area expansion.
\( \Delta A = \beta A \Delta T \)
β is the coefficient of area expansion.
3.3. Volume Expansion
All solids expand in volume when heated. The formula for volume expansion is:
\( \Delta V = \gamma V \Delta T \)
γ is the coefficient of volume expansion.
4. Relation Between α, β and γ
For most solids, the three coefficients are approximately related as:
\( \beta \approx 2\alpha \)
\( \gamma \approx 3\alpha \)
This means area expansion is roughly twice linear expansion, and volume expansion is roughly three times linear expansion for small temperature changes.
5. Real-Life Applications
Understanding expansion of solids is important in many everyday situations. Engineers and designers take expansion into account to prevent damage or ensure proper functioning.
5.1. Railway Tracks
Small gaps are left between rails so they can expand safely in hot weather without bending or buckling.
5.2. Bridges and Roads
Bridges use expansion joints that allow parts to expand or contract with temperature without cracking.
5.3. Tight Metal Lids
A tight metal lid on a jar opens easily when dipped in hot water because the metal expands more than the glass.
5.4. Electric Wires
Overhead wires are hung with slack because they contract during cold weather and might snap if stretched too tightly.
6. Factors Affecting Expansion of Solids
The amount of expansion in a solid depends on various factors:
6.1. Material
Metals generally expand more than wood or glass due to their loosely packed particle arrangement at the atomic scale.
6.2. Initial Length, Area or Volume
Larger objects show more expansion because there is more material to expand.
6.3. Temperature Change
Greater temperature changes cause greater expansion. For small changes, the relation is nearly proportional.
7. Examples of Expansion of Solids
- Telephone poles and wires sag more in summer due to expansion.
- Rivets used in shipbuilding become tight after cooling because they contract and hold plates together.
- Concrete slabs on sidewalks have small gaps between them to allow for safe expansion.
- Glassware can crack if heated too quickly because different parts expand at different rates.