## Learning objectives

## After completing the topic, the student will be able to:

- Discuss, explore and relate the concept of thermal expansion to everyday science.
- Determine the coefficient of linear expansion of solids and apply it in real life situations.
- Examine, explore and compare superficial expansion of solids with linear expansion of solids.
- Compare cubical expansion with linear expansion of solids, in relation with its applications.
- Explore and operate cubical expansion of solids on real world applications.
- Explore and investigate about thermal stress and relate to daily life scenarios.
- Outline, analyze and relate the anomalous expansion of water to everyday science.

Thermal expansion means "increase in size on heating". Various substances expand (increase in size) when their temperature is raised and contract (decrease in size) when their temperature is lowered. In general, thermal expansion is increase in the volume of a material as its temperature is increased. It is usually expressed as a fractional change in length or area or volume per unit temperature change.

For example, when a metal block is heated, it generally expands in length, breadth and height. This indicates that the metal block expands in volume and is called as **volume expansion or cubical expansion**. However, if we heat a solid, which is in the form of a sheet (its thickness can be neglected as compared to its surface area), then the increase in area is called **superficial expansion**. Similarly, if we heat a solid, which is in form of a wire (its cross–section area is too small compared to its length and hence can be neglected), then the increase in length is called **linear expansion**.

A linear expansion coefficient is usually employed in describing the expansion of a solid, while a volume expansion coefficient is more useful for a liquid or a gas. If a crystalline solid is isometric (has the same structural configuration throughout), the expansion will be uniform in all dimensions of the crystal. If it is not isometric, there may be different expansion coefficients for different crystallographic directions.

In a solid or liquid, there is a dynamic balance between the cohesive forces holding the atoms or molecules together and the conditions created by temperature; higher temperatures imply greater distance between atoms. Different materials have different bonding forces and therefore different expansion coefficients.

Materials generally change their size when subjected to a temperature change while the pressure is held constant. In the special case of solid materials, the pressure does not appreciably affect the size of an object, and so, for solids, it's usually not necessary to specify that the pressure be held constant.

When a metal rod is heated, its length increases (it expands). The increase in length depends on the original length of the rod, the rise in temperature, and the nature of the material of the rod.

Consider a rod of length L_{0} at 0°C. Let the rod be heated through t°C, such that final length is L_{t}.

Increase in length = L_{t} – L_{0}

Also we know, increase in length ∝ initial length i.e. L_{t} – L_{0} ∝ L_{0} ...... (i)

Similarly, increase in length ∝ rise in temperature i.e. L_{t} – L_{0} ∝ t ......(ii)

Combining (i) and (ii)

L_{t} – L_{0} ∝ L_{0} × t

L_{t} – L_{0} = α × L_{0} × t {α is the coefficient of linear expansion.}

**α = (L _{t} – L_{0}) / (L_{0} × t)**

**Coefficient of Linear Expansion = Increase in length /(Initial length x Rise in temp)**

**Coefficient of linear expansion for some materials:**