Temperature and Matter

What Is Thermal Expansion?

Thermal expansion is the increase in the dimensions of a material when its temperature increases.

When most materials are heated, they expand. When they are cooled, they contract.

This means that an object's:

• length can increase
• width can increase
• height can increase
• volume can increase

The opposite generally happens when temperature decreases.

Heating → expansion

Cooling → contraction

An important point is that thermal expansion normally changes the dimensions of an object, not the amount of matter in it. A metal rod does not gain mass simply because it becomes warmer.

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Explaining Thermal Expansion Using Particles

Thermal expansion can be explained using the particle model of matter.

Particles in solids, liquids, and gases are always moving.

When a material is heated:

• energy is transferred to the material
• the particles gain kinetic energy
• particle motion becomes more energetic
• the average separation between particles generally increases
• the material occupies more space

The individual atoms or molecules do not simply become larger. Instead, the average spacing between them changes.

When the material cools, the opposite occurs:

• particles lose kinetic energy
• particle motion becomes less energetic
• their average separation generally decreases
• the material contracts

A Simple Example

Imagine a metal rod.

At a lower temperature, its particles vibrate around fixed positions.

When the rod is heated, the particles vibrate more energetically. Their average separation increases slightly.

Each individual increase is extremely small, but there are enormous numbers of particles along the rod.

The result is a measurable increase in the rod's length.

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Thermal Expansion in Solids

In a solid, particles are held in relatively fixed positions by forces between them.

They cannot freely move around the material, but they vibrate.

Heating increases the energy of these vibrations. The average separation of the particles increases, causing the solid to expand.

Solids can expand in all three dimensions.

For example, a metal block may become:

• slightly longer
• slightly wider
• slightly taller

Therefore, its overall volume increases.

For long objects such as railway tracks, bridges, pipes, and electrical cables, even a very small percentage expansion can become important.

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Linear Expansion

When dealing with long, thin objects such as rods, rails, or wires, we are often most interested in the change in length.

The amount of expansion depends on three main factors:

• the original length of the object
• the change in temperature
• the material from which the object is made

This can be represented by:

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

where:

• $\Delta L$= change in length
• $L_0$= original length
• $\Delta T$= change in temperature
• $\alpha$= coefficient of linear thermal expansion

The coefficient

$\alpha$

tells us how strongly a particular material expands when its temperature changes.

You do not always need to calculate thermal expansion to understand the relationship:

larger original length → more expansion

larger temperature increase → more expansion

larger expansion coefficient → more expansion

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Worked Example: Comparing Two Metal Rods

Two identical aluminium rods are heated.

Rod A increases in temperature by

$20^\circ\text{C}$

.

Rod B increases in temperature by

$60^\circ\text{C}$

.

Which rod expands more?

Both rods have the same:

• starting length
• material
• coefficient of expansion

The only difference is the temperature change.

Rod B experiences three times the temperature increase, so it will undergo approximately three times as much linear expansion, provided the temperature range is one over which the linear approximation is suitable.

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Thermal Expansion in Liquids

Liquids also expand when heated.

Unlike solids, liquid particles are not fixed in particular positions. They can move past one another.

As a liquid becomes warmer, its particles generally become more widely separated, increasing the liquid's volume.

This principle is used in liquid-in-glass thermometers.

As the temperature increases:

• the liquid in the bulb expands
• its volume increases
• the liquid rises through the narrow tube

When the temperature decreases, the liquid contracts and the level falls.

Different liquids expand by different amounts for the same temperature change. This is one reason the choice of liquid matters when designing a thermometer.

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Thermal Expansion in Gases

Gases can show very large changes in volume when their temperature changes, particularly when they are free to expand at approximately constant pressure.

Gas particles are already much farther apart than particles in solids or liquids.

When a gas is heated:

• its particles gain kinetic energy
• they move faster
• collisions with the walls of the container become more energetic and frequent
• if the container can expand, the gas can occupy a greater volume

A familiar example is a balloon.

If a flexible balloon containing gas is warmed, its volume may increase. If it is cooled, its volume may decrease.

However, if a gas is trapped inside a rigid sealed container, it cannot simply expand outward. Instead, heating it can cause its pressure to increase.

This distinction is important.

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Comparing Solids, Liquids, and Gases

In general, the effects of heating can be summarized as:

These are general trends. The exact amount of expansion depends on the particular substance and the conditions.

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Different Materials Expand by Different Amounts

Not all materials expand equally.

Suppose equal-length pieces of aluminium, steel, and another material experience the same temperature increase. Their changes in length will generally not be identical.

This happens because different materials have:

• different atomic structures
• different types and strengths of bonding
• different responses to increased particle energy

The coefficient of thermal expansion describes this behaviour quantitatively.

A material with a larger coefficient expands more for the same original length and temperature change.

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Bimetallic Strips

The fact that different materials expand by different amounts can be useful.

A bimetallic strip consists of two different metals bonded together.

When heated:

• one metal expands more than the other
• the two metals cannot separate
• the strip bends

When cooled, it bends back toward its original shape.

Bimetallic strips have been used in devices such as:

• thermostats
• temperature-sensitive switches
• circuit breakers
• older mechanical temperature-control systems

The device works precisely because the two materials have different thermal expansion coefficients.

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Thermal Expansion in Bridges

A bridge may be hundreds or even thousands of metres long.

Although each metre expands only slightly when heated, the total change in length across a long structure can become significant.

Engineers therefore design bridges so that parts of the structure can move safely as temperature changes.

One solution is an expansion joint.

Expansion joints allow sections of a structure to move relative to one another as the materials expand and contract.

Without appropriate engineering allowances, repeated temperature changes could produce large stresses that contribute to:

• bending
• buckling
• cracking
• damage to connections

Expansion joints are used in many structures, including bridges and some sections of buildings and piping systems.

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Thermal Expansion and Railway Tracks

Railway rails become warmer in hot weather and cooler in cold weather.

As their temperature rises, steel tends to expand.

If thermal expansion is strongly restrained, large internal stresses can develop.

Historically, jointed tracks could include small gaps between rail sections. Modern railways also use continuous welded rail, where thermal effects are managed through careful engineering of the rails, fastenings, installation temperature, and track structure rather than simply leaving frequent gaps.

Special rail expansion devices may still be used in locations such as some bridge transitions where substantial relative movement must be accommodated.

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Thermal Expansion of Power Lines

Overhead electrical wires also expand and contract.

On a hot day, the metal conductors expand and become longer. This can cause the wires to sag farther downward.

During colder weather, they contract and become shorter, increasing their tension and reducing the sag.

Engineers must therefore consider the range of temperatures that power lines will experience throughout the year.

If wires were installed too tightly, contraction during very cold conditions could produce excessive tension.

If they were allowed to sag too much, hot conditions could cause clearance problems.

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Heating a Metal Lid

Thermal expansion can even be useful in the kitchen.

Suppose a metal lid is stuck tightly on a glass jar.

Running warm water over the lid can make it easier to open.

Why?

The metal lid expands when heated. Its diameter increases slightly, which can loosen its grip on the jar.

This is a simple everyday application of thermal expansion.

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Hot-Air Balloons

Thermal effects in gases are also important in hot-air balloons.

When air inside the balloon is heated, it expands. Because the balloon is open at the bottom and remains close to atmospheric pressure, some air leaves the balloon.

The warmer air remaining inside is therefore less dense than the cooler surrounding air.

The resulting buoyant force can lift the balloon.

Thermal expansion is therefore connected to changes in density as well as volume.

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Predicting Changes in Dimensions

You can often predict thermal expansion without performing a calculation.

Situation A

A metal rod is heated.

Prediction:

Length increases.

Situation B

The same rod is cooled below its original temperature.

Prediction:

Length decreases.

Situation C

Two rods of the same material experience the same temperature increase, but one is twice as long.

Prediction:

The longer rod undergoes a greater absolute change in length.

Situation D

Two equal-length rods made from different materials experience the same temperature increase.

Prediction:

The material with the larger coefficient of thermal expansion expands more.

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Worked Example: Bridge Expansion

Suppose a steel bridge section is:

$L_0=50.0\text{ m}$

and its coefficient of linear thermal expansion is approximately:

$\alpha=12\times10^{-6}/^\circ\text{C}$

The temperature increases by:

$\Delta T=30^\circ\text{C}$

Use:

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

Substitute:

$\Delta L=(12\times10^{-6})(50.0)(30)$$\Delta L=0.018\text{ m}$

Therefore:

$\Delta L=18\text{ mm}$

The bridge section becomes approximately 18 mm longer.

That may sound small, but structures contain long sections and experience repeated temperature changes. Engineers must allow for these movements rather than assuming a structure remains exactly the same size.

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Worked Example: Cooling

A metal pipe is 10.0 m long.

Its temperature decreases significantly overnight.

Without calculating an exact value, predict what happens.

The temperature decreases, so particle vibrations become less energetic and the average particle separation decreases.

Therefore:

the pipe contracts and becomes slightly shorter.

If the pipe is prevented from contracting, thermal stresses may develop.

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Thermal Expansion Can Be Useful

Thermal expansion is not always a problem.

It can deliberately be used in engineering and technology.

Examples include:

• liquid thermometers
• bimetallic thermostats
• heat-sensitive switches
• fitting metal components together
• loosening metal lids
• shrink-fitting components

For example, a metal ring can be heated so that its diameter increases. It can then be fitted over another object. When it cools, it contracts and forms a tight fit.

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Thermal Expansion Can Cause Problems

Thermal expansion becomes particularly important when a material is not free to change dimensions.

Imagine a long metal beam trapped rigidly between two immovable walls.

When heated, the beam tries to expand.

If it cannot expand freely, large forces and stresses can develop.

This can contribute to:

• deformation
• buckling
• cracking
• structural damage

For this reason, engineers do not simply ask:

“How much will this material expand?”

They also ask:

“What will happen if the material is prevented from expanding?”

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Common Mistakes

“The particles themselves get bigger.”

Usually incorrect.

Thermal expansion mainly occurs because the average separation between particles changes, not because individual atoms suddenly become much larger.

“Heating increases mass.”

Heating an ordinary object does not add more matter to it. Its dimensions can increase while its mass remains essentially unchanged for ordinary classroom purposes.

“Everything expands by the same amount.”

Incorrect.

Different materials have different coefficients of thermal expansion.

“Only solids undergo thermal expansion.”

Incorrect.

Solids, liquids, and gases can all expand when heated.

“Gases always increase in volume when heated.”

Not necessarily.

A gas in a flexible or movable container can expand. A gas trapped in a rigid sealed container cannot significantly increase the container's volume, so its pressure generally rises instead.

“Modern railway tracks simply need gaps everywhere.”

This is an oversimplification.

Modern continuous welded rail is specifically engineered to manage thermal stresses. Expansion devices are used where required by the design and structural conditions.

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Check Your Understanding

1. What normally happens to the dimensions of a solid when it is heated?

2. Explain thermal expansion using the particle model.

3. Do the individual particles become larger when a material expands?

4. Why can thermal expansion be especially important in very long structures?

5. Why are expansion joints used in some bridges?

6. Why do overhead power lines sag more during hot weather?

7. Two equal-length metal rods are heated through the same temperature change. Rod A expands more than Rod B. What does this tell you about the materials?

8. A 2 m aluminium rod and a 10 m aluminium rod undergo the same temperature increase. Which experiences the greater change in length?

9. Why does a bimetallic strip bend when heated?

10. Predict what happens to a metal pipe when its temperature decreases overnight.

11. Why can heating the metal lid of a glass jar make the lid easier to remove?

12. A gas is heated inside a rigid sealed container. Why might its pressure increase rather than its volume increasing significantly?

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Key Terms

• Thermal expansion – increase in a material's dimensions caused by an increase in temperature.
• Thermal contraction – decrease in dimensions caused by a decrease in temperature.
• Coefficient of thermal expansion – measure of how much a material expands for a given temperature change.
• Linear expansion – change in the length of an object due to temperature change.
• Expansion joint – structure designed to accommodate movement caused by expansion and contraction.
• Bimetallic strip – two different metals bonded together that bend when their different rates of expansion cause unequal length changes.
• Kinetic energy – energy associated with particle motion.
• Thermal stress – stress produced when thermal expansion or contraction is restricted.

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Key Takeaways

• Most materials expand when heated and contract when cooled.
• Thermal expansion occurs because heating changes particle motion and their average separation.
• Solids, liquids, and gases can all undergo thermal expansion.
• Gases generally show much larger volume changes than solids when they are free to expand.
• Different materials expand by different amounts because they have different structures, bonding, and thermal expansion coefficients.
• Greater temperature changes generally produce greater dimensional changes.
• Longer objects generally experience larger absolute changes in length for the same material and temperature change.
• Thermal expansion must be considered when designing bridges, railway systems, pipes, power lines, and other structures.
• Differences in thermal expansion can also be useful, as in bimetallic strips and thermostats.
• The particles themselves should not be pictured as simply becoming larger; it is mainly the spacing between particles that changes.