Conduction

What Is Conduction?

Conduction is the transfer of thermal energy through a material by interactions between neighboring particles, without the material as a whole moving from one place to another.

When one part of an object is heated, particles in that region gain energy. They vibrate or move more rapidly and interact with nearby particles, transferring energy through the material.

The overall direction of thermal energy transfer is:

higher temperature → lower temperature

For example, if one end of a metal rod is placed in a flame, the heated end becomes hot first. Over time, thermal energy is conducted along the rod, causing the other end to become warmer.

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Conduction at the Particle Level

In a solid, particles are packed closely together in fixed positions.

They cannot move freely through the material, but they can vibrate about their equilibrium positions.

When part of a solid is heated:

• particles in the hotter region gain kinetic energy
• their vibrations become more energetic
• they interact with neighboring particles
• energy is transferred to those neighboring particles
• the process continues through the material

As a result, thermal energy spreads from warmer regions toward cooler regions.

The particles themselves do not travel from the hot end to the cold end. It is the energy that is transferred.

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Why Conduction Is Effective in Solids

Conduction can occur in solids, liquids and gases, but it is generally most effective in solids.

In solids, particles are:

• closely packed
• strongly interacting
• able to transfer energy efficiently to neighboring particles

In gases, particles are much farther apart. Collisions occur less frequently, so conduction is generally much slower.

This is one reason trapped air can be a useful thermal insulator.

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Conduction in Metals

Metals are particularly effective thermal conductors.

Energy transfer in a metal occurs through both:

• vibrations of the metal lattice
• movement and collisions of delocalized electrons

Metals contain electrons that can move relatively freely through the material.

At the hot end of a metal object, these electrons gain energy. They move through the metal and transfer energy through interactions with other electrons and ions.

This makes thermal conduction in many metals much faster than in non-metallic solids.

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Why Metals Feel Cold

Touch a metal object and a wooden object that have been sitting in the same room.

They may both be at exactly the same temperature, yet the metal often feels colder.

Why?

Your hand is warmer than both objects.

Thermal energy therefore transfers:

hand → object

Metal conducts this energy away from the contact point quickly, so your skin loses thermal energy rapidly.

Wood transfers the energy away much more slowly.

Therefore, the metal feels colder even though it may be at the same temperature as the wood.

This demonstrates an important idea:

How hot or cold something feels depends partly on the rate of heat transfer, not simply its temperature.

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Thermal Conductors

A thermal conductor is a material through which thermal energy can be transferred relatively easily.

Many metals are excellent thermal conductors.

Examples include:

• copper
• aluminium
• silver
• iron
• steel

Copper is particularly useful because it combines high thermal conductivity with practical properties such as durability and workability.

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Thermal Insulators

A thermal insulator is a material that transfers thermal energy relatively slowly.

Examples include:

• air
• wood
• plastic
• rubber
• foam
• wool
• fibreglass
• cork

These materials have low thermal conductivity.

Insulators are useful whenever we want to reduce the rate of heat transfer.

For example, the plastic handle on a cooking pot reduces conduction from the hot metal pot to a person's hand.

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Thermal Conductivity

The ability of a material to conduct thermal energy is described by its thermal conductivity.

The symbol commonly used for thermal conductivity is:

k

Its SI unit is:

W/(m·K)

A material with a large value of k is a good thermal conductor.

A material with a small value of k is a good thermal insulator.

Approximate values illustrate the enormous differences between materials:

Exact values vary with temperature, composition and other conditions.

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Factors Affecting the Rate of Conduction

The rate at which thermal energy is conducted depends on several factors.

Temperature Difference

A greater temperature difference generally produces a greater rate of energy transfer.

For example, a metal rod with one end at 200°C and the other at 20°C will initially conduct energy more rapidly than the same rod with its ends at 30°C and 20°C.

Thermal Conductivity

Materials with larger thermal conductivity transfer energy more rapidly.

larger k → faster conduction

Cross-Sectional Area

A thicker piece of material provides a larger area through which energy can be transferred.

larger area → faster conduction

Thickness or Length

Increasing the distance through which thermal energy must travel reduces the rate of conduction.

greater thickness → slower conduction

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The Conduction Equation

For steady conduction through a flat material, the rate of thermal energy transfer can be approximated by:

P = kAΔT/L

where:

• P = rate of energy transfer, in W
• k = thermal conductivity, in W/(m·K)
• A = cross-sectional area, in m²
• ΔT = temperature difference, in K or °C
• L = thickness of the material, in m

This equation shows why thick layers of low-conductivity materials are effective insulation.

Increasing L decreases the rate of heat transfer.

Decreasing k also decreases the rate of heat transfer.

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Worked Example

A wall has:

k = 0.50 W/(m·K)

A = 10 m²

L = 0.20 m

The temperature difference between its two sides is:

ΔT = 20°C

Calculate the rate of thermal energy transfer through the wall.

Use:

P = kAΔT/L

Substitute:

P = (0.50 × 10 × 20) / 0.20

P = 500 W

Therefore:

P = 500 W

Thermal energy is being conducted through the wall at a rate of 500 J every second.

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Cooking and Conduction

Cookware demonstrates how engineers use both conductors and insulators in the same object.

The base of a saucepan is usually made from metal because the base needs to transfer energy efficiently:

stove → saucepan → food

Aluminium and copper are particularly effective for spreading thermal energy across cookware.

The handle has a different purpose.

We want to reduce:

hot pan → hand

Therefore, handles may be made from materials such as plastic, silicone or wood.

The same object therefore uses:

conductor where fast heat transfer is useful

and:

insulator where heat transfer should be reduced

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Building Insulation

Buildings lose thermal energy through walls, windows, roofs and floors.

Insulation reduces this transfer.

Common insulating materials include:

• fibreglass
• mineral wool
• foam
• cellulose
• trapped air

Many insulation materials contain numerous small pockets of air.

Air has very low thermal conductivity, so trapping it reduces conduction.

Insulation does not completely stop energy transfer. It reduces the rate at which thermal energy is conducted.

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Double-Glazed Windows

Double-glazed windows contain two sheets of glass separated by a gap.

The gap contains air or another gas.

Because gases have relatively low thermal conductivity, the gap reduces conduction between the inside and outside of the building.

Some high-performance windows use gases such as argon because they can provide better insulation than ordinary air.

The principle is:

trapped low-conductivity gas → reduced thermal conduction

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Clothing and Conduction

Clothing does not normally keep you warm by producing thermal energy.

Instead, clothing reduces the rate at which your body loses energy to its surroundings.

Materials such as:

• wool
• fleece
• down
• synthetic insulation

trap layers or pockets of air.

Because air is a poor conductor, these trapped air pockets reduce thermal conduction.

This is why several layers of clothing can be more effective than one thin layer.

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Vacuum Flasks

A vacuum flask is designed to reduce several forms of heat transfer.

The space between its walls contains very little matter.

Because conduction requires particles to transfer energy, removing most of the particles dramatically reduces conduction.

A vacuum also prevents convection across the gap.

Reflective surfaces are often added to reduce thermal radiation.

This makes vacuum flasks useful for keeping hot substances hot and cold substances cold.

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Heat Sinks

Sometimes we want conduction to happen as rapidly as possible.

Electronic components such as computer processors generate thermal energy during operation.

A heat sink is usually made from a highly conductive metal such as aluminium or copper.

Thermal energy is conducted:

processor → heat sink

The heat sink then transfers energy to the surrounding air.

Fins increase the surface area, helping energy transfer from the heat sink to the surroundings.

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Conduction in Different States of Matter

Solids

Conduction is generally most effective because particles are closely packed.

Metals are particularly effective because mobile electrons also transfer energy.

Liquids

Conduction occurs through particle interactions, but liquids often transfer substantial thermal energy through convection as well.

Gases

Gases are generally poor conductors because their particles are widely separated.

However, gases can transfer energy effectively through convection if they are free to circulate.

This explains why insulation works best when air is trapped rather than allowed to move freely.

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Conduction vs Convection

These processes should not be confused.

Conduction:

Energy is transferred through particle interactions without bulk movement of the material.

Convection:

Energy is transferred by the bulk movement of a fluid.

Consider a pot of water on a stove.

Energy conducts:

stove → metal pot

Energy then conducts:

metal pot → nearby water

Movement of the water can then establish convection currents that distribute energy throughout the liquid.

Multiple heat-transfer processes can therefore occur at the same time.

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Choosing Materials for Different Applications

There is no material that is always "better."

The correct material depends on whether we want thermal energy to move quickly or slowly.

Engineers therefore consider thermal conductivity when selecting materials.

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Common Mistakes

Mistake: "Conduction means particles move from the hot side to the cold side."
The particles in a solid mainly remain in their positions. Energy is transferred through interactions and vibrations.

Mistake: "Only solids conduct heat."
Conduction occurs in solids, liquids and gases, although its effectiveness differs greatly.

Mistake: "Insulators do not conduct any energy."
Insulators still conduct thermal energy, but at a much lower rate.

Mistake: "Metal feels cold because its temperature is lower."
A metal and wooden object in the same room may have the same temperature. Metal often feels colder because it removes thermal energy from your hand more quickly.

Mistake: "Air is always a good insulator."
Air is most effective when it is trapped. If air can circulate, convection can increase energy transfer.

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Key Terms

Conduction — transfer of thermal energy through interactions between neighboring particles without bulk movement of the material.

Thermal conductor — a material that transfers thermal energy relatively easily.

Thermal insulator — a material that transfers thermal energy relatively slowly.

Thermal conductivity — a measure of how effectively a material conducts thermal energy.

Delocalized electrons — mobile electrons in metals that help transfer thermal energy rapidly.

Temperature gradient — change in temperature with distance through a material.

Insulation — material used to reduce the rate of thermal energy transfer.

Heat sink — a conductive component designed to transfer thermal energy away from another object.

Vacuum — a region containing very little matter, greatly reducing conduction and convection.

Steady-state conduction — a condition in which the temperature distribution remains constant while energy continues to transfer through a material.

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Key Takeaways

• Conduction transfers thermal energy through interactions between particles.
• Net thermal energy moves from regions of higher temperature to lower temperature.
• Solids generally conduct better than gases because their particles are much more closely packed.
• Metals are particularly good conductors because mobile electrons help transfer energy.
• Copper and aluminium have high thermal conductivity.
• Air, foam, wood and many plastics have low thermal conductivity.
• Thermal insulators reduce heat transfer; they do not completely prevent it.
• Greater temperature difference and larger area generally increase the rate of conduction.
• Greater thickness reduces the rate of conduction.
• Trapped air provides useful insulation because air has low thermal conductivity.
• Engineers use conductors when rapid energy transfer is desirable and insulators when energy transfer should be reduced.
• Everyday applications include cookware, building insulation, clothing, vacuum flasks and electronic heat sinks.

Check Your Understanding

1. Describe conduction using the particle model.
2. Why is conduction generally more effective in solids than in gases?
3. Why are metals particularly good thermal conductors?
4. Explain why a metal object may feel colder than a wooden object even when both are at the same temperature.
5. Why are saucepan bases often metal while their handles may be plastic?
6. Explain why trapped air is useful in building insulation.
7. What happens to the rate of conduction if the thickness of an insulating wall increases?
8. A material has a very high thermal conductivity. Would it be suitable for an oven glove? Explain.
9. Calculate the rate of conduction through a material with k = 0.20 W/(m·K), A = 5.0 m², ΔT = 15°C and L = 0.10 m.
10. Explain why aluminium or copper is commonly used in electronic heat sinks.