Know that there are many solids that conduct thermal energy better than thermal insulators but do so less well than good thermal conductors

2.3.1 Conduction

Objective

To understand that all solids conduct thermal energy, but the rate varies widely:

• Good conductors (metals) ≫ moderate conductors (most non‑metals) ≫ thermal insulators.
• The rate is quantified by the material’s thermal conductivity \(k\) (W·m⁻¹·K⁻¹).

What is Thermal Conduction?

• Transfer of kinetic energy between neighbouring particles of a material without any overall movement of the material itself.
• Energy always flows from the hotter region to the cooler region.
• In solids the particles are so close together that the transfer occurs by direct collisions (phonons) or, in metals, by the rapid motion of free electrons.

Conduction in Different States of Matter

Solids – particles are tightly packed; heat is carried mainly by lattice vibrations (phonons). In metals a sea of free electrons adds an extremely efficient transport channel.

Liquids and gases – particles are farther apart, collisions are less frequent and the mean free path is larger. The dominant mechanism is molecular diffusion, giving thermal conductivities that are orders of magnitude lower than in solids.

Example: a metal spoon becomes hot quickly when left in boiling water, whereas the water itself transfers heat only slowly to the spoon’s handle.

Fourier’s Law (steady‑state, one‑dimensional conduction)

The rate of heat transfer through a uniform slab is

\[

Q = \frac{k\,A\,\Delta T}{d}

\]

• Q – heat transferred per unit time (W)
• k – thermal conductivity of the material (W·m⁻¹·K⁻¹)
• A – cross‑sectional area normal to the heat flow (m²)
• ΔT – temperature difference between the two faces (K)
• d – thickness of the material (m)

Only valid when the temperature gradient is constant (steady state) and heat flows in one dimension.

Factors Influencing the Rate of Conduction

1. Material (thermal conductivity k) – intrinsic property; higher k → faster heat flow.
2. Cross‑sectional area (A) – larger area provides more parallel pathways for heat.
3. Thickness (d) – a thicker slab offers a longer path, reducing the rate.
4. Temperature gradient (ΔT) – a larger difference creates a stronger driving force.

Types of Solids – Linking the Particle Model to Conductivity

• Good thermal conductors (metals) – contain a sea of free electrons that move rapidly and transport kinetic energy efficiently.
• Moderate conductors (most non‑metallic solids) – heat is carried mainly by phonons. Imperfections, grain boundaries and complex unit cells scatter phonons, limiting the rate.
• Thermal insulators – very strong phonon scattering and the absence of free electrons give a very low k.

This explanation directly follows the particle‑model concepts described in syllabus section 2.1.2.

Comparative Table of Thermal Conductivity (k)

Why Some Solids Are Only Moderate Conductors

In non‑metallic solids the dominant heat‑carrying agents are phonons. Their propagation is hindered by:

• Crystal imperfections and grain boundaries.
• Complex unit cells that cause frequent scattering.
• Complete absence of a free‑electron sea.

These factors reduce the effective thermal conductivity, placing such materials between metals and true insulators.

Practical Implications (exam‑style focus)

• Cooking utensils – metal pans heat quickly (good conductors); handles are made of wood or polymer to limit heat transfer to the hand. Exam question: “Explain why a wooden handle is preferred on a metal saucepan.”
• Building construction – bricks or concrete (moderate conductors) provide structural strength, while layers of foam or mineral wool (insulators) reduce heat loss.
• Electronics – aluminium or copper heat sinks draw heat away from chips, whereas the outer casing may be a polymer for safety and tactile comfort.

Safety Box

Practical Activity – Demonstrating Conductivity Differences (AO3)

Key Points to Remember

• All solids conduct heat; the magnitude is expressed by the thermal conductivity \(k\).
• Metals are the best conductors because free electrons transport energy very efficiently.
• Non‑metallic solids are moderate conductors – phonons carry heat, but scattering limits the rate.
• Insulators have very low \(k\) due to strong phonon scattering and lack of free electrons.
• Fourier’s law (steady‑state, one‑dimensional) links the four controllable factors \(k, A, d, ΔT\) directly to the heat‑transfer rate.

Check Your Understanding

1. Explain why a glass window lets heat pass more readily than a wooden door.
2. Given a copper rod (\(k = 400\) W·m⁻¹·K⁻¹) and a glass rod (\(k = 1.2\) W·m⁻¹·K⁻¹) of identical dimensions, which transfers heat faster? By what factor?
3. Identify a real‑world situation where a material with moderate conductivity is preferred over a good conductor, and justify the choice.
4. Describe how you could use the activity above to estimate the relative values of \(k\) for copper and wood.
5. Convert the thermal conductivity of copper from \(400\) W·m⁻¹·K⁻¹ to mW·cm⁻¹·°C⁻¹. (Recall that 1 W = 1000 mW and 1 m = 100 cm.)

Link to Other Modes of Heat Transfer

In most practical situations conduction occurs together with convection and/or radiation. For example, a metal pot on a stove transfers heat to the water by conduction through the metal, while the water circulates (convection) and the surface loses heat to the surroundings by radiation. Understanding the dominant mode helps choose appropriate materials and designs.