The big idea: Thermal energy is always on the move from a hotter place to a colder one. It can travel in three ways: conduction, convection and radiation.
You feel it every day
- Wrap your hands round a hot mug and they warm up.
- Steam rises off the top.
- You feel a fire's glow from across the room.
- The three ways differ in what actually moves — and whether any material is needed at all.
| Mechanism | What moves | Needs a material? | Everyday example |
|---|---|---|---|
| Conduction | energy passes along, particles stay put | Yes — best in solids (esp. metals) | a metal spoon's handle getting hot |
| Convection | the hot fluid itself rises and circulates | Yes — only in fluids (liquids/gases) | warm air rising off a radiator |
| Radiation | infrared waves (no particles needed) | No — even works through a vacuum | the Sun's heat reaching Earth |
Spot the difference: Conduction = energy passed particle-to-particle (the particles stay put).
Convection = the hot fluid itself moves and carries the energy.
Radiation = infrared waves — the only one that crosses empty space (a vacuum).
Why convection happens
Convection in a star: In the outer layers of the Sun, plasma near the hot interior expands, becomes less dense and rises; near the cooler surface it becomes denser and sinks. The rising and sinking cells carry energy outwards.
No particles, no conduction: Conduction and convection both need particles. High in the atmosphere the air is so thin that very little energy is conducted away, and the near-vacuum between the walls of a vacuum flask stops both. Only radiation crosses a vacuum.
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Conduction passes energy through a material from particle to particle.
How conduction works
- In a solid, faster-vibrating hot particles jostle their cooler neighbours, passing energy along.
- In a metal, free-moving electrons carry it too — which is why metals conduct so well.
The data booklet gives an equation for how fast heat flows by conduction through a flat slab:
- rate of heat flow — energy transferred each second (W, i.e. J s⁻¹)
- thermal conductivity of the material (W m⁻¹ K⁻¹)
- cross-sectional area the heat flows through (m²)
- temperature difference across the slab (K, or °C — a difference is the same in both)
- thickness of the slab (m)
The minus sign in the booklet: The booklet writes ΔQ/Δt = −kA ΔT/Δx. The minus sign only says that energy flows down the temperature gradient, from hot to cold. For a size, use kAΔT/Δx with ΔT positive.
What makes conduction faster?: Bigger k, bigger area A, or a bigger temperature difference ΔT → faster heat flow.
A thicker slab (bigger Δx) → slower heat flow. Δx is on the bottom, so rate ∝ 1 ÷ thickness.
A glass window has area 2.0 m², thickness 4.0 × 10⁻³ m, and thermal conductivity k = 0.80 W m⁻¹ K⁻¹. Inside is 21 °C, outside is 5 °C. Find the rate at which heat conducts through it.
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How the rate scales: Rate ∝ A, and for a round rod A = πd²/4, so the rate ∝ d²: twice the diameter, four times the rate.
Rate ∝ 1/Δx: twice the thickness, half the rate.
Two bars joined end to end: With the sides insulated, the same rate of energy flows through both bars, so k₁A(T₁ − T)/x = k₂A(T − T₂)/x for the joint temperature T.
A copper bar (k = 8 units) joined to an equal steel bar (k = 1 unit), ends at 80 °C and 20 °C: 8(80 − T) = T − 20, so T ≈ 73 °C. Most of the temperature drop is across the poor conductor.
Energy is conducted at 2.0 W through a block of ice 0.10 m thick with an area of 0.060 m² (k = 2.2 W m⁻¹ K⁻¹). Its top is at −5.0 °C. Estimate the temperature of its bottom face.
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How this is tested — heat transfer shows up on both papers:
Paper 1A / short answer
- Describe the conduction mechanism.
- Or outline why a cooling graph's gradient flattens.
Paper 2
- Estimate the rate of heat flow through a wall, ice layer or window with ΔQ/Δt = kA·ΔT/Δx — and state the unit (W).
The classic trap: Explain how the rate changes as a layer gets thicker — Δx is on the bottom, so the rate falls (rate ∝ 1 ÷ thickness).
Thicker layer ⇒ slower conduction: In ΔQ/Δt = kA·ΔT/Δx, the thickness Δx is in the denominator.
So if everything else stays the same, doubling the thickness halves the rate of heat flow: rate ∝ 1 ÷ Δx.
The words to know
| Word | What it means |
|---|---|
| Conduction | Energy passed by collisions between neighbouring particles (and free electrons in metals) |
| Convection | A fluid moves because of density differences, carrying energy with it |
| Thermal radiation | Energy carried by electromagnetic waves from a surface; needs no material |
| Thermal conductivity k | How well a material conducts (W m⁻¹ K⁻¹) |
| Temperature gradient | ΔT ÷ Δx across a layer (K m⁻¹) |
A frozen lake loses heat by conduction up through its ice. The ice has conductivity k = 2.2 W m⁻¹ K⁻¹. The water below is at 0 °C and the top of the ice is at −10 °C. When the ice is 5.0 × 10⁻² m thick, find the rate of heat loss per square metre (take A = 1.0 m²), then state what happens to this rate as the ice gets thicker.
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