Key Idea: Topic 2.1 is about how thermal energy is stored in matter and how it moves from hot to cold. It ties together four ideas: what internal energy is (and the particle model), how much energy a temperature change needs (Q = mcΔT), the hidden energy of a state change (Q = mL), and the three ways heat travels — conduction, convection and radiation. It is examined on Paper 1A (quick MCQs — define internal energy, compare densities, spot which formula a heating-curve part needs) and on Paper 2 (rearrange Q = mcΔT, energy-balance/calorimetry with latent heat, and the conduction rate ΔQ/Δt = kA·ΔT/Δx with its unit, the watt).
📐 Key formulas (all four are given)
Every equation in this topic is given in the data booklet — so you do not memorise them, but you must know which one to reach for and how to rearrange it.
- density (kg m⁻³)
- mass (kg)
- volume (m³)
- thermal energy added or removed (J)
- mass (kg)
- specific heat capacity (J kg⁻¹ K⁻¹)
- temperature change (K, or °C — same size)
- thermal energy transferred (J)
- mass changing state (kg)
- specific latent heat (J kg⁻¹)
- rate of heat flow — energy 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)
- thickness of the slab (m)
🧭 Which equation, and when?
The single most-tested decision in this topic: is the temperature changing (a slope) or is the state changing (a flat plateau at constant temperature)?
| Situation | What is changing | Equation to use |
|---|---|---|
| Warming or cooling a substance | Temperature (a sloping line) | Q = mcΔT |
| Melting / freezing, boiling / condensing | State, at constant temperature (a flat line) | Q = mL |
| Comparing how tightly matter is packed | Mass per volume | ρ = m/V |
| Heat conducting through a wall, window or ice | Rate of heat flow (per second) | ΔQ/Δt = kA·ΔT/Δx |
🔥 The three ways heat travels
| Mechanism | What actually 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 | warm air rising off a radiator |
| Radiation | infrared waves (no particles needed) | No — crosses a vacuum | the Sun's heat reaching Earth |
🧊 Latent heats — fusion vs vaporisation
| Quantity | State change it covers | Relative size |
|---|---|---|
| Latent heat of fusion (Lf) | melting ↔ freezing | smaller — the shorter plateau |
| Latent heat of vaporisation (Lv) | boiling ↔ condensing | much larger — the longer plateau |
✍️ IB-style worked examples
A heater warms 0.40 kg of water from 15 °C to 65 °C. The specific heat capacity of water is 4200 J kg⁻¹ K⁻¹. Calculate the thermal energy supplied.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
0.20 kg of ice at −10 °C is heated until it is water at 0 °C. Take c(ice) = 2.1 × 10³ J kg⁻¹ K⁻¹ and L(fusion) = 3.3 × 10⁵ J kg⁻¹. Find the total energy needed.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
Heat conducts through a wall of area 5.0 m² and thickness 0.25 m, with k = 0.60 W m⁻¹ K⁻¹. Inside is 21 °C and outside is 6 °C. Calculate the rate of heat loss, give its unit, and state what happens to it if the wall is made twice as thick.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
0.15 kg of water at 40 °C is poured onto ice already at 0 °C; the water cools to 0 °C and some ice melts. Take c(water) = 4.2 × 10³ J kg⁻¹ K⁻¹ and L(fusion) = 3.3 × 10⁵ J kg⁻¹. Assuming no energy is lost, find the mass of ice melted.
🔒 Model answer plan
See the mark-by-mark plan — for / against / judgement, with marking guidance — in study mode.
✅ Quick self-check
Tap each card to reveal the answer.
What are the two parts of internal energy? Total random kinetic energy of the particles (sets the temperature) + total intermolecular potential energy (depends on spacing).
What does ΔT mean in Q = mcΔT? The temperature change (final − start), not the actual temperature. A change of 1 K equals a change of 1 °C, so never convert.
Slope vs flat on a heating curve — which formula? Sloping (temperature changing) → Q = mcΔT. Flat (state changing at constant temperature) → Q = mL.
Why is the boiling plateau longer than the melting one? For one substance Lv ≫ Lf: vaporising fully separates the particles, needing far more energy than melting.
Which heat transfer works through a vacuum? Radiation only — it travels as infrared waves and needs no material; conduction and convection both need particles.
A wall is made twice as thick. What happens to the conduction rate? It halves — Δx is on the bottom of ΔQ/Δt = kA·ΔT/Δx, so rate ∝ 1 ÷ thickness.
🎯 Highest-yield exam reminders
Exam Tips
- Internal energy = random KE + intermolecular PE — always name BOTH parts; never forget the PE. Temperature tracks only the KE part.
- ΔT in Q = mcΔT is a temperature CHANGE (final − start), and a change in K equals a change in °C — never convert ΔT to kelvin.
- Decide slope vs flat: temperature changing ⇒ Q = mcΔT; state changing at constant temperature ⇒ Q = mL (no ΔT). Multi-step problems need one Q-term per step.
- Lv ≫ Lf for the same substance, so boiling needs much more energy than melting — that is the longer plateau and the reason steam burns are worse than hot-water burns.
- Calorimetry with no losses: energy lost by the hot part = energy gained by the cold part. A measured value is usually 'off' because heat escapes to the surroundings or the container.
- The conduction rate ΔQ/Δt = kA·ΔT/Δx is a RATE — its unit is the watt (W). Work out ΔT first; thickness Δx is on the bottom, so a thicker layer conducts more slowly (rate ∝ 1 ÷ thickness).
- A cooling curve flattens because the temperature difference driving the heat loss keeps shrinking — smaller difference, smaller gradient. Only radiation crosses a vacuum.