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Notes/Physics/Paper 4/Temperature
CAIEA Level9702§14.1–14.3

Temperature

Thermal energy transfer and thermal equilibrium, thermometric properties and practical thermometers, the kelvin and Celsius scales with absolute zero, and the two energy equations Q = mcΔθ and Q = mL.

115 min read 6 sub-topics
102
question parts
2021–2025 · 32 papers
6 marks
per paper
≈ 6% of the paper
1.8/3
avg difficulty
moderate
#14
most examined
of 16 topics by marks

Temperature is the quiet achiever of Paper 4. Nothing here moves, orbits or radiates — the entire topic runs on one idea: energy. Heat a thing and either its temperature climbs (Q=mcΔθQ = mc\Delta\theta, §04) or its state changes at constant temperature (Q=mLQ = mL, §05). Measure its temperature with anything whose own property shifts smoothly as it warms (§02) — and trust the reading only once the thermometer and the object have settled into thermal equilibrium (§01). The kelvin scale (§03) then rewrites the numbers so that zero really means zero. Two short equations and a handful of word-perfect definitions carry almost every mark.

The bank says this is the softest touching point on the paper: 200 marks across 2021–2025 (yearly haul 34, 29, 37, 43, 57 — about 40 a year) from 102 question parts in 32 paper sittings, at a mean difficulty of 1.82, the lowest of any core A2 topic. Ranked 14th by marks it may look minor, but the trend matters more than the rank: the total has grown every year since 2022, and 2025 was the heaviest sitting ever recorded — 57 marks, roughly 14 on every variant paper you could sit. The marks are cheap because so many of them are recall: definitions of specific heat capacity, specific latent heat and thermal equilibrium appear almost every sitting, worth 1–2 marks each, awarded clause by clause for word-perfect sentences.

The route through is: §01 thermal energy transfer and thermal equilibrium — §02 thermometric properties and the thermometers built on them — §03 the kelvin and Celsius scales and absolute zero — §04 specific heat capacity Q=mcΔθQ = mc\Delta\theta — §05 specific latent heat Q=mLQ = mL, heating curves and the molecular story behind both — and §06 how the examiner marks it. You need AS electrical power (P=VIP = VI, E=PtE = Pt) throughout §04 and §05, and nothing else beyond careful arithmetic.

Before you start you should be able to

  • Use electrical energy and power fluently: E=PtE = Pt and P=VIP = VI, converting minutes to seconds first (AS Electricity notes)

  • Convert grams to kilograms without thinking: 24.0 g = 0.0240 kg, 37.0 g = 0.0370 kg — half the arithmetic errors in this topic are unit mismatches

  • Substitute into and rearrange a three-symbol equation, carrying units through every line

  • Recall from the AS kinetic model that temperature reflects the average random kinetic energy of the molecules of a substance

  • Apply conservation of energy to a closed system: energy lost by the hot part = energy gained by the cold part (AS Work-Energy-Power note)

By the end of this page you can

  • Understand that (thermal) energy is transferred from a region of higher temperature to a region of lower temperature, and define thermal equilibrium: equal temperatures and no net transfer of thermal energy

  • Understand that a physical property that varies with temperature may be used to measure temperature, and state examples: density of a liquid, volume of a gas at constant pressure, resistance of a metal, e.m.f. of a thermocouple

  • Judge whether a thermometric property is suitable (varies continuously, uniquely and preferably linearly), and choose a practical thermometer to match a situation — platinum for precision, thermocouple for speed, gas thermometer for calibration

  • Understand that the thermodynamic temperature scale does not depend on the property of any particular substance, and explain why a liquid-in-glass laboratory thermometer therefore does not measure it

  • Recall and use T/K=θ/∘C+273.15T/\text{K} = \theta/^\circ\text{C} + 273.15, treat temperature differences identically in both units, and state absolute zero as 0 K = −273.15 °C

  • Define specific heat capacity word-perfectly and use Q=mcΔθQ = mc\Delta\theta, including electrical heating (E=PtE = Pt) and beaker/container corrections in calorimetry

  • Define specific latent heat word-perfectly, distinguish fusion from vaporisation, use Q=mLQ = mL, and combine it with Q=mcΔθQ = mc\Delta\theta in cooling–condensing and melting–warming chains

  • Explain phase changes in terms of molecular energies — potential energy rises while kinetic energy (and hence temperature) stays constant — and explain, conceptually, why a gas has a larger specific heat capacity at constant pressure than at constant volume

01

Thermal energy transfer and thermal equilibrium

Syllabus requirement · §14.1

“

understand that (thermal) energy is transferred from a region of higher temperature to a region of lower temperature; understand that regions of equal temperature are in thermal equilibrium

”

Energy has one fixed itinerary: hot → cold

Wrap your hands round a mug of tea and they warm up; hold an ice cube and they cool down. In both cases something invisible crossed the boundary — thermal energy — and in both cases it moved the same way: from the hotter region to the cooler one. Never the reverse, never by accident. The temperature difference is what drives the transfer, exactly as a height difference drives a ball downhill: bigger difference, faster flow; zero difference, no drive at all. That is the whole of the first syllabus statement, and mark schemes restate it constantly:

(thermal) energy is transferred from a region of higher temperature to a region of lower temperature.

The second statement defines the destination of that journey. Leave the mug standing and the tea cools, the air warms, and eventually everything in the room shares one temperature. The mug and the air are then in thermal equilibrium. Two clauses buy this definition — and both are examined, separately, in every recent sitting (9702/42 F/M 2025 Q3(a)(i), 9702/42 O/N 2025 Q3(a), 9702/44 M/J 2025 Q2(a)):

objects in thermal equilibrium are at the same temperature (B1) …and there is no net transfer of thermal energy between them (B1).

The word doing the quiet work is net. Even at equilibrium, molecules on both sides of the boundary keep colliding and passing energy back and forth — but the two directions carry equal amounts, so the exchanges cancel. Nothing observable changes. "No energy passes at all" would be wrong physics; "no net transfer" is the sentence that scores.

BEFORE — different temperatures80 °Chot20 °Ccoldthermal energyflows hot → coldAFTER — thermal equilibrium50 °C50 °Cequal both ways…NO net transferequilibrium needs BOTH clauses1  same temperature2  no net transfer of thermal energymark schemes pay one B1 for each —either half alone caps you at 1 of 2.Equilibrium is not frozen stillness:molecules still pass energy both waysat the boundary — the two rates areequal, so nothing changes any more.

Thermal contact before and after. While a temperature difference exists, energy flows from hot to cold; once the temperatures match, equal two-way exchanges cancel and the state freezes — that frozen state is thermal equilibrium.

How any thermometer exploits this

Every temperature measurement in this topic leans on §01 directly. Place a thermometer in contact with an object: if their temperatures differ, thermal energy transfers between them until the thermometer and the object reach the same temperature — thermal equilibrium. At that instant the thermometer's reading is the object's temperature, because they share it.

This quietly explains a practical fact you will meet again in §02: a thermometer with a large heat capacity — how much energy it must absorb to warm by one degree (made precise as C=mcC = mc in §04) — soaks up a lot of energy on its way to equilibrium, perturbing the object and taking ages to settle — while a tiny thermocouple junction barely disturbs anything and settles almost instantly. Equilibrium is not just a definition here; it is the operating principle of every instrument in §02.

One sentence to carry

Thermal energy flows from higher temperature to lower temperature; regions of equal temperature are in thermal equilibrium — same temperature, and no net transfer of thermal energy between them.

Common mistakes

  • Defining thermal equilibrium as only "the objects are at the same temperature".

    Both clauses: same temperature AND no net transfer of thermal energy between them.

    The scheme pays B1 + B1 (9702/42 F/M 2025 Q3(a)(i)) — one clause per mark. Half the sentence caps you at half the marks.

  • Saying that at equilibrium "no thermal energy passes between the objects".

    Molecules still exchange energy in both directions; it is the NET transfer that is zero.

    Equilibrium is dynamic, not frozen. Dropping the word 'net' claims energy flow stops entirely — wrong physics, and it can cost the mark in 'explain' variants.

  • Deciding the direction of flow from which object has MORE internal energy.

    The direction is set by the TEMPERATURE difference alone: hot → cold.

    A bath of lukewarm water holds far more internal energy than a white-hot spark, yet energy flows from the spark into the water — temperature, not total energy, drives transfer.

Your turn

The two-clause definition as the examiner asks it, the single-clause variant, then the concept put to work on a real thermometer.

  1. 19702/42 F/M 2025 Q3(a)(i)2 marks

    P and Q are two objects in thermal contact. P and Q are in thermal equilibrium. State what is meant by thermal equilibrium.

    Stuck? Show hint

    Two separate statements: one about temperature, one about energy transfer.

    Show solution
    1. 1

      (P and Q are at the) same temperature (B1);

      Clause one — the state both objects share.

    2. 2

      no net transfer of thermal energy between P and Q (B1).

      Clause two — the consequence. Remember 'net': two-way exchanges still happen, they merely balance.

    Answer

    They are at the same temperature as each other, with no net transfer of thermal energy between them.

  2. 29702/41 M/J 2023 Q3(a)1 mark

    State the reason why two objects that are at the same temperature are described as being in thermal equilibrium.

    Stuck? Show hint

    Same temperature ⇒ which energy quantity is zero?

    Show solution
    1. 1

      (No) net thermal energy is transferred between them (B1).

      This is the reverse-direction question: given equal temperatures, name the defining consequence. One mark, one phrase.

    Answer

    Because no net thermal energy is transferred between them.

  3. 33 marks

    A mercury-in-glass thermometer standing in a room at 19 °C is placed into a beaker of water at 62 °C. Using the idea of thermal equilibrium, describe and explain how the thermometer reading behaves over the next few minutes.

    Stuck? Show hint

    Three beats: which way does energy flow at first, what does the mercury physically do, and what condition stops the change?

    Show solution
    1. 1

      At first the water is hotter, so thermal energy transfers from the water to the thermometer (hot → cold).

      The temperature difference drives the flow — the syllabus's first statement in action.

    2. 2

      The warming mercury expands and rises up the capillary, so the reading increases.

      The property that varies with temperature (here density/volume) converts energy flow into a readable change — the bridge to §02.

    3. 3

      When the mercury reaches the water's temperature, both are in thermal equilibrium: the same temperature, so no net transfer remains, and the reading becomes steady at 62 °C.

      Equilibrium is what makes the final reading trustworthy — it equals the water's temperature because they now share it.

    Answer

    Energy flows water → thermometer until both reach the same temperature; the mercury expands up the stem as it warms; the reading rises steadily, then holds constant at 62 °C once thermal equilibrium (same temperature, no net transfer) is reached.

Practise thermal equilibrium questionsReal past-paper questions · Thermal energy transfer and thermal equilibrium

The rest of this note

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Can you do all of these?

  • Quote thermal equilibrium with BOTH clauses: same temperature AND no net transfer of thermal energy between them

  • Quote specific heat capacity with BOTH clauses: (thermal) energy per unit mass AND per unit change in temperature

  • Quote specific latent heat with BOTH clauses: (thermal) energy per unit mass AND to change state at constant temperature

  • Name the four thermometric properties on demand: density of a liquid, volume of a gas at constant pressure, resistance of a metal, e.m.f. of a thermocouple

  • Judge a thermometric property on three counts: continuous variation, a unique value at each temperature, preferably linear

  • Match thermometer to job: platinum = precise but slow (large heat capacity); thermocouple = fast (tiny thermal mass); constant-volume gas = bulky and slow but calibrates other laboratory thermometers

  • Explain why a liquid-in-glass thermometer does not measure thermodynamic temperature: it depends on the properties of one real substance (and 0 °C is not absolute zero)

  • State absolute zero both ways: 0 K and −273.15 °C

  • Add 273.15 only to absolute temperatures, never to Δθ — a 223 K cooling span is 223 °C too

  • In calorimetry, write the energy-balance line (lost = gained) before substituting anything, and fold the container's mcΔθ in as its own term

  • Distinguish heat capacity mc (object, J K⁻¹) from specific heat capacity c (material, J kg⁻¹ K⁻¹) before comparing two bodies

  • Give the molecular account of boiling: separation increases, potential energy rises, kinetic energy unchanged — so temperature unchanged

Now do the questions
102 real Paper 4 parts from 2021–2025, sorted by difficulty, with mark schemes
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