Close the Notes. Start the Clock.

Sections 1 to 13 taught you this chapter — temperature against heat, the scales and the gas thermometer, linear, areal and volume expansion, the applications from rails to bimetallic strips, specific and molar heat capacity, calorimetry, latent heat and the heating curve, conduction and thermal resistance, convection, radiation with Wien and Stefan-Boltzmann, Newton's law of cooling, a full set of worked problems and an advanced toolkit on top.

This section asks one different question: can you use any of it with a timer running?

There is no new theory below. There are 30 single-correct questions built to the exam pattern, and a marking scheme designed to punish the three habits this chapter rewards most cruelly — putting a Celsius number where a fourth power demands kelvin, forgetting that a hole expands along with everything else, and assuming a phase change went to completion when it did not.

The rules of engagement

Key Point: This is not a reading exercise. Blank sheet, pen, timer. Attempt all 30 questions in one unbroken sitting, and do not open a single explanation until the last answer is written.

Topic spread of the thirty questions, the marking scheme and guessing odds

The setup What it is
Number of questions 30, single correct option
Marking scheme +4+4 correct, −1-1 incorrect, 00 unattempted
Maximum score 30×4=12030 \times 4 = 120 marks
Minimum possible score 30×(−1)=−3030 \times \left(-1\right) = -30 marks
Suggested time limit 45 minutes (a shade under a minute and a half per question)
Take 0°C as 273 K throughout, unless a question says 273.15
Allowed rough sheet, your own head
Not allowed calculator, formula sheet, a glance back at the earlier sections

The constants sheet

Every question that needs a number uses these and no others. Copy them to the top of your sheet before you start.

Quantity Value
Specific heat capacity of water 4186 J/(kg K)
Specific heat capacity of ice 2100 J/(kg K)
Specific heat capacity of air 1005 J/(kg K)
Latent heat of fusion of ice, LfL_f 3.33×1053.33 \times 10^{5} J/kg
Latent heat of vaporisation of water, LvL_v 22.6×10522.6 \times 10^{5} J/kg
αsteel\alpha_{\text{steel}} 1.2×10−51.2 \times 10^{-5} K−1^{-1}
αbrass\alpha_{\text{brass}} 1.8×10−51.8 \times 10^{-5} K−1^{-1}
αglass\alpha_{\text{glass}} 9.0×10−69.0 \times 10^{-6} K−1^{-1}
KiceK_{\text{ice}} 1.6 W/(m K)
Stefan-Boltzmann constant σ\sigma 5.67×10−85.67 \times 10^{-8} W/(m2^2 K4^4)
Wien's constant bb 2.9×10−32.9 \times 10^{-3} m K
Density of air 1.2 kg/m3^3
Solar constant 1.4 kW/m2^2
Useful values π=3.14\pi = 3.14, ln⁡2=0.693\ln 2 = 0.693

The constants used throughout this drill. Nothing else is needed.

A note on symbols, so nothing is ambiguous under time pressure. TT is always an absolute temperature in kelvin and tt or tCt_C a Celsius one. LL bare is a length; LfL_f and LvL_v are the latent heats. α\alpha is linear expansion, β\beta areal, γ\gamma volume, and γ=3α\gamma = 3\alpha for an isotropic solid. ss is specific heat capacity in J/(kg K), KK is thermal conductivity in W/(m K), and lowercase kk is the cooling constant in Newton's law. σ\sigma is the Stefan-Boltzmann constant, ee emissivity, aa absorptive power. Where a question says "net", it means net.

What this set covers

Topic Questions How many
Temperature, scales and the gas laws Q1 to Q3 3
Thermal expansion of solids and liquids Q4 to Q8 5
Expansion in use: tape, stress, clock Q9 to Q11 3
Specific heat capacity and calorimetry Q12 to Q15 4
Change of state and latent heat Q16 to Q18 3
Conduction and thermal resistance Q19 to Q23 5
Convection Q24 1
Radiation, Wien and Stefan-Boltzmann Q25 to Q28 4
Newton's law of cooling and the solar constant Q29 to Q30 2

That spread mirrors how the paper actually samples this chapter. Expansion and conduction together are 10 of the 30, because those two topics carry the most multi-step questions and therefore the most marks, and because a slip in either ruins everything downstream.

The difficulty mix is roughly 25% easy, 45% medium and 30% hard. A handful will feel brutal. They are meant to.

[Exam Tip] That −1-1 changes the arithmetic of guessing. A blind guess among four options returns 44−34=+0.25\frac{4}{4} - \frac{3}{4} = +0.25 marks on average — barely worth the minute it costs. A question narrowed to two options returns 4−12=+1.50\frac{4-1}{2} = +1.50 marks on average, six times as much. Narrow first, then commit. Leave blank only what you could not narrow at all.

[Exam Tip] Before you start, write five lines at the top of your sheet: kelvin or Celsius?, does the vessel expand too?, did I include the phase change?, is this heat added or heat removed?, is it α\alpha, β\beta or γ\gamma? Those five questions catch the overwhelming majority of the marks lost in this chapter.

Scoring Yourself Honestly

Mark your sheet with the real scheme — +4+4, −1-1, 00 — and total it. No half marks for "I knew that one really". The number you get is the number that matters.

Four score bands and the three piles to sort your mistakes into

The bands

Your score (out of 120) Verdict What to do next
96 to 120 Exam ready. 80% or more on a hard set, inside the time. Move on. This chapter will not cost you marks. Revisit only the specific items you missed.
72 to 95 Solid, but leaking marks. Almost always slips rather than gaps — a Celsius temperature in a fourth power, a γ\gamma where an α\alpha was wanted, cm2^2 converted as 10−210^{-2} instead of 10−410^{-4}. Redo every wrong question without the explanation first.
42 to 71 Shaky. The ideas are there; the execution is not. For each wrong answer go back to the section that owns it (use the topic map above) and rework its solved examples before re-attempting.
Below 42 Start again. Work Sections 1 to 11 properly, then Section 12's worked problems, then Section 13. Re-attempting this set now teaches you nothing but the answer key.

Read your own answer sheet

Before you touch a single explanation, sort your mistakes into three piles. This is the most valuable ten minutes in the whole section.

  1. Method errors — you put a Celsius temperature into a fourth power or a temperature ratio. You used a slab formula on a pipe or a shell. You assumed all the ice melted, or all the steam condensed, instead of testing it. You used γapparent\gamma_{\text{apparent}} where the question wanted γreal\gamma_{\text{real}}. These are the expensive ones, because the whole solution is wrong from line one.
  2. Execution errors — right method, wrong arithmetic. The classic four in this chapter: the factor of 12\frac{1}{2} dropped from the pendulum-clock formula; α\alpha used where γ=3α\gamma = 3\alpha was wanted; cm2^2 converted as 10−210^{-2} m2^2 instead of 10−410^{-4} m2^2; and a thickness in centimetres left unconverted inside KAΔTL\frac{KA\Delta T}{L}.
  3. Reading errors — the question asked for the heat removed, not supplied; for the time of the second interval, not the total; for the net rate of loss, not the gross emission; for the apparent expansion, not the real one; for the mass expelled, not the mass remaining.

Key Point: In this chapter pile 3 is unusually fat, because so many quantities in it come in near-identical pairs: kelvin against Celsius, real against apparent expansion, gross emission against net exchange, α\alpha against γ\gamma, latent heat against specific heat, total time against interval time. Underline the quantity the question actually wants before you start solving.

The eight habits this set is drilling

  • Write K next to every absolute temperature. Fourth powers, ratios and the gas equation demand kelvin. Only a difference ΔT\Delta T may be quoted in either scale, and then the number is the same.
  • A hole expands. Rings, bores, gaps and cavities all grow by the same factor as solid material of the same substance.
  • α:β:γ=1:2:3\alpha : \beta : \gamma = 1 : 2 : 3. Areas use 2α2\alpha, volumes use 3α3\alpha. Check which one the question is about before substituting.
  • A liquid in a vessel shows only its apparent expansion, γapp=γreal−γvessel\gamma_{\text{app}} = \gamma_{\text{real}} - \gamma_{\text{vessel}}.
  • Never skip the phase change. If a body crosses 0°C or 100°C, an mLfmL_f or mLvmL_v term belongs in the balance, and you must test whether the change goes to completion.
  • Thermal resistance R=LKAR = \frac{L}{KA} adds in series and combines reciprocally in parallel. Almost every conduction question is a two-resistor circuit in disguise.
  • The temperature drop divides in proportion to thermal resistance, so a junction always sits close to the end of the better conductor.
  • Newton's law of cooling is a linearisation. Reliable for a small excess, badly optimistic for a large one.

[Exam Tip] Every explanation below is a full step-by-step solution, so this set doubles as revision. Read the explanation even for the questions you got right — several of these have a two-line route and a two-page route, and it is the two-line route you will need in the hall.