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Thermal Properties

Expansion, calorimetry, conduction and cooling. A small chapter of direct calculations.

Questions in the bank
66
q/paper in 2025–26
0.57
Numeric answer
29%
Notes pages
4

Tier: Long tail

When you’ll see it

A reading on another temperature scale, a length or volume that grows when heated, hot and cold bodies mixed, heat flowing through a rod, or a body cooling or radiating.

How this chapter is tested

Thermal Properties of Matter sits in the long tail, and almost every question is a line or two of arithmetic once the right relation is chosen. The relations are few: a reading is a fraction of the way between two fixed points, a length grows by LαΔT, heat lost equals heat gained, and a heat current behaves like an electric current.

Expansion and calorimetry carry most of the work. In expansion, choose α, 2α or 3α by what grows. In a mixture with ice, test first whether all the ice can melt; if the water's heat falls short, the final temperature is 0 °C. Conduction is circuit work: thermal resistances L/(KA) add in series and conductances add in parallel, the same rules as Current Electricity.

Marks are lost on small slips, not hard physics: α used for an area, conductivities added for rods in series, and a Celsius temperature put into Stefan's law. Many answers are numbers rather than options, so the units have to be right at the end.

The sub-skills

The distinct skills inside the chapter, in the order to learn them.

  • Temperature scales and expansion

    Convert a reading by its fraction between the ice and steam points; ΔL = LαΔT, with 2α for an area and 3α for a volume; a clamped rod carries a stress YαΔT instead of growing.

  • Calorimetry and latent heat

    Q = msΔT changes a temperature, Q = mL changes a phase at a fixed temperature; in a mixture, heat lost equals heat gained once you know how much ice melts.

  • Heat conduction

    H = KAΔT/L; each slab is a thermal resistance L/(KA), resistances add in series, conductances add in parallel, and the heat into a junction equals the heat out.

  • Radiation and cooling

    P = eσAT⁴ with T in kelvin, λₘT = b for the peak of the spectrum, and for a small excess a cooling rate proportional to the excess over the surroundings.

Traps to expect

Distractor shapes this chapter reuses. The Traps page covers the ones that cut across chapters.

  • α for an area or a volume

    An area grows by 2αΔT and a volume by 3αΔT. Using α alone gives an answer two or three times too small, and that value is usually an option.

  • Assuming all the ice melts

    Solving the balance without the test can give a final temperature below 0 °C with water present. Compare the heats first; if the water's is smaller, the answer is 0 °C.

  • Conductivities added in series

    In series it is the resistances L/(KA) that add. Adding or averaging the conductivities gives a heat current that is too large.

  • Celsius in Stefan's law

    P = eσAT⁴ needs kelvin. A body at 127 °C against one at 27 °C radiates (400/300)⁴ times as much, not (127/27)⁴.

Learn it before you drill it

This chapter has full teaching notes — foundations, worked examples, self-checks and a mastery check for each page. Read the notes once, then drill page by page below.

Thermal Properties notes

Drill every Thermal Properties question

66 questions from the bank, across 4 subtopics.

Drill the 66 questions

Drill one subtopic at a time

The 4 subtopics, in teaching order.

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