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Topic 2 · 2.2

Thermal properties and temperature

Core and Extended · Papers 1–6

🎯What you need to be able to do

  • Describe thermal expansion and its applications and consequences; explain the relative expansion of solids, liquids and gases EXTENDED.
  • Know that a rise in temperature increases internal energy; define specific heat capacity, use \( c = \dfrac{\Delta E}{m\Delta\theta} \) and describe experiments to measure it EXTENDED.
  • Describe melting, boiling, condensation, solidification and evaporation; know the melting and boiling points of water.
  • Distinguish boiling and evaporation; explain the factors affecting evaporation and cooling by evaporation EXTENDED.

📚The physics

Thermal expansion

Solids, liquids and gases expand when heated (at constant pressure). For the same temperature rise, solids expand least, liquids more and gases most.

Overhead cables between two poles: nearly taut on a cold winter day, sagging much more on a hot summer day. Two railway rails separated by a small expansion gap, as also used in bridges and roads.
Applications and consequences: gaps and slack allow for expansion; liquid-in-glass thermometers rely on it.

EXTENDED In a solid the particles are held tightly by strong forces, so heating makes them vibrate further but they stay close; in a liquid the forces are weaker and the particles move further apart; in a gas the forces are negligible, so the particles move much further apart.

Specific heat capacity

A rise in the temperature of an object increases its internal energy. EXTENDED The increase in temperature is an increase in the average kinetic energy of all the particles. Specific heat capacity is the energy required per unit mass per unit temperature increase:

\[ c = \frac{\Delta E}{m\,\Delta\theta} \qquad \Delta E = mc\,\Delta\theta \]

Units: J/(kg °C). Water has a high value, 4200 J/(kg °C).

A lagged 1.0 kg aluminium block with an electric heater and a thermometer in two holes. The heater is in a circuit with a power supply and an ammeter in series and a voltmeter across the heater. Measure the mass, the starting temperature, the current, voltage and time, and the highest temperature, then use c equals E over m delta theta.
EXTENDED For a liquid, heat a measured mass of it in an insulated cup with the same heater, stirring.

Melting, boiling, condensation, solidification

While a substance melts or boils, energy is supplied but the temperature does not change: the energy separates the particles rather than speeding them up. At standard atmospheric pressure, water melts at 0 °C and boils at 100 °C. In condensation and solidification the particles come closer together and give out energy.

A heating curve of temperature against time: ice warms from minus 20 to 0 degrees Celsius, stays at 0 while it melts, the water warms to 100 degrees, stays at 100 for a long time while it boils, then the steam warms further.
Boiling takes much longer than melting: more energy is needed to separate the particles completely.

Evaporation

Particles in a liquid; the most energetic ones escape from the surface. The particles left behind have less kinetic energy on average, so the liquid cools. A box lists what speeds up evaporation: a higher temperature, a larger surface area and more air movement, and compares evaporation, at any temperature from the surface only, with boiling, at the boiling point throughout the liquid.
Evaporation causes cooling.

Evaporation is the escape of more-energetic particles from the surface of a liquid, and it cools the liquid. EXTENDED It is faster at a higher temperature, with a larger surface area and with more air movement over the surface. An object in contact with an evaporating liquid cools, because energy passes from the object to the liquid to replace what the escaping particles take away — which is how sweating cools you.

✏️Worked example

In the experiment above, a 50 W heater warms the 1.0 kg aluminium block for 300 s. The temperature rises from 20.0 °C to 36.5 °C. (a) Calculate the energy supplied. [1] (b) EXTENDED Calculate the specific heat capacity of aluminium. [2] (c) The accepted value is 900 J/(kg °C). Explain why the result is too high, and suggest one improvement. [2]

(a) E = Pt = 50 × 300 = 15 000 J.

(b) \( c = \dfrac{15\,000}{1.0 \times 16.5} = \) 910 J/(kg °C) (909).

(c) Some energy is lost to the surroundings, so the temperature rise is smaller than it should be and c comes out too large. Improve: better insulation (lagging) around the block, a lid, or oil in the thermometer hole for better thermal contact.

Check it. Aluminium’s c is about a fifth of water’s, so 910 is reasonable; a value of 4200 would mean you used the water figure.
Using the final temperature instead of the change. Δθ = 36.5 − 20.0 = 16.5 °C, not 36.5.

📝Practise

In the style of the multiple-choice and theory papers. EXTENDED marks Supplement content.

1. (Theory.) EXTENDED Water flows through an electric shower at 0.0060 m3/min and is heated from 12 °C to 40 °C. Density of water 1000 kg/m3; c = 4200 J/(kg °C). (a) Show that 30 kg of water flows through in 5.0 min. (b) Calculate the energy needed to heat it. (c) Calculate the power supplied to the water. [6] (Modelled on 0625/42 June 2026 Q3.)
(a) m = ρV = 1000 × 0.0060 × 5.0 = 30 kg. (b) E = mcΔθ = 30 × 4200 × 28 = 3.5 × 106 J (3 528 000). (c) P = E/t = 3 528 000 / 300 = 12 000 W (11 760 W, about 12 kW).
2. (Theory.) The same shower, at the same power, delivers hotter water on another day. Suggest one reason. [1]
The water entering the shower is warmer, or the flow rate is lower (a smaller mass of water per minute).
3. (Theory.) EXTENDED A girl splashes water on her arms on a hot day. Explain, in terms of particles, why her skin cools as the water evaporates. [3] (Modelled on 0625/42 June 2026 Q5(a).)
The more energetic water particles escape from the surface; the particles left have a lower average kinetic energy, so the water is cooler; energy is transferred from her skin to the water by heating, so her skin cools.
4. (Theory.) EXTENDED Give two ways to make washing on a line dry faster. [2]
Any two: hang it on a warmer (sunny) day; hang it where there is more wind; spread it out for a larger surface area.
5. (Multiple choice.) EXTENDED 630 kJ of energy heats some water from 15 °C to 45 °C (c = 4200 J/(kg °C)). What is the mass of the water? A: 0.20 kg. B: 3.3 kg. C: 5.0 kg. D: 10 kg.
C. m = E / (cΔθ) = 630 000 / (4200 × 30) = 5.0 kg.
6. (Theory.) Explain why the temperature of boiling water stays at 100 °C even though the heater stays on. [2]
The energy supplied is used to separate the particles (change the state from liquid to gas), not to increase their kinetic energy, so the temperature does not rise.
7. (Theory.) EXTENDED State two differences between boiling and evaporation. [2]
Boiling happens only at the boiling point; evaporation happens at any temperature. Boiling happens throughout the liquid (bubbles form); evaporation only at the surface.
8. (Theory.) Railway rails are laid with small gaps between them. Explain why. [2]
The rails expand in hot weather; without gaps they would push against each other and bend (buckle).

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • Institute of Physics — practical guidance on measuring specific heat capacity
  • PhET “States of Matter” — heating and phase changes at the particle level