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Thermal physics · Subtopic 2 of 4

Thermal Expansion and Specific Heat Capacity

Heating makes particles move faster and push further apart, so most materials expand: gases most, liquids less, solids least. Heating also raises the internal energy. The energy needed for a temperature rise depends on the mass and the material: $\Delta E=mc\Delta\theta$ , where $c$ is the specific heat capacity.

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Section 1 of 14

Learning objectives

Describe thermal expansion and give uses and problems it causes.
Explain the order of expansion of gases, liquids and solids.
Use $\Delta E=mc\Delta\theta$ to find energy, mass, $c$ or temperature change.
Describe an experiment to measure specific heat capacity.

Pause and think

On a hot beach, sand burns your feet but the sea feels cool, even though the Sun shines equally on both. Why?

Section 2 of 14

Core idea

Start hereHot sand, cool sea

On a sunny day the sand burns your feet while the sea stays cool, though both get the same sunshine. Water needs far more energy to warm up by each degree. That property is its specific heat capacity.

The big idea

$E=mc\Delta\theta$ , $c$ in J/kg °C. Most materials expand when heated.

1. Specific heat capacity

Heating 1 kg of water and 1 kg of aluminium with the same heater

Water needs much more energy per degree, so it heats up slowly and cools slowly. That is why it is used in radiators and why coastal climates are milder.

E=mc\Delta\theta

$E$: energy supplied (J).
$m$: mass (kg).
$c$: specific heat capacity (J/kg °C).
$\Delta\theta$: temperature change (°C).

Worked exampleWater vs aluminium

Warm 1 kg of each by 20 °C ( $c=4200$ , $900$ ).

Goal: Energies.
Strategy: Formula.

$1\times4200\times20=84000\text{ J}$
Water.
$1\times900\times20=18000\text{ J}$
Aluminium.

Answer

84

kJ vs

18

kJ.

✓ CheckRatio

4200/900=4.7

✓: why water stores heat well.

Worked exampleMeasuring c

50 W heater for 5 min warms 0.5 kg of oil by 15 °C.

Goal: $c$ .
Strategy: $E=Pt$ , then rearrange.

$E=50\times300=15000\text{ J}$
5 min = 300 s.
$c=\frac{15000}{0.5\times15}=2000$
Rearrange.

Answer

2000

J/kg °C.

✓ CheckHeat lost to the room makes this an overestimate ✓.

Common misconceptionMinutes Power × time needs time in seconds.

2. Thermal expansion

Gaps in railway lines and sagging power cables allow for expansion

Without gaps, hot rails would buckle. A bimetallic strip (two metals expanding by different amounts) bends when heated and is used in thermostats.

Particles vibrate more and push slightly apart.
Gases expand most, then liquids, then solids.
Uses: thermometers, bimetallic strips.

Pause and think

Why do bridges have expansion joints?

Summary

$E=mc\Delta\theta$ .
Expansion: allow gaps.

Specific heat capacity: Energy to raise 1 kg by 1 °C.

HistoryBlack and "latent" heat. Joseph Black, a Scottish chemist, noticed in the

1760

s that equal masses of different substances needed different amounts of heat for the same temperature rise. His idea of "heat capacity" separated temperature (how hot) from heat (how much energy).

Fun factThe Eiffel Tower grows in summer. The Eiffel Tower is about

15

cm taller on a hot summer day than on a cold winter one, because its

7300

tonnes of iron expand with heat.

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