PhysicsICSE Class 8 · Heat Transfer

Thermal Expansion of Solids, Liquids and Gases: Linear, Superficial and Volume (ICSE Class 8)

Updated 17 October 2026 · Fact-checked

When heated, substances expand because their particles move more and spread apart: solids expand in length (linear), area (superficial) and volume, liquids in volume, and gases the most. For the same temperature rise, gases > liquids > solids. Expansion explains gaps in rails, sagging wires and bimetallic strips.

For the same temperature rise, particles spread apart a little in solids, more in liquids and most in gases, so gases expand the most.

Illustration drawn for QuestionBuddy.

Understand Thermal Expansion of Solids, Liquids and Gases

Why substances expand. On heating, the particles vibrate or move more vigorously and push one another farther apart, so the substance takes up more space. On cooling it contracts. The mass does not change, so the density decreases on heating (volume up, mass same).

Kinds of expansion.

Linear: increase in length (rails, wires, pipes).
Superficial: increase in area of a sheet. A hole in a metal plate becomes larger when the plate is heated, as if the hole were made of the same metal.
Volume (cubical): increase in volume; solids, liquids and gases all show it. Liquids have no fixed shape, so only volume expansion makes sense for them.

Dependence (same material). The increase in length is approximately proportional to

the original length, and
the rise in temperature.

Different materials expand by different amounts. For example, a 10 m steel rail grows by about 1.2 mm for a 10 °C rise, and a 10 m copper wire by about 1.7 mm for 10 °C.

Comparison. For the same rise in temperature: gases expand most, then liquids, and solids least, because the forces between particles are strongest in solids and weakest in gases.

Demonstrations: solid, the ball-and-ring experiment; liquid, coloured water in a flask with a narrow tube, whose level rises on warming; gas, a balloon over the mouth of a bottle that swells in hot water.

Applications and precautions.

gaps between rails and concrete slabs, and rollers under bridge ends, allow for expansion in summer;
overhead wires are left slightly slack so that they do not snap when they contract in winter;
a tight metal lid is loosened by hot water because the metal expands more than the glass;
a bimetallic strip (two metals such as brass and iron joined together) bends on heating because brass expands more than iron, so the brass is on the outside of the curve; it is used in thermostats and fire alarms;
thermometers use the expansion of a liquid in a narrow tube;
hot-air balloons rise because heated air expands and becomes less dense.

Thermal Expansion of Solids, Liquids and Gases: formulas and key facts

Order of expansion: $gases > liquids > solids$; Same rise in temperature.
Linear expansion (proportion): $Δ L \propto L \times Δ T$; Same material.
Data used: 10 m steel rail: about 1.2 mm for 10 °C | 10 m copper wire: about 1.7 mm for 10 °C; Scale by length and temperature rise.
Density on heating: $ρ = \frac{m}{V}$; m fixed, V up, ρ down.

How to solve Thermal Expansion of Solids, Liquids and Gases questions

For proportional-expansion problems, find the expansion per metre per degree from the given data, then scale.

1From the data, find the expansion for 1 m and 1 °C: for steel, $\frac{1.2}{10 \times 10} = 0.012$ mm.
2Multiply by the new length and the new temperature rise.
3For comparisons, use ratios: doubling length or rise doubles the expansion.
4For density, mass stays the same: $ρ = \frac{m}{V}$ with the new V.
5For explanations, name the material that expands more.

Thermal Expansion of Solids, Liquids and Gases in real life

Each concept, met in an everyday situation. Read the situation, try the problem, then check the solution. The one-line hook is what to remember.

Rails in summer

Suppose a steel rail 25 m long is laid on a day when the temperature is 20 °C and later heats to 50 °C. Use the rule that a 10 m steel rail grows 1.2 mm for 10 °C.

Find the increase in length.

Try it first, then show the solutionSolution

Expansion per metre per °C $= \frac{1.2}{10 \times 10} = 0.012$ mm.
Rise $= 30$ °C: $Δ L = 25 \times 30 \times 0.012 = 9$ mm.

Answer: 9 mm; engineers leave a gap for this.

Memory hook: Long and hot: more expansion.

The bridge on rollers

Imagine a steel bridge 100 m long with one end fixed and the other end resting on rollers.

Why are rollers used, and what would happen on a hot day without them?

Try it first, then show the solutionSolution

The steel expands in the heat; the rollers let the free end move forward.
Without them the bridge would push hard on its supports and could bend or crack.

Answer: Rollers allow for expansion; without them the bridge could bend or crack.

Memory hook: Let the long things move.

Tricks to remember Thermal Expansion of Solids, Liquids and Gases

Short memory aids. Say each one aloud once, then use it on a question the same day.

G-L-S
Gas, Liquid, Solid: from most to least expansion.
Use it when: Order.
Scale, do not guess
Double the length, double the expansion; double the rise, double the expansion.
Use it when: Proportion.
Brass on the outside
Brass expands more, so it takes the longer outer curve when heated.
Use it when: Bimetallic strip.

Thermal Expansion of Solids, Liquids and Gases: solved examples

Ordered from board level to HOTS. Try each one before you open the solution.

Example 1: Order of expansion · 1 mark · MCQBoard level

For the same rise in temperature, the correct order of expansion from greatest to least is:
(a) solid, liquid, gas
(b) liquid, solid, gas
(c) gas, liquid, solid
(d) gas, solid, liquid

Try it first, then show the solutionSolution

Particles in a gas are least tightly held, in a solid most tightly, so gas > liquid > solid.

Answer: (c) gas, liquid, solid

Example 2: Railways and wires · 2 marks · Short answerBoard level

Give reasons: (a) a small gap is left between rails, (b) overhead telephone wires are not stretched tight in summer.

Try it first, then show the solutionSolution

(a) Rails expand in summer; the gap allows for expansion so they do not bend. (1)
(b) Wires contract in winter; a slack wire does not snap. (1)

Answer: Allowance for expansion and contraction.

Example 3: Length of a rail · 3 marks · Short answerHarder board level

A 10 m steel rail expands by 1.2 mm for a 10 °C rise. A 25 m rail is laid at 20 °C. Find its expansion at 50 °C. What would it be for a 50 m rail?

Try it first, then show the solutionSolution

Per metre per °C: $\frac{1.2}{10 \times 10} = 0.012$ mm. (1)
25 m, rise 30 °C: $25 \times 30 \times 0.012 = 9$ mm. (1)
50 m: $50 \times 30 \times 0.012 = 18$ mm (double the length, double the expansion). (1)

Answer: 9 mm; 18 mm

Example 4: Density of heated metal · 3 marks · Short answerHarder board level

A metal block of mass 540 g occupies 200 cm³ at 20 °C and 202 cm³ when heated. (a) Find the density before and after. (b) Find the percentage decrease. (c) What does this tell us about density and heating?

Try it first, then show the solutionSolution

(a) Before: $\frac{540}{200} = 2.7$ g/cm³; after: $\frac{540}{202} = 2.67$ g/cm³. (1)
(b) Decrease $\approx \frac{0.027}{2.7} \times 100 \approx 1%$ . (1)
(c) Mass is unchanged but volume increases, so density decreases on heating. (1)

Answer: (a) 2.7 and 2.67 g/cm³ (b) about 1% (c) density falls

Example 5: The bimetallic strip · 4 marks · Case-basedHOTS / competency

A strip of brass and iron riveted together is heated. (a) Why does it bend? (b) Which metal is on the outside of the curve? (c) What happens on cooling below the starting temperature? (d) Give one use.

Try it first, then show the solutionSolution

(a) The two metals expand by different amounts; being joined, the strip must bend. (1)
(b) Brass, which expands more, is on the outer (convex) side. (1)
(c) It bends the other way, with iron on the outer side, because brass contracts more. (1)
(d) Thermostat or fire alarm. (1)

Answer: (a) unequal expansion (b) brass (c) bends the other way (d) thermostat or fire alarm

Where students lose marks in Thermal Expansion of Solids, Liquids and Gases

The slips examiners see most often, and what to write instead.

Mistake: Thinking mass changes on expansion
Expansion changes size and density, not mass.
Wrong working
"A heated block gets heavier as it is bigger."
Right working
"Mass is the same; volume increases, so density decreases."
Do this: Mass is conserved.
Mistake: Forgetting the temperature rise
Expansion depends on the rise, not the final temperature.
Wrong working
$25 \times 50 \times 0.012 = 15$ mm.
Right working
$25 \times (50 - 20) \times 0.012 = 9$ mm.
Do this: Subtract initial from final temperature.
Mistake: Hole shrinking
A hole expands on heating like the material.
Wrong working
"The hole shrinks as the metal swells."
Right working
"The hole gets larger."
Do this: Treat the hole as if made of the metal.

Exam tips

State the order gas > liquid > solid for comparison questions.
For numericals using given data, show the expansion per metre per °C.
Use the term "unequal expansion" for bimetallic strips.
Answer "why" questions with the effect and the remedy (gap, slack, roller).

Practice questions on Thermal Expansion of Solids, Liquids and Gases

Write each answer on paper first. Open the hint only if you are stuck, and the answer only when you have finished.

Q1 · 1 mark · Very short answerBoard level
Arrange in decreasing order of expansion for the same temperature rise: iron rod, air, mercury.
Hint
Gas, liquid, solid.
Answer
Air > mercury > iron rod.
Q2 · 3 marks · Short answerHarder board level
A copper wire 10 m long expands by 1.7 mm for a 10 °C rise. Find the expansion of a 40 m wire for a 20 °C rise.
Hint
Scale by length and by rise.
Answer
Per metre per °C: $\frac{1.7}{10 \times 10} = 0.017$ mm. $Δ L = 40 \times 20 \times 0.017 = 13.6$ mm.
Q3 · 2 marks · Short answerHarder board level
Rail A is twice as long as rail B of the same material. Rail A is heated through 15 °C and rail B through 30 °C. Compare their expansions.
Hint
$Δ L \propto L \times Δ T$ .
Answer
$\frac{Δ L _{A}}{Δ L _{B}} = \frac{2 \times 15}{1 \times 30} = 1$ : the expansions are equal.
Q4 · 3 marks · Short answerHarder board level
A hole is drilled in a brass plate. When the plate is heated, does the hole become larger, smaller or stay the same? Explain, and say how this helps in fitting a metal ring over a rod.
Hint
The hole expands as if made of brass.
Answer
The hole becomes larger, as though it were made of the same metal. A ring is heated so that its hole widens and fits over the rod; on cooling it contracts and grips tightly.
Q5 · 4 marks · Long answerHOTS / competency
A flask of coloured water with a narrow tube is placed in hot water. The level in the tube first falls a little and then rises steadily. Explain both observations.
Hint
The glass is heated first.
Answer
The glass flask is warmed first and expands, so its volume increases and the level dips. Then the heat reaches the water, which expands more than glass, so the level rises. This also shows liquids expand more than solids.

Test your recall

Answer in your head or on paper first, then open the card. Pulling an answer out of memory makes it stick far better than re-reading.

1.Which expands most for the same rise?Show answer
Gases.
2.What is linear expansion?Show answer
Increase in length.
3.What happens to density on heating?Show answer
It decreases.
4.Why does a bimetallic strip bend?Show answer
Unequal expansion of the two metals.
5.Why gaps in rails?Show answer
To allow for expansion in summer.

Thermal Expansion of Solids, Liquids and Gases: frequently asked questions

What is thermal expansion?

Thermal expansion is the increase in the size of a substance when it is heated, because its particles move more and spread farther apart.

Why do gases expand more than solids?

The forces between gas particles are very weak, so heating pushes them much farther apart; in solids the particles are held strongly and move apart only slightly.

How does a bimetallic strip work?

It has two metals joined; on heating, one expands more than the other, so the strip bends. This is used in thermostats and fire alarms.