PhysicsICSE Class 9 · Heat and Energy

Anomalous Expansion of Water and Hope's Experiment: Maximum Density at 4 °C (ICSE Class 9)

Updated 17 October 2026 · Fact-checked

Water contracts when heated from 0 °C to 4 °C and expands above 4 °C, so it has minimum volume and maximum density (about 1000 kg m⁻³) at 4 °C. Hope's experiment shows this: the lower thermometer settles at 4 °C while the upper falls to 0 °C. Ice (about 917 kg m⁻³) floats, which lets aquatic life survive in frozen lakes.

Water at 4 °C is densest, so it sinks and the bottom thermometer stays at 4 °C while the top falls to 0 °C.

Illustration drawn for QuestionBuddy.

Understand Anomalous Expansion of Water, Hope's Experiment and Its Consequences

Normal and anomalous expansion. Most liquids expand steadily when heated and contract when cooled. Water does not behave this way between 0 °C and 4 °C.

Heated from 0 °C to 4 °C: water contracts; volume decreases, density increases.
Heated above 4 °C: water expands as other liquids do.
So a fixed mass of water has its minimum volume and maximum density at 4 °C (density about 1000 kg m⁻³ = 1 g cm⁻³).
On freezing at 0 °C, water expands (about 9%): ice has a lower density than water, about 917 kg m⁻³, so ice floats.

Graphs (0 °C to 10 °C). Temperature on the horizontal axis.

*Volume of a fixed mass of water:* falls smoothly to a minimum at 4 °C, then rises.
*Density:* rises smoothly to a maximum at 4 °C, then falls. It is the mirror image of the volume graph because $ρ = \frac{m}{V}$ with $m$ fixed.

Neither graph has a sharp corner at 4 °C.

Hope’s experiment. A tall metal cylinder is filled with water. A trough (jacket) around its middle holds a freezing mixture of ice and salt. Two thermometers are placed, one near the top and one near the bottom, each away from the walls.

Sequence of events (start at about 10 °C):
1. The water in the middle is cooled, becomes denser, sinks, and the lower thermometer falls steadily.
2. When the lower thermometer reaches 4 °C it stops falling and stays at 4 °C: water at 4 °C is the densest, so it collects at the bottom.
3. Water cooled below 4 °C is now less dense and does not sink; it rises, and the upper thermometer begins to fall, finally reaching 0 °C.
4. In the steady state the top is at about 0 °C and the bottom at 4 °C.

Conclusion. Water has its maximum density at 4 °C.

Consequences.

Frozen lakes and fish. As air cools the lake, surface water cools, becomes denser and sinks, until the whole lake reaches 4 °C. Further cooling makes the surface water lighter, so it stays on top and freezes. Ice is a poor conductor of heat, so the deeper water remains near 4 °C and aquatic life survives.
Burst pipes and bottles. Water expands on freezing and breaks pipes and sealed bottles. This is why a bottle should not be filled right to the top before freezing.
Weathering. Water in cracks of rocks freezes, expands and splits the rock.
Ice floats with the fraction $\frac{917}{1000} = 0.917$ of its volume under water.

Common confusion. The anomaly applies to the range 0 to 4 °C. Do not say water "contracts when heated" without that range, and do not say it has maximum density at 0 °C.

Anomalous Expansion of Water, Hope's Experiment and Its Consequences: formulas and key facts

Maximum density of water: $ρ_{ma x} \approx 1000 kg m^{- 3} at 4 ° C$; Minimum volume at the same temperature.
Density relation: $ρ = \frac{m}{V}$; m fixed, so min V = max ρ.
Volume of ice from water: $V_{i ce} = V_{w a t er} \times \frac{ρ _{w a t er}}{ρ _{i ce}}$; ρ_ice ≈ 917 kg m⁻³.
Floating ice: $fraction immersed = \frac{ρ _{i ce}}{ρ _{w a t er}} \approx 0.917$; About 8.3% above the surface.

How to solve Anomalous Expansion of Water, Hope's Experiment and Its Consequences questions

Use the density relation and the 4 °C anomaly together.

1State the temperature range and the direction of volume change.
2For freezing problems, keep the mass constant and compute volumes with $V = m / ρ$ .
3For floating ice use the fraction $ρ_{i ce} / ρ_{w a t er}$ .
4For Hope’s experiment, say which thermometer moves first and where each stops.
5Explain consequences with the densities, not just the words "expands".

Anomalous Expansion of Water, Hope's Experiment and Its Consequences 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.

A bottle in the freezer

Suppose you fill a sealed glass bottle completely with 1 kg of water at 4 °C and leave it in a freezer.

By what percentage must the volume increase to turn all the water into ice (ρ_ice = 917 kg m⁻³)? Will the bottle be safe?

Try it first, then show the solutionSolution

$V_{w a t er} = \frac{1}{1000} = 1.000$ L; $V_{i ce} = \frac{1}{0.917} = 1.0905$ L.
Increase $\approx 9.05%$ (between 9% and 10%).
A completely full rigid bottle has no room for this, so it may crack.

Answer: About 9%; the bottle is unsafe unless it has at least this much air space.

Memory hook: Leave a tenth empty.

Tricks to remember Anomalous Expansion of Water, Hope's Experiment and Its Consequences

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

Four is the floor
4 °C is the floor of the volume curve and the peak of the density curve.
Use it when: Graph questions.
Lower first, upper later
In Hope’s experiment the lower thermometer drops first and stops at 4 °C; the upper one drops later to 0 °C.
Use it when: Hope’s experiment.
Ice on top, 4 °C below
Ice floats; water at the lake bottom stays at 4 °C.
Use it when: Frozen-lake answers.

Anomalous Expansion of Water, Hope's Experiment and Its Consequences: solved examples

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

Example 1: Temperature at the bottom of a frozen lake · 1 mark · MCQBoard level

In winter, when the surface of a deep lake is covered with ice, the temperature of water at the bottom of the lake is about:
(a) 0 °C
(b) 4 °C
(c) 10 °C
(d) below 0 °C

Try it first, then show the solutionSolution

The densest water (4 °C) collects at the bottom.

Answer: (b) 4 °C

Example 2: Describe the anomaly · 2 marks · Short answerBoard level

Describe how the volume and density of a fixed mass of water change when it is heated from 0 °C to 10 °C.

Try it first, then show the solutionSolution

From 0 °C to 4 °C the volume decreases and the density increases. (1)
From 4 °C to 10 °C the volume increases and the density decreases; at 4 °C the volume is least and the density greatest. (1)

Answer: Minimum volume and maximum density at 4 °C

Example 3: Melting a block of ice · 3 marks · Short answerHarder board level

A block of ice at 0 °C has a volume of 1200 cm³ (ice density 0.917 g cm⁻³ or 917 kg m⁻³; water at 0 °C about 1 g cm⁻³). Find its mass, the volume of water it melts into, and the percentage decrease in volume.

Try it first, then show the solutionSolution

Mass $= 1200 \times 0.917 = 1100.4$ g. (1)
Water volume $= \frac{1100.4}{1} = 1100.4$ cm³. (1)
Decrease $= 99.6$ cm³, i.e. $\frac{99.6}{1200} \times 100 \approx 8.3%$ . (1)

Answer: 1100.4 g; 1100.4 cm³; about 8.3% decrease

Example 4: Layers in a lake · 3 marks · Short answerHarder board level

A deep lake is exposed to very cold air. Its surface is at 0 °C under a layer of ice. State (a) the temperature of the water just below the ice, (b) the temperature at the bottom, and (c) explain why the bottom is not at 0 °C.

Try it first, then show the solutionSolution

(a) Close to 0 °C. (½)
(b) About 4 °C. (½)
(c) Water at 4 °C is the densest and sinks to the bottom. Water cooled below 4 °C is less dense and stays above it. Ice is a poor conductor of heat, so the lake does not lose heat quickly from below. (2)

Answer: (a) ~0 °C (b) ~4 °C (c) density maximum at 4 °C

Example 5: The sealed bottle · 4 marks · Case-basedHOTS / competency

A rigid bottle is filled to the brim with 1.00 kg of water at 4 °C and placed in a freezer.
(a) Find the volume of the water.
(b) Find the volume it would occupy as ice ( $ρ_{i ce} = 917$ kg m⁻³).
(c) Find the extra volume as a percentage of the water volume.
(d) Explain why the bottle may break, and what air space would be enough.

Try it first, then show the solutionSolution

(a) $V = \frac{1.00}{1000} = 1.00 \times 1 0^{- 3}$ m³ $= 1.00$ L. (½)
(b) $V_{i ce} = \frac{1.00}{917} \approx 1.091 \times 1 0^{- 3}$ m³. (1)
(c) Extra $= 0.091$ L; $9.05%$ (about 9%). (1)
(d) Water expands on freezing and presses on the walls; the bottle needs at least about 9% (roughly one-tenth) air space. (1½)

Answer: (a) 1.00 L (b) 1.09 L (c) about 9% (d) leave at least about one-tenth of the volume empty

Where students lose marks in Anomalous Expansion of Water, Hope's Experiment and Its Consequences

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

Mistake: Temperature range of the contraction omitted
Water contracts only between 0 and 4 °C.
Wrong working
Water contracts on heating.
Right working
Water contracts when heated from 0 °C to 4 °C.
Do this: Always give the range.
Usually costs: 1 mark.
Mistake: Maximum density placed at 0 °C
It is at 4 °C.
Wrong working
Density is maximum at 0 °C.
Right working
Density is maximum at 4 °C.
Do this: Use the graph shape.
Usually costs: 1 mark.
Mistake: Hope’s experiment readings reversed
The lower thermometer settles at 4 °C; the upper goes to 0 °C.
Wrong working
Upper thermometer stays at 4 °C.
Right working
Lower stays at 4 °C, upper falls to 0 °C.
Do this: Recall the order: lower first, then upper.
Usually costs: 2 marks.

Exam tips

Draw the density–temperature graph with the peak at 4 °C and label both axes.
In Hope’s experiment state where the freezing mixture is (the middle) and which thermometer falls first.
Link frozen-lake survival to both the density maximum and ice being a poor conductor.
Quote ice as less dense than water (about 917 kg m⁻³).

Practice questions on Anomalous Expansion of Water, Hope's Experiment and Its Consequences

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 · MCQBoard level
A fixed mass of water has its minimum volume at:
(a) 0 °C
(b) 4 °C
(c) 10 °C
(d) 100 °C
Hint
Maximum density.
Answer
(b) 4 °C
Q2 · 1 mark · Very short answerBoard level
Name the apparatus used to demonstrate that water has maximum density at 4 °C.
Hint
Named after a person.
Answer
Hope’s apparatus.
Q3 · 2 marks · Short answerHarder board level
A tray holds 450 g of water at 0 °C (density 1 g cm⁻³). It freezes completely (ice 0.917 g cm⁻³). Find the volume of the ice and the increase in volume.
Hint
V = m/ρ.
Answer
$V_{w a t er} = 450$ cm³; $V_{i ce} = \frac{450}{0.917} \approx 490.7$ cm³; increase $\approx 40.7$ cm³.
Q4 · 3 marks · Short answerHarder board level
A floating sheet of ice on a pond is 10 cm thick (917 kg m⁻³ in water of 1000 kg m⁻³). How much of the thickness lies below the water surface and how much above it?
Hint
Fraction immersed is ρ_ice/ρ_water.
Answer
Below $= 0.917 \times 10 = 9.17$ cm; above $= 10 - 9.17 = 0.83$ cm.
Q5 · 2 marks · Assertion-reasonHarder board level
Assertion (A): Water pipes in cold countries can burst in winter.
Reason (R): Water contracts on freezing.
(a) Both true, R explains A.
(b) Both true, R does not explain A.
(c) A true, R false.
(d) A false, R true.
Hint
Which way does water change on freezing?
Answer
(c). Water expands on freezing, which bursts the pipes.
Q6 · 3 marks · Long answerHOTS / competency
Suppose water behaved like an ordinary liquid and kept growing denser until it froze. Describe how a deep lake would then freeze and why fish would be in danger.
Hint
Think of which layer would be coldest.
Answer
If water kept getting denser until it froze, the cold surface water would keep sinking and the whole lake would cool to 0 °C throughout, including the bottom. There would be no layer of water at 4 °C for fish to stay in. The lake would be likely to freeze to a great depth or even solid, so fish and other aquatic life would be in danger. Because the maximum density is at 4 °C, the surface water becomes lighter below 4 °C and freezes first, while the water at the bottom stays at about 4 °C.

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.Temperature of maximum density of water?Show answer
4 °C.
2.Density of water at 4 °C?Show answer
About 1000 kg m⁻³.
3.Where is the freezing mixture in Hope’s apparatus?Show answer
In a jacket around the middle of the cylinder.
4.Why does ice float?Show answer
Its density (about 917 kg m⁻³) is less than that of water.
5.Bottom temperature of a frozen lake?Show answer
About 4 °C.

Anomalous Expansion of Water, Hope's Experiment and Its Consequences: frequently asked questions

What is the anomalous expansion of water?

Between 0 °C and 4 °C water contracts on heating, so its volume is least and density greatest at 4 °C; above 4 °C it expands like other liquids.

What does Hope's experiment show?

It shows that water has maximum density at 4 °C: the lower thermometer stops at 4 °C while the upper one falls to 0 °C.

How do fish survive in frozen lakes?

The water at the bottom remains at about 4 °C, because ice floats and is a poor conductor of heat, so the lake does not freeze through.