7 min readConcept sheetPart II (2 marks) for the definitions, and Part III (4 marks) or Part IV (7 marks) for the experiment with a diagram

Expansion of liquids: real and apparent

A liquid expands along with its container. The expansion we see is apparent expansion; adding the container's expansion gives the real expansion.

Real expansionThe actual increase in the volume of a liquid

Apparent expansionThe increase in volume as seen, without allowing for the container's expansion

RelationReal expansion = apparent expansion + expansion of the container; γr = γa + γv

Unit of the coefficientsK⁻¹

Why liquids show two kinds of expansion

Liquids have no fixed shape, so we always heat them in a container. On heating, both the liquid and the container expand. The rise in the liquid level that we see is less than the true expansion of the liquid. This is because the container has also grown. The expansion we see is apparent expansion. The true expansion of the liquid is real expansion. Liquids expand more than solids for the same rise in temperature.

Real vs apparent expansion

Real expansionThe actual increase in volume of the liquid, allowing for the expansion of the container. Coefficient of real expansion (γr): the real rise in volume per degree rise in temperature, per unit original volume. Unit K⁻¹.

Apparent expansionThe increase in volume as it appears, without allowing for the container's expansion. Coefficient of apparent expansion (γa): the apparent rise in volume per degree rise in temperature, per unit original volume. Unit K⁻¹.

Real expansion = apparent expansion + expansion of the container. So γr = γa + γv, where γv is the cubical expansion coefficient of the container. Real expansion is always more than apparent expansion.

Experiment: real and apparent expansion

Use a flask fitted with a long, narrow glass tube and filled with a coloured liquid.

1
Mark the starting level of the liquid in the tube as L₁.
2
Heat the flask from below with a burner.
3
At first the level falls to L₂. The flask is heated first and expands, so it holds more liquid.
4
Soon the liquid warms up too, and the level rises to L₃, above L₁.
5★
Apparent expansion = L₃ − L₁. Expansion of the container = L₁ − L₂. Real expansion = L₃ − L₂.
6
So real expansion (L₃ − L₂) = apparent expansion (L₃ − L₁) + container expansion (L₁ − L₂).

★ key step

How to draw the experiment

Draw a round-bottomed flask with a long narrow glass tube fixed through its cork.
Shade the flask and part of the tube to show the coloured liquid.
Draw a burner below the flask.
On the tube, mark three levels from bottom to top: L₂ (lowest), L₁ (start) and L₃ (highest).
Label the gaps: L₁ to L₂ expansion of container, L₁ to L₃ apparent expansion, L₂ to L₃ real expansion.

Reading the experiment

Problem

In the experiment, the liquid level first falls 0.5 cm below L₁ and then rises to 4.5 cm above L₁. Find the apparent and real expansion, measured along the tube.

Working

Expansion of the container = L₁ − L₂ = 0.5 cm.
Apparent expansion = L₃ − L₁ = 4.5 cm.
Real expansion = apparent expansion + container expansion = 4.5 + 0.5 = 5.0 cm, which is L₃ − L₂.

Answer

Apparent expansion = 4.5 cm and real expansion = 5.0 cm of the tube. Real expansion is the larger one.

In real life

A bottle of oil filled to the brim and left in hot sun can overflow, because the oil expands more than the bottle. A thermometer uses the expansion of a liquid in a thin glass tube.

Exam angle

1 marks: “Which is greater for a liquid: real expansion or apparent expansion?” Real expansion.

2 marks: “Define real expansion and apparent expansion of a liquid.” Real: the actual increase in volume, allowing for the container's expansion. Apparent: the increase as seen, without allowing for the container's expansion.

7 marks: “Describe an experiment to show the real and apparent expansion of a liquid, with a diagram. Define the coefficients of real and apparent expansion.” Flask with tube; mark L₁; heat: level falls to L₂, then rises to L₃; apparent L₃ − L₁, container L₁ − L₂, real L₃ − L₂; real = apparent + container; define γr and γa, unit K⁻¹; labelled diagram.

Remember it

Falls first, then rises: the flask warms first (level falls), then the liquid (level rises). Real = Apparent + Container.