GCSE · Physics · AQA · Spec 8463

Density of materials (ρ = m/V)

Density explains why a ship of steel floats but a coin sinks.

What you need to know

Density is defined by ρ = m / V — you must be able to recall and apply this equation.
The SI unit of density is kg/m³; mass must be in kg and volume in m³ before substituting.
Solids are generally denser than liquids, which are denser than gases, because of particle spacing.
When mass is conserved but volume changes (for example when a material changes state), density changes accordingly.

The big picture

Density measures how much mass is packed into a given volume, defined by ρ = m / V. Every material has a characteristic density determined by how closely its particles are arranged. Solids are generally densest because particles are tightly packed in fixed positions; gases are least dense because particles are far apart with vast empty space between them. Understanding density lets you predict whether objects float or sink and explains everyday differences between materials.

TONIGHT'S REVISION

Density of materials (ρ = m/V)

Why some things sink, some float, and how particle spacing controls it all.

From particles to density — the three states

Follow one material through the three states and watch how density changes as particle spacing changes.

Stop and predict

Commit to an answer before you reveal — this is where the understanding sticks.

A block of wax is melted. Its mass stays exactly the same. What happens to its density when it becomes liquid wax?

Density — the causal chain

Reason it through

Why does a gas made of the same particles as a solid have a dramatically lower density?

Link 1 of 3

First link · your turn

What changes about the particles when a solid becomes a gas?

Locked — reveal the link above first

Relationship matrix

Tap any cell to reveal it. Tap a column header to read one property down every item.

	Particle spacing	Volume (same mass)	Density	Compressible?
Solide.g. iron block
Liquide.g. liquid iron
Gase.g. steam / air

Each cell hides a short answer and the reason behind it. Predict before you tap.

AQA Paper 1 — 3-mark question

AQA mark-scheme practice

Does your answer hit the mark-scheme phrases?

Question

Explain why a solid is denser than a gas made of the same substance. [3 marks]

Student answer

In a solid the particles are closely packed together so the same mass occupies a much smaller volume. In a gas the particles are far apart with large spaces between them giving a much larger volume for the same mass. Because density equals mass divided by volume the smaller volume of the solid gives it a higher density than the gas.

Method marks0/3

Equations you need

Taken directly from the exam-board specification.

ρ = m / V

ρ = density (kg/m^3) · m = mass (kg) · V = volume (m^3)

Learn it — you must recall this in the exam

Key points

1ρ = m / V — mass divided by volume gives density in kg/m³.

2Solids: particles closely packed in fixed positions → high density.

3Liquids: particles close but mobile → slightly lower density than the same solid.

4Gases: particles far apart and moving freely → very low density, roughly 1000× lower than the solid.

5RP5: measure mass with a balance and volume by ruler (regular) or displacement (irregular), then apply ρ = m / V.

Worked example

Problem

A metal block has a mass of 270 g and a volume of 100 cm³. Calculate its density in kg/m³.

🧠

Memory hook

Think 'More Mess, Tiny Volume = Dense'. Imagine squeezing a whole roomful of air into a brick-sized block — that brick would be incredibly dense. The equation ρ = m / V captures exactly that: small V, same m, big ρ.

★ Exam tip

AQA Paper 1 often gives mass in grams and volume in cm³. Convert BEFORE substituting: 1 g = 0.001 kg and 1 cm³ = 1 × 10⁻⁶ m³. Write the conversion as a separate line — it earns a method mark even if your arithmetic slips.

⚠ Watch out

Leaving mass in grams and volume in cm³ — always convert to kg and m³ before substituting into ρ = m / V, or your answer will be wrong by a factor of 1000.

✓

Check yourself

Without looking — a solid block of wax is melted into liquid wax and no mass escapes. Has its density increased, decreased, or stayed the same? Explain your answer using ρ = m / V.

Flashcards

(24)

State the equation for density.

ρ = m / V

What are the SI units of density?

kg/m³

What does ρ (rho) represent in ρ = m / V?

Density, measured in kg/m³

What does m represent in ρ = m / V?

Mass, measured in kg

What does V represent in ρ = m / V?

Volume, measured in m³

Convert 450 g to kg.

0.450 kg

Convert 200 cm³ to m³.

2.00 × 10⁻⁴ m³

A block has mass 0.500 kg and volume 2.00 × 10⁻⁴ m³. What is its density?

ρ = 0.500 ÷ 2.00 × 10⁻⁴ = 2500 kg/m³

If density is 8000 kg/m³ and mass is 2 kg, what is the volume?

V = m ÷ ρ = 2 ÷ 8000 = 2.5 × 10⁻⁴ m³

If density is 1000 kg/m³ and volume is 0.003 m³, what is the mass?

m = ρ × V = 1000 × 0.003 = 3 kg

Describe the particle arrangement in a solid.

Particles are closely packed in fixed, regular positions — they vibrate but do not move past each other.

Describe the particle arrangement in a liquid.

Particles are close together but can move past each other; they have no fixed positions.

Describe the particle arrangement in a gas.

Particles are far apart, moving rapidly and randomly in all directions with large spaces between them.

Why are gases so much less dense than solids?

Gas particles are far apart with large empty spaces between them. The same mass fills a volume roughly 1000 times larger than the solid, so density is roughly 1000 times smaller.

Which state of matter has the lowest density?

Gas — particles are spread far apart, so a large volume contains very little mass.

When a solid melts to a liquid and mass is conserved, what generally happens to density?

Density decreases slightly — the same mass now occupies a slightly larger volume as particles are no longer held in fixed positions.

Why is the unit conversion step critical in a density calculation?

ρ = m / V only balances in consistent SI units. Mixing grams with m³ gives an answer with the wrong unit and wrong numerical value.

How do you find the volume of an irregular solid in RP5?

Submerge it in a measuring cylinder of water and record the volume of water displaced (the rise in water level).

How do you find the volume of a regular solid in RP5?

Measure its dimensions (length, width, height for a cuboid) and calculate using the appropriate formula.

What is RP5?

The required practical for determining the densities of regular and irregular solid objects and liquids using ρ = m / V.

A piece of wood floats on water (density 1000 kg/m³). What does this tell you about the wood's density?

The wood's density is less than 1000 kg/m³ — it is less dense than water.

If two objects have the same mass but different volumes, which is denser?

The one with the smaller volume — same mass packed into less space gives a higher density via ρ = m / V.

What happens to the density of a gas if you compress it (reduce its volume) while keeping mass constant?

Density increases — same mass, smaller volume means ρ = m / V gives a larger value.

Draw and label a simple diagram showing particle arrangement in a solid.

Regularly spaced circles touching each other in rows — particles in fixed positions with minimal gaps.

Tap any card to flip it, or use Study as deck to go through them one at a time. In the full lesson these run as a spaced-repetition deck — you rate each card Hard, Good or Easy and the tricky ones keep coming back until they stick.

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Density of materials (ρ = m/V)

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