GCSE — physicsFoundational4 min read

Density and States of Matter

ρ = m/V; particle arrangements in solids, liquids, gases; changes of state

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# Density and States of Matter — GCSE Physics

Density links mass and volume, telling us how "packed" a material is. Understanding density alongside the particle model of matter helps explain why objects float or sink and how materials change state.

1. Density

ρ=mV\boxed{\rho = \frac{m}{V}}

Where:

  • ρ\rho = density (kg/m³)
  • mm = mass (kg)
  • VV = volume (m³)

Typical Densities

Material Density (kg/m³)
Air 1.2
Water 1000
Ice 920
Aluminium 2700
Iron 7870
Gold 19,300

Floating rule: An object floats if its density is less than the fluid it's in. Ice floats on water because 920 < 1000.

2. The Particle Model

Solids

  • Particles close together in a regular pattern
  • Strong forces between particles
  • Vibrate about fixed positions
  • Fixed shape and fixed volume
  • Generally high density

Liquids

  • Particles close together but irregularly arranged
  • Weaker forces than solids
  • Can move past each other
  • No fixed shape (takes shape of container) but fixed volume
  • Density similar to solids

Gases

  • Particles far apart, randomly moving
  • Very weak/negligible forces between particles
  • Move quickly in all directions
  • No fixed shape and no fixed volume (fills container)
  • Low density (particles spread out)

3. Changes of State

Change From → To Energy
Melting Solid → Liquid Energy absorbed
Freezing Liquid → Solid Energy released
Boiling/Evaporation Liquid → Gas Energy absorbed
Condensation Gas → Liquid Energy released
Sublimation Solid → Gas Energy absorbed

Key Facts

  • Changes of state are physical changes (reversible, no new substances formed)
  • During a change of state, temperature stays constant (energy goes into breaking/forming bonds between particles, not increasing KE)
  • Mass is conserved — the number of particles doesn't change
  • Evaporation occurs at any temperature from the surface; boiling occurs at a specific temperature throughout the liquid

4. Required Practical: Measuring Density

Regular Solid

  1. Measure mass using a balance
  2. Measure dimensions with a ruler/callipers
  3. Calculate volume (e.g., cuboid: V=l×w×hV = l \times w \times h; cylinder: V=πr2hV = \pi r^2 h)
  4. Calculate ρ=m/V\rho = m/V

Irregular Solid

  1. Measure mass on a balance
  2. Measure volume by displacement: submerge in water in a measuring cylinder and note the increase in water level
  3. Calculate ρ=m/V\rho = m/V

Liquid

  1. Measure mass of empty measuring cylinder
  2. Pour in a known volume of liquid
  3. Measure mass of cylinder + liquid
  4. Mass of liquid = difference
  5. Calculate ρ=m/V\rho = m/V

Worked Example: Example 1

Problem

Question: A block has a mass of 500 g and dimensions 10 cm × 5 cm × 4 cm. Calculate the density in kg/m³.

m=0.5m = 0.5 kg, V=0.10×0.05×0.04=0.0002V = 0.10 \times 0.05 \times 0.04 = 0.0002 m³ ρ=m/V=0.5/0.0002=2500 kg/m3\rho = m/V = 0.5/0.0002 = 2500 \text{ kg/m}^3

Solution

Worked Example: Example 2

Problem

Question: Will an object of density 800 kg/m³ float or sink in water (1000 kg/m³)?

Answer: It will float because 800 < 1000.

Solution

Worked Example: Example 3

Problem

Question: A rock has a mass of 120 g. When placed in a measuring cylinder, the water level rises from 50 ml to 95 ml. Calculate the density.

V=95−50=45V = 95 - 50 = 45 ml = 45 cm³ = 4.5×10−54.5 \times 10^{-5} m³ m=0.12m = 0.12 kg ρ=0.12/4.5×10−5=2667 kg/m3\rho = 0.12/4.5 \times 10^{-5} = 2667 \text{ kg/m}^3

Solution

6. Practice Questions

    1. Calculate the density of a 2 kg object with a volume of 0.0005 m³. (2 marks)
    1. Describe the arrangement and movement of particles in a liquid. (2 marks)
    1. Explain why gases have a much lower density than solids. (2 marks)
    1. During melting, the temperature of the substance remains constant. Explain why. (3 marks)
    1. Describe how you would measure the density of an irregular solid. (4 marks)

    Answers

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Summary

  • Density ρ=m/V\rho = m/V (kg/m³)
  • Solids: close, regular, vibrate; Liquids: close, irregular, flow; Gases: far apart, random, fast
  • Changes of state are physical, reversible; temperature is constant during change
  • Float if density < fluid density
  • Measure density: regular solids (ruler + balance), irregular (displacement)
Tags:
#gcse#physics#particle-model#density#states-of-matter

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