PhysicsCore20 min read

Kinetic Particle Model of Matter

Solids, liquids and gases explained by what the particles are doing

This topic appears in:

O Level Physics (5054) · ch.2A Level Physics (9702) · ch.15
01

The three states in terms of particles

All matter is made of particles in constant motion. What separates a solid from a liquid from a gas is not the particles themselves but how closely they are packed, how strongly they are held and how freely they move.

In a solid the particles are packed closely in a regular arrangement, held by strong forces. They cannot move past one another; they only vibrate about fixed positions. That is why a solid keeps both its shape and its volume.

In a liquid the particles are still close together and still touching, but the arrangement is irregular and they can slide past each other. A liquid therefore keeps its volume but takes the shape of its container.

In a gas the particles are far apart, the forces between them are negligible, and they move rapidly and randomly in all directions. A gas has neither a fixed shape nor a fixed volume, and fills whatever it is put in.

SolidLiquidGas
Spacingtouching, regulartouching, irregularfar apart
Forcesstrongmoderatenegligible
Motionvibrate in placeslide past each otherfast and random
Fixed shape?yesnono
Fixed volume?yesyesno
Compressible?barelybarelyeasily

Why a gas compresses and a liquid does not

A gas is mostly empty space, so squeezing it simply reduces the gaps. In a liquid the particles are already touching — there is no space left to remove. Both halves of that comparison are needed for the marks.

02

Brownian motion: the evidence

The kinetic model is not a guess. Smoke particles suspended in air, viewed under a microscope, are seen to jiggle about in a random, jerky path that never settles. This is Brownian motion.

The smoke particles are far too large to be moved by anything visible, and nothing is stirring the air. What is moving them is the constant bombardment by air molecules, which are far too small to see. At any instant slightly more molecules strike one side than the other, and the smoke particle is knocked that way.

The observation therefore shows three things at once: that the air is made of particles, that those particles are in continuous random motion, and that they are very much smaller than the smoke particle they are pushing around.

03

Temperature and the pressure of a gas

The temperature of a substance is a measure of the average kinetic energy of its particles. Heat something and its particles move faster; cool it and they slow. At absolute zero, −273 °C, the particles have the least possible energy and molecular motion has effectively stopped.

Gas pressure comes from collisions. The particles of a gas are constantly striking the walls of the container, and each collision exerts a tiny force. Pressure is the total force from all those collisions divided by the area of wall.

That picture explains every gas law question. Heat a sealed container and the particles move faster, so they hit the walls harder and more often — the pressure rises. Squeeze a gas into a smaller volume and the same number of particles strike a smaller area more frequently — the pressure rises again.

p₁V₁ = p₂V₂(constant temperature, fixed mass of gas)pressure and volume are inversely proportional — Boyle's law
p
pressurePa
V
volumem³

Follow the temperature as energy goes in. It climbs while the substance is warming, then flattens during melting and boiling — that energy is going into breaking the forces between particles, not into speeding them up.

04

Boyle's law in use

For a fixed mass of gas at constant temperature, pressure and volume are inversely proportional: halve the volume and the pressure doubles. Their product stays the same, which is why the equation is usually written as p₁V₁ = p₂V₂.

The two conditions are not optional. The mass of gas must be fixed — no leaks — and the temperature must be constant. Compressing a gas quickly heats it, so the law strictly applies to slow compression, and questions say "at constant temperature" for exactly this reason.

Quoting that condition before you substitute is often worth the method mark even if the arithmetic afterwards slips.

Worked example 15 marks

A cylinder holds 0.40 m³ of gas at 1.5 × 10⁵ Pa. It is compressed to 0.10 m³ at constant temperature. Find the new pressure, and explain in terms of particles why it rises.

  1. Conditions met: fixed mass, constant temperature, so p₁V₁ = p₂V₂.State the condition — it carries a mark.
  2. 1.5 × 10⁵ × 0.40 = p₂ × 0.10.
  3. 6.0 × 10⁴ = 0.10 p₂.
  4. p₂ = 6.0 × 10⁵ Pa.Volume down by four, pressure up by four — check the inverse relationship holds.
  5. The same number of particles now strike a smaller wall area, so collisions per second per unit area increase.The explanation must be in terms of collisions, not "because it is squashed".

6.0 × 10⁵ Pa

Key points

  1. Solid, liquid and gas differ in spacing, forces and motion.
  2. Brownian motion is the evidence that particles exist and move randomly.
  3. Temperature measures the average kinetic energy of the particles.
  4. Gas pressure is the total force of particle collisions per unit area.
  5. p₁V₁ = p₂V₂ needs a fixed mass of gas at constant temperature.

Practice questions

6 questions · 24 marks · full working on every one

Try each one on paper first, then open the working. The marks are shown where they are actually awarded, because that is where they are actually lost.

Short questions

2 · 4 marks

Two marks each, in the style of the short-question section of the paper. Answer in two or three lines.

SQ1[2 marks]
Explain, in terms of particles, why a gas can be compressed but a liquid cannot.
Model answer

In a gas the particles are far apart with large spaces between them, which can be reduced. In a liquid the particles are already touching, so there is no space to remove.

Examiner tip. Both halves are needed — describing only the gas scores one.

SQ2[2 marks]
State two ways in which the pressure of a fixed mass of gas in a sealed container can be increased.
Model answer

Raise its temperature, so the particles move faster and collide harder and more often. Or reduce its volume, so the same particles strike a smaller area more frequently.

Examiner tip. Two distinct methods, each with its reason. Giving one method twice in different words scores one.

Solved numericals

1 · 3 marks

Full working, one step per line, with the marks shown where they are awarded.

N1[3 marks]
A bubble of gas of volume 2.0 cm³ at the bottom of a lake is at a pressure of 3.0 × 10⁵ Pa. It rises to the surface where the pressure is 1.0 × 10⁵ Pa. Assuming the temperature is unchanged, calculate the new volume.

Given. p₁ = 3.0 × 10⁵ Pa, V₁ = 2.0 cm³, p₂ = 1.0 × 10⁵ Pa

Full working
  1. Uses p₁V₁ = p₂V₂temperature constant, so Boyle's law applies[1]
  2. 3.0 × 10⁵ × 2.0 = 1.0 × 10⁵ × V₂[1]
  3. V₂ = 6.0 cm³lower pressure, larger bubble — check the direction[1]

6.0 cm³

Long questions

1 · 8 marks

Theory and numerical together, as they appear in the long-question section.

LQ1[8 marks]
A cylinder contains 0.50 m³ of gas at a pressure of 2.0 × 10⁵ Pa.
  1. Explain, in terms of particles, what causes the gas to exert a pressure on the cylinder walls. [3]
  2. The gas is compressed to 0.20 m³ at constant temperature. Calculate the new pressure. [3]
  3. State and explain what would happen to the pressure if the gas were then heated at constant volume. [2]
Mark scheme
  1. Particles move rapidly and randomly, colliding with the walls[1]
  2. Each collision exerts a small force on the wall[1]
  3. Pressure is the total force per unit area of wall[1]
  4. Uses p₁V₁ = p₂V₂, stating that the temperature is constant[1]
  5. 2.0 × 10⁵ × 0.50 = p₂ × 0.20[1]
  6. p₂ = 5.0 × 10⁵ Pa[1]
  7. The pressure would increase[1]
  8. The particles gain kinetic energy, so they hit the walls harder and more often[1]

(b) 5.0 × 10⁵ Pa (c) pressure rises

Examiner tip. Quoting the condition "at constant temperature" before using Boyle's law is often worth the method mark even if the arithmetic then slips.

Exam questions

2 · 9 marks

Multi-part questions with a full mark scheme.

Q1[5 marks]
A student observes smoke particles in a small glass cell using a microscope, and sees them moving in a random, jerky way.
  1. Name this effect.
  2. Explain, in terms of particles, what causes the motion.
  3. State what the observation tells us about air molecules.
Mark scheme
  1. Brownian motion[1]
  2. The smoke particles are bombarded by air molecules[1]
  3. The bombardment is uneven / random, so the resultant force keeps changing directionthe mark that separates a full answer[1]
  4. Air molecules are very smalltoo small to see individually[1]
  5. They are moving rapidly and randomly[1]

Examiner tip. The word "uneven" or "random" is doing the work here. Saying only "air molecules hit them" does not explain why the motion changes direction.

Q2[4 marks]
A sealed container of gas is heated while its volume stays constant.
  1. State what happens to the pressure.
  2. Explain your answer in terms of the particles.
Mark scheme
  1. The pressure increases[1]
  2. The particles gain kinetic energy and move faster[1]
  3. They collide with the walls more frequently[1]
  4. Each collision exerts a greater force, so the total force per unit area risesboth "more often" and "harder" are needed for full marks[1]

Examiner tip. Two separate reasons — more frequent collisions and harder collisions — are two separate marks. Most answers give only one.