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Topic 2 · 2.1

Kinetic particle model and gases

Core and Extended · Papers 1–6

🎯What you need to be able to do

  • Know the properties of solids, liquids and gases and the names of the changes of state.
  • Describe and draw the particle structure of each state; link particle motion to temperature and absolute zero.
  • Describe Brownian motion as evidence for the kinetic particle model.
  • Explain gas pressure, and its changes with temperature and volume, in terms of particles; use force per unit area EXTENDED.
  • Convert between kelvin and degrees Celsius; use \( pV = \) constant EXTENDED.

📚The physics

States of matter

Particle diagrams. Solid: particles in a regular pattern, touching, vibrating about fixed positions; fixed shape and volume. Liquid: particles irregular but still touching, sliding past one another; fixed volume and flows. Gas: particles far apart, moving fast and randomly in all directions; fills its container.
Draw liquids with the particles still touching — the most common mistake.

EXTENDED The forces and distances between particles (atoms, molecules, ions, electrons) and the motion of the particles decide the properties. In a solid, strong forces hold particles close in fixed positions; in a liquid, the forces still hold them close but they can move past each other; in a gas, the forces are very weak and the particles are far apart.

Solid changes to liquid by melting; liquid changes to solid by solidification or freezing; liquid changes to gas by boiling or evaporation; gas changes to liquid by condensation. Water melts at 0 degrees Celsius and boils at 100 degrees Celsius at standard atmospheric pressure.
Gas-to-solid and solid-to-gas changes are not required.

Temperature and particles

The higher the temperature, the faster the particles move (the more kinetic energy they have). There is a lowest possible temperature, absolute zero, −273 °C, where the particles have the least kinetic energy.

The kelvin and Celsius scales side by side: 373 K is 100 degrees Celsius, where water boils; 273 K is 0 degrees Celsius, where water freezes; 0 K is minus 273 degrees Celsius, absolute zero. T in kelvin equals theta in degrees Celsius plus 273.
\( T \text{ (in K)} = \theta \text{ (in °C)} + 273 \)

Brownian motion

A glass cell of smoke lit from the side is viewed through a microscope. The smoke particles appear as bright specks that jiggle about along a random zigzag path, because they are hit unevenly by fast, light, invisible air molecules.
Pollen grains in water show the same motion.

The random motion of microscopic particles in a suspension is evidence for the kinetic particle model. The visible particles (smoke, pollen) are hit at random by the particles of the gas or liquid, which are far too small to see. EXTENDED The air molecules are light and fast-moving; the smoke particle is far more massive, so each collision moves it only slightly, and the uneven number of hits on different sides makes it jiggle.

Gas pressure

Three boxes of gas particles. First: particles move randomly and hit the walls, exerting a force on each unit area. Second, hotter at the same volume: longer arrows, faster particles, more frequent and harder collisions, higher pressure. Third, a smaller box with the same number of particles: more frequent collisions with the walls, higher pressure.
Pressure comes from particles colliding with the walls.
  • Gas particles move randomly and collide with the walls of the container, exerting a force. EXTENDED Each collision changes a particle’s momentum, so exerts a force; pressure is the total force of the collisions per unit area.
  • Temperature up, volume constant: particles move faster, hit the walls more often and harder, so pressure increases.
  • Volume down, temperature constant: the same particles in a smaller space hit the walls more often, so pressure increases.
\[ pV = \text{constant} \]

EXTENDED For a fixed mass of gas at constant temperature: \( p_1V_1 = p_2V_2 \). A graph of p against V is a curve; p against 1/V is a straight line through the origin.

Left: pressure in kilopascals against volume in cubic centimetres, a curve through 300 kPa at 20, 200 at 30, 150 at 40 and 100 at 60. Right: pressure against one over volume, a straight line through the origin passing through the same four points.
EXTENDED Halve the volume and the pressure doubles.

✏️Worked example

A sealed syringe holds 60 cm3 of air at 100 kPa. The plunger is pushed in slowly, so the temperature does not change, until the volume is 24 cm3. (a) Explain, in terms of particles, why the pressure increases. [2] (b) EXTENDED Calculate the new pressure. [2] (c) The room is at 22 °C. Give this temperature in kelvin. [1]

(a) The same number of particles are in a smaller volume, so they hit the walls (the plunger) more frequently; the force per unit area increases.

(b) \( p_2 = \dfrac{p_1V_1}{V_2} = \dfrac{100 \times 60}{24} = \) 250 kPa.

(c) 22 + 273 = 295 K.

Check it. The volume went down by a factor of 2.5, so the pressure must go up by the same factor: 100 × 2.5 = 250.
“The particles move faster when the gas is squashed.” At constant temperature their speed is unchanged; only the frequency of collisions rises.

📝Practise

In the style of the multiple-choice and theory papers. EXTENDED marks Supplement content.

1. (Theory.) Molten metal is poured into a mould and cools until it is solid. Name this change of state, and describe the arrangement, separation and motion of the particles in the solid. [4] (Modelled on 0625/32 June 2026 Q4.)
Solidification (freezing). Particles in a regular pattern (lattice), very close together (touching), vibrating about fixed positions.
2. (Theory.) State the name for the lowest possible temperature and its value in °C. [2]
Absolute zero; −273 °C.
3. (Theory.) EXTENDED A weather balloon is filled with hydrogen. Explain, in terms of particles, how the gas exerts a pressure on the inside of the balloon, and convert the air temperature at its highest point, 218 K, into °C. [4] (Modelled on 0625/42 June 2026 Q2(b).)
The particles move fast and randomly and collide with the inside of the balloon; each collision changes the particle’s momentum and exerts a force on the wall; pressure is the total force per unit area. 218 − 273 = −55 °C.
4. (Multiple choice.) Tyre pressure is lower on a cold night than on a warm afternoon, with no leak. Why? A: The air particles are smaller. B: The air particles move more slowly and hit the walls less often. C: There are fewer air particles. D: The air particles stick to the rubber.
B.
5. (Theory.) Describe what is seen when smoke in air is observed through a microscope, and explain it. [3]
Bright specks (smoke particles) moving in a random, jerky, zigzag way. They are being hit randomly and unevenly by the (invisible) air molecules, which are moving fast in all directions.
6. (Theory.) EXTENDED A gas at 120 kPa occupies 2.0 m3. At constant temperature it expands to 3.0 m3. Calculate the new pressure. [2]
p2 = 120 × 2.0 / 3.0 = 80 kPa.
7. (Multiple choice.) Which equation converts a temperature θ in °C into T in kelvin? A: T = θ − 273. B: T = θ + 273. C: T = 273 − θ. D: T = 273θ.
B.

🔗Go deeper — other people’s work

These are external resources, not mine. If one stops working, tell me and everything above it on this page still stands.

  • PhET “States of Matter” and “Gas Properties” — particles, temperature and pressure
  • Royal Society of Chemistry — Brownian motion demonstrations