From the macroscopic
to the microscopic

Particle model and kinetic theory

3A · Physics · IGCSE 0653 · 6 October 2026

Predict first

A puddle at 20 °C dries up. Water boils at 100 °C. Why does it dry?

The whole puddle slowly heats up to 100 °C, then evaporates.
A few water molecules escape from the surface, even when the water is cold.
Sunlight breaks the water molecules apart.

Looking inside matter

We have never asked what matter is made of

A drop of ink spreads in still water.
A smell crosses the room.
A gas fills any container it is put in.

Idea to test

Matter is made of tiny particles that are always moving. But can we see them?

Brownian motion

Definition

The random, zigzag movement of visible particles, such as smoke or pollen, in a fluid.

Cause: collisions with fast-moving molecules that are too small to see.
Evidence that the molecules exist, and that they move.

Large particle hit by 300 small ones. Not to scale.

Minutes 13–25. FIRST show the simulation with the small molecules hidden: this is what the microscope shows (a particle that jiggles for no visible reason). Ask the class: what is pushing it? Collect hypotheses (a current? something alive?). Then click "Show the invisible molecules": many small fast particles, too small to see, hit the large one more on one side than the other at each instant. Why the widget: the cause is invisible by definition, so we make it visible. Point out the zigzag path (clear the trail and watch it grow). Historical line only after the phenomenon: Robert Brown observed pollen grains in 1827; the explanation came from Einstein (1905) and the experiments of Perrin. Keep the history to 30 seconds. Syllabus: the 0653 asks for the description and the cause, not the mathematics.

Solids, liquids and gases: complete the table

	Solid	Liquid	Gas
Arrangement	fixed, regular pattern	close together, irregular	far apart, random
Movement	vibrate about fixed positions	slide past each other	fast, random motion
Forces between particles	strong	weaker	almost none
Density	high	high	low
Easily compressed?	no	hardly	yes

Word bank: fixed, regular pattern · close together · far apart · random · vibrate · slide past each other · fast · strong · weaker · almost none · high · low · yes · no

The same particles, three states

Temperature (model units)0.10

Heat slowly, then cool slowly: watch the arrangement, the movement and the spacing.

Schematic 2D model with attractive forces between particles: not a real substance.

Minutes 35–45. The table from the previous slide, now alive. Click "Solid": the particles sit in a regular pattern and vibrate. Ask: what do you expect if we raise the temperature a little? (more vibration), then more, until it breaks the pattern. Drag the slider slowly through the melting zone (about 0.3–0.4) and let them see the pattern disappear while the particles stay close: liquid. Higher still: the particles leave each other: gas, fast and far apart. Then cool back down and note that the particles do not "shrink": the average spacing and the freedom to move change. The model is two-dimensional and the temperature is in arbitrary units (Lennard-Jones type forces): say it explicitly, it is a schematic model and not a simulation of water. Expected question: why does the liquid in the model not stay put at the bottom? (the walls and a small gravity are included only to keep the particles in the box). In the real world melting and boiling are also affected by pressure; ignore that here.

Predict first

A sealed syringe is full of air. We push the plunger in until the volume is halved. The temperature does not change. What happens to the pressure of the gas?

It decreases.
It stays the same.
It increases.

The same number of particles is squeezed into half the space: they hit the walls more often, so the pressure increases.

Gas pressure: collisions with the walls

Volume (piston)100 %

Temperature+27 °C

Temperature is held constant while the piston moves: slow compression, heat flows out through the walls.

Wall collisions per second: –

Pressure (relative to the start)100 %

Simulation of 80 non-interacting particles in 2D. The pressure bar is measured from the momentum given to the walls (smoothed over about 3 s).

Minutes 48–60. Come back to the syringe prediction: lower the piston to 50 % and check: the wall collisions per second increase and the pressure bar goes up (it takes about three seconds to settle because it is averaged: say it, it is not a bug). Second prediction before touching the temperature slider: "if I heat the gas, what changes in the collisions?" Answer: the particles move faster, so they hit harder AND more often. Raise the temperature and watch both the counter and the bar. Why the widget: pressure is a statistical effect of a huge number of impacts; with the counter the students see that it is made of impacts. Do NOT introduce p·V = constant now. Ask at the end: what is the force on the wall when only one particle hits it? (tiny and intermittent, but with 10^23 particles it becomes steady). Note: the temperature is shown in °C here because kelvin comes in the next section. IMPORTANT: when you move the piston the temperature does NOT change in this model, and students may expect it to. Say why before they ask: the compression is slow and the walls conduct heat to the surroundings, so the gas stays at the same temperature (an isothermal compression). A fast compression would heat the gas, because the moving piston gives kinetic energy to the particles that bounce on it: this is the effect behind the bicycle pump getting warm, and we keep it for the lesson of 9/10. So here we isolate one cause at a time: the volume changes with T fixed, then T changes with the volume fixed.

Temperature and the kinetic model

What is temperature?

Definition

The temperature of a substance is related to the average kinetic energy of its particles.

Temperature+25 °C

Average kinetic energy, relative to 25 °C× 1.00

Arrows: velocities. No collisions in this simplified model.

Quick revision, and why we need it now

The kelvin scale

T/\mathrm{K}=\theta/{}^{\circ}\mathrm{C}+273

θ25 °C

Celsius

–

Kelvin

–

Why now? The average kinetic energy is proportional to T in kelvin, not to θ in °C. From 50 °C to 100 °C the energy is not doubled: 323 K → 373 K is only ×1.15.

Minutes 65–70. The kelvin scale was already covered in the Italian syllabus, so this is a quick revision with a purpose: on the previous slide the energy bar (× 1.08 from 25 °C to 50 °C) was computed in kelvin, and this is the reason why. Say it explicitly and show the card at the bottom: halving or doubling a temperature only makes sense on a scale that starts at the lowest possible temperature. Skip the worked examples if the class answers the three conversions quickly. Worked examples with the buttons: 25 °C → 298 K; 77 K → −196 °C (boiling point of liquid nitrogen); 0 K → −273 °C: absolute zero. Why the kelvin: the scale starts at the lowest possible temperature, where the particles have the minimum kinetic energy; kinetic energy is proportional to T in kelvin. A change of 1 K is the same as a change of 1 °C (only the zero changes). 0653: T/K = θ/°C + 273. Ask before moving the slider: what is the temperature of boiling water in kelvin? (373 K). Typical error: adding 273 to a temperature that is already in kelvin, or subtracting in the wrong direction (check by absolute zero).

Three common mistakes

Mistake

“When a substance is heated, its particles get bigger.”

Fix

The particles keep their size. They move faster (or vibrate more), and the spacing may change.

Mistake

“Temperature and heat are the same thing.”

Fix

Temperature is related to the average kinetic energy of the particles. The thermal energy transferred also depends on how many particles there are.

Mistake

“At 0 K the particles disappear.”

Fix

They do not disappear: absolute zero is the lowest temperature, where the particles have the minimum possible energy.

“Average” does not mean “equal”

At one temperature, the particles have a range of speeds.
Temperature is linked to the average kinetic energy only.
A few particles are much faster than the average. A few are much slower.

Fastest ≈ – × averageSlowest ≈ – × average

Ring in dark red: the fastest; ring in teal: the slowest (in this sample).

Beyond the 0653 syllabus · support slide

How are the speeds distributed?

Temperature300 K

Speed threshold v*1100 m/s

v_p = – m/s most probable
v̄ = – m/s mean
v_rms = – m/s root mean square

Particles faster than v*: –dashed: 300 K

Curves computed for an ideal gas (Maxwell–Boltzmann distribution); k_B = 1.380649×10⁻²³ J/K, molecular masses from molar masses.

Minutes 75–80. Support slide, only to explain qualitatively. Say before everything: this is not in the 0653, it is here to understand the hook. Axes: speed on the horizontal axis; the vertical axis is the fraction of particles per unit speed. Three characteristic speeds (N₂ at 300 K, computed): most probable v_p ≈ 422 m/s, mean ≈ 476 m/s, root mean square ≈ 517 m/s; they are in the ratio 1 : 1.128 : 1.225, always in this order, because the curve is asymmetric (long tail on the right). v_rms is the one linked to the mean kinetic energy: ½ m v_rms² = (3/2) k T in 3D. Interactions to run: (1) raise the temperature: the peak moves to the right, gets lower and the curve widens (the area stays the same: the number of particles does not change); (2) at fixed v* (for instance 1100 m/s) compare the shaded fraction at 300 K and at 600 K: it grows by orders of magnitude; (3) change the gas: lighter molecules are faster at the same temperature (same average kinetic energy, smaller mass). Ask the class to predict before every move. The percentages are computed numerically from the same function, they are not rounded by hand.

Beyond the 0653 syllabus · support slide

Where does the shape come from?

Maxwell–Boltzmann speed distribution (ideal gas)

f(v)=4\pi\left(\frac{m}{2\pi k T}\right)^{3/2}\,\textcolor{#16283F}{v^{2}}\;\textcolor{#7B1E28}{e^{-\,m v^{2}/2kT}}

Factor v²

It rises with v: there are more ways to have a large speed.

Factor e^{-E_k/kT}

It falls with v: a high kinetic energy E_k=\tfrac12 mv^2 is unlikely unless kT is large.

v_{p}=\sqrt{\tfrac{2kT}{m}}\quad\bar v=\sqrt{\tfrac{8kT}{\pi m}}\quad v_{\mathrm{rms}}=\sqrt{\tfrac{3kT}{m}}

Back to the puddle

At 20 °C the average speed is not enough to break free.
But some molecules at the surface are much faster than the average: they escape. The water evaporates.
The molecules left behind are slower on average: the water cools.

Your predictions

Key idea

Average does not mean equal: the fastest particles can escape.

Minutes 82–87 (the hook closes here; the answer is B). Show the recap with the votes cast at the beginning and say who was right without judging: A is the most natural idea. Reconstruct B with the fast tail of slide 15: at 20 °C a few molecules are fast enough, they are many in absolute number because a drop contains billions of billions of molecules. Then go back to the beakers: the ink in the hot water has spread more: the same mechanism, higher average speed, more collisions that carry the ink around (diffusion is faster at higher temperature). If a student asks why the puddle dries faster in the sun: higher temperature → bigger fraction of fast molecules. And the wind? It removes the molecules above the surface so they do not come back: leave it as a question for homework. Do not move to slide 18 until someone has said "the fastest escape".

Evaporation and boiling

	Evaporation	Boiling
Where?	only at the surface	throughout the liquid (bubbles of vapour)
Temperature?	at any temperature below the boiling point	only at the boiling point
Which particles?	the fastest ones escape	enough energy is supplied for particles throughout the liquid to form vapour
Effect on the liquid	the liquid cools	temperature stays constant while boiling (energy is supplied)
Speed	slow; faster if warmer, with a larger surface, with wind	rapid

Reading a heating curve

Sloping part

Energy is supplied and the temperature rises: the average kinetic energy of the particles increases. The state does not change.

Flat part (plateau)

Energy is still supplied but the temperature stays constant. The substance is changing state: the energy is used to overcome the forces between the particles, not to make them move faster.

The temperature of a plateau is the melting point or the boiling point.

Schematic: no numbers.

Heating curve of a solid

time 0.0 min θ 20 °Cmove the point along the curve

State the physical state of the substance in regions P, R and T.
Give the melting point and the boiling point.
In region Q, energy is supplied but the temperature does not rise. What happens to the energy?
Explain, using the particle model, why the temperature rises in region P.
In which region do the particles have the highest average speed?

Minutes 90–100 (after the reading-a-curve slide; individual work first, then correction). Exercise, qualitative (no latent heat formula). Solutions: (1) P solid, R liquid, T gas. (2) Melting point 80 °C, boiling point 200 °C (the plateaus Q and S). (3) In Q (melting) the energy is used to overcome the forces between the particles, so the particles leave the fixed pattern; their average kinetic energy does not change, so the temperature stays constant. (4) In P the energy supplied increases the average kinetic energy of the vibrating particles, so the temperature rises. (5) Region T: gas at the highest temperature, so the highest average kinetic energy (and speed, for the same particles). Slider: use it to answer "what is the temperature after 11 minutes?" (140 °C, in region R) and to show that the temperature does not change between 3 and 8 min. Typical errors: "the particles stop moving in Q" (no, they keep moving but the energy goes to the potential energy between particles); "melting point = 3 min" (the melting point is a temperature, not a time). Graph style: 0653 past-paper (black grid, axes with quantity and unit).

Homework

Explain, using the particle model, why a gas fills its container but a solid does not.
A student says: “When a gas is heated, its particles expand.” Explain what is wrong and what really happens.
Explain why the pressure of the air in a sealed syringe rises when the plunger is pushed in.
Convert −40 °C and 100 °C to kelvin, and 250 K to °C.
Explain why evaporation cools the liquid that remains.

Minute 100 – assign (discursive, written by the student, to be handed in at the next lesson). Expected answers: (1) gas: particles far apart, almost no forces, fast random motion, so they spread to fill the space; in a solid, strong forces keep the particles in fixed positions that they vibrate about. (2) The particles do not get bigger: they move faster, hit the walls harder and more often, so the pressure rises (or the volume increases if the walls can move). (3) Same particles in smaller volume, more collisions per second with the walls, so more pressure. (4) −40 °C → 233 K; 100 °C → 373 K; 250 K → −23 °C (watch for the sign). (5) The fastest particles escape, so the average kinetic energy of the remaining particles decreases, therefore the temperature falls. Ask them to write complete sentences, not only words.

Three points to keep

Matter is made of particles that are always moving: Brownian motion is the evidence.
Gas pressure comes from collisions with the walls. Temperature is related to the average kinetic energy of the particles, with T in kelvin.
Average does not mean equal: the fastest particles can escape, so water evaporates below 100 °C.

From the macroscopicto the microscopic

A puddle at 20 °C dries up. Water boils at 100 °C. Why does it dry?

Looking inside matter

We have never asked what matter is made of

Brownian motion

Solids, liquids and gases: complete the table

The same particles, three states

A sealed syringe is full of air. We push the plunger in until the volume is halved. The temperature does not change. What happens to the pressure of the gas?

Gas pressure: collisions with the walls

Temperature and the kinetic model

What is temperature?

The kelvin scale

Three common mistakes

“Average” does not mean “equal”

How are the speeds distributed?

Where does the shape come from?

Back to the puddle

Evaporation and boiling

Reading a heating curve

Heating curve of a solid

Homework

Three points to keep

From the macroscopic
to the microscopic