Physics · 2 Thermal physics
2.1.2 Particle model
Before you start
- Pressure is force per unit area, , measured in pascals (Pa), where Pa is N/m² (from 1.8).
- A moving object has kinetic energy, and the faster it moves, the more kinetic energy it has.
- All matter is made of atoms, and atoms can join together to form molecules.
- The everyday behaviour of solids, liquids and gases: which keep their shape, which flow, and which spread out to fill a container (2.1.1).
- Temperatures in degrees Celsius (°C), including temperatures below zero.
Syllabus objectives covered (8)
- Describe the particle structure of solids, liquids and gases in terms of the arrangement, separation and motion of the particles and represent these states using simple particle diagrams
- Describe the relationship between the motion of particles and temperature, including the idea that there is a lowest possible temperature (−273 °C), known as absolute zero, where the particles have least kinetic energy
- Describe the pressure and the changes in pressure of a gas in terms of the motion of its particles and their collisions with a surface
- Know that the random motion of microscopic particles in a suspension is evidence for the kinetic particle model of matter
- Describe and explain this motion (sometimes known as Brownian motion) in terms of random collisions between the microscopic particles in a suspension and the particles of the gas or liquid
- Know that the forces and distances between particles (atoms, molecules, ions and electrons) and the motion of the particles affects the properties of solids, liquids and gases
- Describe the pressure and the changes in pressure of a gas in terms of the forces exerted by particles colliding with surfaces, creating a force per unit area
- Know that microscopic particles may be moved by collisions with light fast-moving molecules and correctly use the terms atoms or molecules as distinct from microscopic particles
Part 1 of 7
Solids, liquids and gases: arrangement, separation, motion
- The particle model says that all matter is made of tiny particles that are always moving. A solid, a liquid and a gas of the same substance are made of the same particles. What changes from one state to another is how the particles are arranged, how far apart they are, and how they move.
- Those three words — arrangement, separation and motion — are your checklist. The objective asks you to describe each state in terms of all three, so a description that leaves one out is incomplete.
- Solid. Arrangement: the particles are in a regular pattern. Separation: very close together, each particle touching its neighbours. Motion: the particles vibrate about fixed positions. They do not move from place to place.
- The trap here is to write 'the particles in a solid do not move'. They do move: they vibrate. What they cannot do is leave their positions.
- Liquid. Arrangement: irregular, with no pattern. Separation: still close together, most particles touching their neighbours. Motion: the particles move around at random, sliding past one another.
- Notice what did not change between solid and liquid: the separation. The particles of a liquid are almost as close together as those of a solid. The arrangement and the motion are what change. So never draw a liquid with wide gaps between its particles.
- Gas. Arrangement: random. Separation: far apart — the distances between the particles are large compared with the size of the particles. Motion: the particles move quickly in random directions, travelling in straight lines between collisions with each other and with the walls of the container.
- To draw a simple particle diagram, use a box for each state and a circle for each particle. Use circles of the same size in all three boxes, because the particles themselves are the same in every state.apparatus diagram — not drawn yet
Three square boxes side by side labelled solid, liquid and gas, all using circles of the same size: the solid as rows of touching circles in a regular grid, the liquid as about the same number of circles mostly touching but jumbled with no pattern and a few small gaps, and the gas as five or six circles spread far apart at random, each with a short arrow showing its direction of motion.
The same particles in every box. The solid and the liquid have almost the same spacing; only the gas is spread out. - Three things make the diagrams correct: circles of the same size in every box, a regular pattern only in the solid, and wide gaps only in the gas. A liquid drawn as touching but jumbled circles is right; a liquid drawn with large spaces is a gas.
Part 2 of 7
Why the particles decide the properties
- The particles in this model can be atoms, molecules or ions. In a metal there are also electrons that are free to move between the ions. Whatever the particles are, three things about them decide how a material behaves: the forces between them, the distances between them, and how they move.
- Particles that are close together, as in a solid or a liquid, have strong forces between them. Particles that are far apart, as in a gas, have only very weak forces between them, except when they collide.
- A solid has a fixed shape and a fixed volume. Its particles are close together and held in fixed positions by strong forces. They cannot move past one another, so the solid keeps its shape.
- A liquid has a fixed volume but flows. The forces between its particles are still strong enough to keep them close together, so the volume stays the same. But the particles are not held in fixed positions. They can slide past one another, so the liquid flows and takes the shape of its container.
- A gas has no fixed shape and no fixed volume. The forces between its particles are very weak and the particles move quickly, so nothing holds them together. They spread out to fill whatever container they are in.
- Compressing. A gas is easy to compress because there are large spaces between its particles, and those particles can be pushed closer together. A solid or a liquid is very hard to compress because its particles are already close together: there is almost no space to remove.
- Density. For the same reason, a substance as a gas has a much lower density than the same substance as a liquid or a solid. The same mass of particles is spread through a much larger volume.
- This gives you the shape of every Extended 'explain this property' answer: name the property, then link it to the distance between the particles, the forces between them, or their motion. 'A gas can be compressed because it is compressible' explains nothing. 'A gas can be compressed because its particles are far apart, with large spaces between them' explains it.
Part 3 of 7
Temperature is how fast the particles move
- Raising the temperature of a substance makes its particles move faster. In a liquid or a gas they move around faster. In a solid they vibrate faster and with larger vibrations.
- Faster particles have more kinetic energy. So the higher the temperature of a substance, the greater the average kinetic energy of its particles.
- The word average matters. At any one temperature the particles do not all move at the same speed: some are faster, some slower, and their speeds keep changing as they collide. It is the average that goes up with temperature.
- Now run it the other way. Cooling a substance slows its particles down and lowers their average kinetic energy. Keep cooling and you reach a limit: a temperature at which the particles have the least kinetic energy they can have.
- That limit is absolute zero, −273 °C. It is the lowest possible temperature. Nothing can be cooled below it, because the particles cannot have less than their least kinetic energy.
- Use the objective's own words: at absolute zero the particles have their least kinetic energy. 'The particles stop moving completely' is a stronger claim than the syllabus makes, so do not write it.
- To find how far a temperature is above absolute zero, subtract from it. For °C that is degrees. Subtracting a negative number adds, which is where the arithmetic goes wrong if you rush it.
- Absolute zero is also the starting point of the kelvin scale of temperature, which is the next subtopic. For this one you need the value in °C and what happens to the particles there.
Part 4 of 7
How a gas makes a pressure
- Picture the molecules of a gas inside a closed box. They move fast in random directions, so they keep hitting the walls of the box and bouncing off.
- Each time a molecule hits a wall and bounces back, its direction of motion changes. That needs a force: the wall pushes the molecule back, and the molecule pushes on the wall. So every collision exerts a small force on the wall.forces diagram — not drawn yet
A closed box containing gas molecules drawn as small circles with arrows in random directions; one molecule is shown arriving at the right-hand wall and bouncing back the way it came, with a small force arrow on the wall at that point pointing outwards.
Each bounce pushes the wall outwards. The pressure is the total of all these pushes on each unit area. - One collision on its own is tiny. But an enormous number of molecules hit every part of the wall every second, and together their collisions give a steady total force on the wall.
- Pressure is force per unit area. So the pressure of the gas is the total force from all those collisions divided by the area of the surface they hit.
- This equation is not given to you on Paper 4, so you must recall it. Pressure is in pascals (Pa), force in newtons (N) and area in square metres (m²). If an area is given in cm², convert it to m² before you divide.
- The Core objective needs two ideas: the particles are moving, and they collide with the surface; those collisions cause the pressure. The Extended objective adds the next link: each collision exerts a force on the surface, and pressure is the force per unit area.
- Because the molecules move at random in all directions, they hit every wall of the box, the floor and the lid alike. A gas pushes outwards on every surface of its container, not only on the bottom.
Part 5 of 7
What makes the pressure change
- Anything that makes the molecules hit the walls more often, or harder, increases the force on each unit area, and so increases the pressure. Every explanation of a change in pressure is built from those two ideas.
- Heating a gas in a fixed volume. The molecules move faster. They hit the walls more often, because they cross the container more quickly. Each collision is also harder, so it exerts a greater force. Both effects increase the force per unit area, so the pressure increases.
- Squashing a gas into a smaller volume at the same temperature. The molecules move at the same speeds as before, so each collision is no harder. But there are now more molecules in each unit of volume, so they hit each unit area of wall more often. More collisions each second on each square metre means a greater force per unit area, so the pressure increases.
- Adding more gas to the same container at the same temperature. More molecules means more collisions with the walls every second, so the pressure increases.
- Each of these works in reverse. Cooling the gas, letting it expand into a larger volume, or letting some gas out all reduce the pressure.
- The trap is the word collisions used loosely. Pressure comes from molecules hitting the walls. The molecules also collide with one another, but those collisions do not push on the container, so 'the molecules collide with each other more' does not explain a change in pressure.
- The other trap is the size of the molecules. Heating a gas does not make its molecules bigger. They move faster, and that is all the explanation needs.
Part 6 of 7
Brownian motion: what you see
- Atoms and molecules are far too small to see, even with a microscope. So how can you have evidence that they are there and moving? You watch something bigger that they bump into.
- In a smoke cell, a little smoke is trapped in a small glass cell full of air. A bright light shines into the cell from the side, and you look into it through a microscope.apparatus diagram — not drawn yet
A small glass cell containing air and smoke, a lamp and a lens shining light into it from the side, and a microscope looking down into the cell from above; an inset shows the path of one smoke particle as a series of short straight lines in random directions.
Light from the side, microscope from above. The specks you see are smoke particles, not molecules. - The smoke particles show up as tiny bright specks of light. Each speck moves in a jerky, random, zig-zag path: a short movement one way, a sudden change of direction, another short movement, with no pattern.
- The smoke particles are an example of microscopic particles in a suspension: particles small enough to need a microscope to see, spread through a gas or a liquid. Tiny particles spread through water show the same kind of motion.
- This random motion of microscopic particles is called Brownian motion. It is evidence for the kinetic particle model of matter: the model in which matter is made of tiny particles that are constantly moving.
- Be clear about what is evidence for what. You never see the air molecules. You see the smoke particles being knocked about by something invisible, and the model that explains it is that the air is made of molecules in constant, random motion.
Part 7 of 7
Why the smoke particles move
- A smoke particle is surrounded by air molecules. They move very fast — at room temperature, hundreds of metres per second — in random directions.
- So the smoke particle is hit by air molecules from all sides, an enormous number of times every second.
- Each air molecule is much smaller and much lighter than the smoke particle, so a single collision has almost no effect on it. What moves the smoke particle is an imbalance.
- Because the collisions are random, at any instant the smoke particle is not hit equally on every side. More molecules, or faster ones, strike it on one side than on the other. That gives a resultant force on the smoke particle, and it moves.
- A moment later the imbalance is on a different side, so the resultant force acts in a new direction and the smoke particle changes direction. Random collisions give random changes of direction: the zig-zag path you see.
- This is how a microscopic particle can be moved by molecules much lighter than itself. The molecules are light but fast-moving, and very many of them strike it unevenly.
- It also explains why a football does not jiggle about like this. A large object is hit by so many molecules that the collisions on its different sides almost exactly balance, and its mass is so large that any tiny imbalance has no visible effect.
- Getting the words right. Atoms and molecules are what the air is made of, and they are far too small to see. A smoke particle is a microscopic particle: a much larger piece of matter, made of a very large number of atoms, big enough to show up in a microscope. Call the things doing the hitting air molecules and the things being hit smoke particles.
- So 'the smoke molecules move about' is wrong, because a smoke particle is not a molecule. 'You can see the air molecules moving' is wrong too, because you see only their effect on the smoke particles. In a liquid the same rule applies: the microscopic particles are hit by the molecules of the liquid.
Worked examples
Example 1. Compare the particles of a liquid with the particles of a gas in terms of their arrangement, separation and motion. Use your answer to explain why a gas can be compressed but a liquid can hardly be compressed at all.
Show the working
- Compare means you say how the two are alike and how they differ. So take the three headings in turn and give both states every time, rather than describing one state and then the other.
- Arrangement: in both the liquid and the gas the particles are arranged at random, with no regular pattern. That is a similarity, and it counts as a comparison.
- Separation: the liquid particles are close together, mostly touching. The gas particles are far apart, with large spaces between them.
- Motion: the liquid particles move around at random, sliding past one another. The gas particles move quickly in random directions, in straight lines between collisions.
- Now the explanation, which comes from the separation. Compressing means pushing the particles closer together. In a gas there are large spaces between the particles, so they can be pushed closer. In a liquid the particles are already close together, so there is almost no space to remove.
Answer: Both have a random arrangement. Liquid particles are close together and slide past one another; gas particles are far apart and move quickly in random directions. A gas can be compressed because there are large spaces between its particles, so they can be pushed closer together. The particles of a liquid are already close together, so a liquid can hardly be compressed.
Example 2. A sealed metal container of gas has a square lid of side m. The gas molecules exert a total force of N on the lid. (a) Calculate the pressure of the gas. (b) The container is heated and the pressure rises to Pa. Calculate the new force on the lid, and explain in terms of the molecules why the force has increased.
Show the working
- Find the area first. The lid is a square of side m. The side is already in metres, so the area comes out in m², which is what you need for an answer in pascals.
- (a) Recall — it is not given on the paper — and substitute the force and the area.
- (b) Now you know the pressure and want the force. Multiply both sides of by , because is what is dividing , and you get . The lid's area has not changed.
- Substitute the new pressure and the same area.
- Then the reason. Heating makes the molecules move faster. They hit the lid more often, and each collision exerts a greater force. So the total force on the same area is greater.
Answer: (a) Pa, which is Pa. (b) N. The molecules move faster, so they hit the lid more often and each collision exerts a greater force.
Example 3. A student looks into a smoke cell through a microscope and writes: 'The smoke molecules are moving about because they keep hitting each other.' Explain what is wrong with this statement, and give a correct explanation of the motion she sees.
Show the working
- First the term. A smoke particle is not a molecule: it is a microscopic particle made of a very large number of atoms. So 'smoke molecules' should be 'smoke particles'.
- Second the cause. The motion is caused by collisions with air molecules, not by smoke particles hitting one another.
- Now the explanation, in the order the ideas depend on each other. Air molecules move fast and at random. They hit each smoke particle from all sides. At any instant the collisions on one side do not balance those on the other side.
- So there is a resultant force on the smoke particle. Its direction keeps changing as the imbalance changes, which gives the random zig-zag motion.
- Finish with what the motion shows: it is evidence that air is made of molecules that are constantly moving at random, which is the kinetic particle model.
Answer: She has called the smoke particles 'molecules', and she has given the wrong cause. Correct explanation: the smoke particles are hit at random from all sides by fast-moving air molecules, which are too small to see. The collisions on different sides are unequal, so there is a resultant force on each smoke particle in a direction that keeps changing, giving the random zig-zag motion. This is evidence that the air molecules are constantly moving.
Example 4. A block of copper at °C is cooled steadily. Determine how many degrees its temperature would have to fall to reach absolute zero, and describe what happens to the motion of its particles as it cools.
Show the working
- Recall the value: absolute zero is °C.
- The fall is the starting temperature minus the final temperature. The final temperature is negative, so subtracting it adds .
- Copper is a solid, so its particles vibrate about fixed positions. As it cools they vibrate more slowly, so their average kinetic energy decreases.
- At absolute zero the particles would have their least kinetic energy. Use those words rather than 'they stop'.
Answer: A fall of °C. As the copper cools, its particles vibrate more slowly and their average kinetic energy decreases; at absolute zero they would have their least kinetic energy.
Where people go wrong
Mistake: Writing that the particles in a solid do not move.
Instead: The particles in a solid vibrate about fixed positions. They move, but they cannot move from place to place.
Strong forces hold each particle in its position, so its motion is a vibration about that position rather than travel.
Mistake: Drawing a liquid with large gaps between its particles, like a gas with a few extra particles.
Instead: Draw liquid particles close together, mostly touching, in a jumbled arrangement with no pattern.
The separation of liquid particles is almost the same as in a solid. That is why a liquid can hardly be compressed.
Mistake: Explaining a rise in gas pressure by saying the molecules collide with each other more, or that the molecules get bigger.
Instead: Pressure comes from molecules hitting the walls. Faster molecules hit the walls more often and harder, giving a greater force per unit area.
Collisions between molecules do not push on the container, and molecules do not change size when they are heated.
Mistake: Calling the specks in a smoke cell 'molecules', or saying that the air molecules can be seen.
Instead: The specks are smoke particles, each made of a very large number of atoms. The air molecules are invisible; you see only their effect.
Supp-8 asks you to use 'atoms' or 'molecules' as distinct from 'microscopic particles'. Swapping the words describes a different thing.
Mistake: Saying that at absolute zero the particles stop moving completely.
Instead: Write that at absolute zero the particles have their least kinetic energy.
That is what the objective states. 'Stop completely' claims more than the syllabus does.
Check yourself
- Describe the particles in a solid in terms of their arrangement, separation and motion.
Answer
Arrangement: a regular pattern. Separation: very close together, touching their neighbours. Motion: they vibrate about fixed positions. - Explain, in terms of the particles, why a liquid flows but a solid does not.
Answer
In both, the particles are close together with strong forces between them. In a solid the forces hold the particles in fixed positions, so they cannot move past one another. In a liquid the particles are not held in fixed positions and can slide past one another, so the liquid flows. - A block of ice is at °C. How many degrees is this above absolute zero, and what is true of the kinetic energy of the particles at absolute zero?
Answer
, so it is °C above absolute zero. At absolute zero the particles have their least kinetic energy. - A gas is squashed into a smaller volume at constant temperature. Explain why its pressure increases.
Answer
The molecules move at the same speeds, but there are more of them in each unit volume, so they hit each unit area of the wall more often. This gives a greater force per unit area, which is a greater pressure. - The gas in a cylinder is at a pressure of Pa. Calculate the force it exerts on a piston of area m².
Answer
N. - State what the random motion of smoke particles in a smoke cell is evidence for.
Answer
The kinetic particle model of matter: matter is made of tiny particles (here, air molecules) that are constantly moving at random. - Predict how the motion of the smoke particles changes if the air in the smoke cell is warmed, and explain your prediction.
Answer
The smoke particles move about more vigorously. The air molecules move faster, so they hit the smoke particles more often and harder, giving larger unbalanced forces. - Explain why the specks seen in a smoke cell are called microscopic particles and not molecules, and how something so much heavier than an air molecule can be moved by air molecules.
Answer
Each speck is a piece of smoke made of a very large number of atoms, big enough to see in a microscope; air molecules are far too small to see. The air molecules are light but fast-moving, and very many of them hit each smoke particle unevenly from different sides, giving a resultant force.
Exam questions
Try each part first. Open the mark scheme after you have written your answer.
Question 1. A student draws particle diagrams for one substance as a solid, as a liquid and as a gas.
(a) Sketch a particle diagram for the substance as a solid. Use a circle to represent each particle. 2 marks No calculator
Mark scheme
- B1 circles of equal size, each touching its neighbours (closely packed)
- B1 circles in a regular arrangement, for example in rows
(b) Describe the arrangement and the motion of the particles in the liquid. 2 marks No calculator
Mark scheme
- B1 arrangement: irregular / random / no regular pattern; ignore references to the particles being close together or touching
- B1 motion: move around at random / slide past one another / move from place to place, owtte; 'vibrate' on its own is insufficient
(c) Explain, in terms of the particles, why the liquid has a fixed volume but the gas does not. 2 marks No calculator
Mark scheme
- B1 liquid: strong forces between the particles keep them close together
- B1 gas: (very) weak / negligible forces between the particles (which are far apart and moving quickly), so they spread out to fill the container, owtte
Question 2. A sealed steel can contains air. The lid of the can has an area of m².
(a) Explain, in terms of the air molecules, how the air exerts a pressure on the lid. 3 marks No calculator
Mark scheme
- B1 the molecules move (randomly, at high speed) and collide with / hit the lid
- B1 each collision exerts a force on the lid
- B1 pressure is the (total) force from the collisions per unit area of the lid
(b) The air exerts a force of N on the lid. Calculate the pressure of the air in the can. 2 marks
Mark scheme
- C1 p = F/A or 450 / 0.0050 seen
- A1 90 000 Pa or 9.0 × 10⁴ Pa (accept N/m²); unit required
(c) The can is placed in hot water. Explain why the pressure of the air in the can increases. 2 marks No calculator
Mark scheme
- B1 the molecules move faster / have a greater (average) kinetic energy
- B1 so they hit the walls more often and/or with greater force (giving a greater force per unit area); ignore 'the molecules collide with each other more'
(d) State the temperature, in °C, at which the particles of any substance have their least kinetic energy. 1 mark No calculator
Mark scheme
- B1 −273 (°C); accept −273.15; the unit is given in the question so need not be repeated
Question 3. A student sets up a smoke cell and looks into it through a microscope. She sees small bright specks of light moving about.
(a) Identify what the bright specks are. 1 mark No calculator
Mark scheme
- B1 smoke particles (lit up by the light); accept smoke / ash / soot particles; 'air molecules' or 'smoke molecules' scores 0
(b) Describe the motion of the specks. 1 mark No calculator
Mark scheme
- B1 random / jerky / zig-zag motion, with sudden changes of direction
(c) Explain why the specks move in this way. 3 marks No calculator
Mark scheme
- B1 the smoke particles are hit by (fast-moving) air molecules
- B1 the collisions come from all directions at random
- B1 the collisions on different sides are unequal, so there is a resultant force on the smoke particle whose direction keeps changing, owtte
(d) State what this motion is evidence for. 1 mark No calculator
Mark scheme
- B1 the kinetic particle model of matter / that air is made of molecules that are constantly moving at random
How this is examined
- Why the smoke particles jiggle, and what that proves: a Describe and Explain built on a smoke cell seen through a microscope, followed by a one-mark State of what the motion is evidence for 'Random, jerky, zig-zag motion' for the Describe. For the Explain: smoke particles are hit by fast-moving air molecules; the hits come from all directions at random; the hits on different sides are unequal, so there is a resultant force whose direction keeps changing. For the State: evidence for the kinetic particle model, or that air molecules are constantly moving. Say 'air molecules' for what does the hitting and 'smoke particles' for what you see.
- Why heating or squashing a sealed gas raises its pressure: a two- or three-mark Explain after a gas is heated in a sealed container or pushed into a smaller volume by a piston Heating: 'the molecules move faster', so they 'hit the walls more often' and 'with greater force', giving a 'greater force per unit area'. Squashing at constant temperature: 'more molecules per unit volume', so 'more frequent collisions with the walls', so a greater force per unit area. 'The molecules collide with each other more' is about the wrong collisions and does not explain the change.
- Arrangement, separation and motion in each state, and the particle diagram: a Describe for one state, or a Sketch of particle diagrams in boxes for solid, liquid and gas One point each for arrangement, separation and motion — for a liquid, 'irregular', 'close together', 'move past one another'. In a diagram: circles of equal size; touching in a regular pattern for the solid; touching but jumbled for the liquid; widely spaced at random for the gas.
- Turning gas pressure into numbers with p = F/A: a two-mark Calculate in which you must recall ; the area may need working out first, or you may be asked for the force instead , or the numbers substituted into it, for the C mark; the final answer with its unit, Pa or N/m², for the A mark. Put the area in m² before you divide. A correct answer with its unit scores both marks.
- Linking a property to the forces and distances between particles: a two-mark Explain of why a gas can be compressed, or why a liquid flows but keeps a fixed volume Name the particle feature behind the property: 'particles far apart, with large spaces' for compressible; 'strong forces keep the particles close together' for fixed volume; 'particles can slide past one another' for flowing; 'particles held in fixed positions' for fixed shape.
- The value and meaning of absolute zero: a one-mark State of the lowest possible temperature, or one line inside a Describe about cooling '−273 °C', with the unit, and 'the particles have their least kinetic energy'.
Words to know
- Kinetic particle model
- The model in which all matter is made of tiny particles that are constantly moving.
- Absolute zero
- The lowest possible temperature, −273 °C, at which the particles of a substance have their least kinetic energy.
- Pressure
- Force per unit area, , measured in pascals (Pa). A gas exerts pressure because its molecules collide with surfaces.
- Brownian motion
- The random motion of microscopic particles in a suspension, caused by random collisions with the molecules of the gas or liquid around them.
- Microscopic particle
- A particle big enough to see through a microscope but too small to see with the eye, made of a very large number of atoms — for example a smoke particle.
- Suspension
- Microscopic particles spread throughout a gas or a liquid, such as smoke particles in air.
- Molecule
- A particle made of atoms joined together. Air is made mostly of nitrogen and oxygen molecules, which are far too small to see.