Kinetic particle model of matter overview

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Kinetic particle model of matter

All 3 topics and the revision summary on one page.

States of matter

Use the arrangement, motion, forces and spacing of particles to explain the properties of solids, liquids and gases.

Particles may be atoms or molecules, depending on the substance. The kinetic particle model describes matter using these particles and their interactions. It links what we observe, such as a liquid flowing, to an explanation at a much smaller scale.

A drawing of circles is a model, not a literal microscope image. Its symbol sizes, gaps and particle counts help show differences; they do not give the actual sizes or numbers in a sample.

Use arrangement and motion to explain the properties

Circles represent particles such as atoms or molecules. The particle symbols stay the same size. These are schematic models, with selected motion indicators shown in blue.

Solid: a crystalline model

Fixed shape and approximately fixed volume. Close particles vibrate about fixed mean positions.

Liquid

Takes the container's shape; approximately fixed volume. Close particles move past one another and change neighbours.

Gas

Fills the available container and is easily compressed. Widely separated particles move randomly through the space.

Compare all four features: particle arrangement, motion, forces and spacing. The solid panel represents a crystalline arrangement. The symbols are the same size across the panels; a change of state does not mean that the atoms or molecules become bigger.

Solid

Observable properties: Usually keeps its own shape and volume under ordinary conditions. It does not flow like a liquid and is difficult to compress.

Arrangement and spacing: Particles are close together and remain near fixed positions. The regular pattern drawn here represents a crystalline solid; not every solid has that regular arrangement.
Motion: Particles vibrate about their positions. They are not motionless, even though they do not move freely through the solid.
Forces: Forces between particles keep them near their positions and resist changes of shape. Their close spacing makes a large reduction in volume difficult.

Liquid

Observable properties: Has a nearly fixed volume but takes the shape of the part of the container it occupies. It flows and is difficult to compress.

Arrangement and spacing: Particles are close together in an irregular arrangement. There is much less space between them than in a gas.
Motion: Particles move randomly and can move past their neighbours. This allows the liquid to flow and change shape.
Forces: Attractions keep the particles close while allowing them to rearrange. Liquid particles do not behave as if there are no forces between them.

Gas

Observable properties: Has no fixed shape or volume. It flows, spreads through the available container and can be compressed much more easily than a solid or liquid.

Arrangement and spacing: Particles are far apart compared with their own sizes. Much of the container is space between the particles.
Motion: Particles move rapidly in random directions through the available volume, changing direction when they collide.
Forces: In the ordinary gas model, attractions are negligible for most of the time between collisions. Particles are not held close together as in a liquid or solid.

Explain two properties of the same liquid

Water can be poured because its particles can move past one another. At the same time, it is difficult to compress because its particles are already close together. Being able to flow does not mean that there must be large empty spaces between the particles.

Worked explanation

Air and water in sealed syringes

Compare two otherwise identical sealed syringes, one containing air and the other filled with water and no trapped air. Apply comparable modest forces to their plungers.

Observation: the air volume decreases much more than the water volume.
Gas explanation: its particles are initially widely separated, so the spaces between them can become much smaller.
Liquid explanation: its particles are already close together, so there is little space to remove without strong resistance.

The air molecules themselves are not being squeezed into much smaller molecules. The large change is in their spacing. Trapped air in the water syringe would make the comparison less useful because that air can compress.

A gas can fill a larger volume without larger particles

If a fixed amount of gas is allowed into a larger container, its random motion spreads the particles through the newly available space. The number and sizes of the particles do not need to increase. Their average spacing becomes greater.

Its mass stays the same while its occupied volume increases, so its density, mass divided by volume, decreases. A particle explanation and a bulk quantity can describe the same change from different viewpoints.

Use the feature that explains the property. Motion past neighbours explains flow. Close spacing explains the difficulty of compression. Forces help explain why particles remain close or near fixed positions. Listing "particles move" alone does not explain all three states.

Optional check Water can be poured from one container into another, but a water-filled sealed syringe is difficult to compress. Which particle explanation accounts for both observations?

Temperature and internal energy

A rise in temperature corresponds to an increase in the average kinetic energy associated with the particles' random motion.

Kinetic energy is associated with motion. The particle model concerns random motion within a substance, including vibration in a solid. It is different from the whole object travelling across a room.

Consider the same gas first at 20°C and then at 50°C. In the warmer sample, the particles have greater average random kinetic energy. Their sizes and number do not increase just because the temperature rises.

Same gas, different temperatures

The particle count, symbol size and gas state are unchanged. The warmer sample has greater average random kinetic energy.

Blue arrows show particle motion. Lengths give a qualitative indication of speed; they do not give a numerical speed or temperature ratio.

20 °C

50 °C

Individual speeds vary. Higher temperature describes the average random kinetic energy of all the particles.

These models show the same gas at 20°C and 50°C. The same number of equally sized particle symbols is used. Motion arrows have varied directions and lengths in both panels; the warmer sample has greater typical speeds, not one identical speed for every particle.

Average does not mean every particle moves alike

Particles have a range of kinetic energies and continually exchange energy in collisions. A temperature rise concerns the average over all the particles, not a requirement that every individual particle speeds up at every instant.

For a solid, particles continue vibrating about their positions. Warming makes the average kinetic energy of that vibration greater; it does not require particles to stream freely through the solid.

The Celsius readings establish which temperature is higher, but their ratio is not an energy ratio. For example, 50°C is not evidence for 2.5 times the average kinetic energy at 20°C. A cooler sample at these temperatures still contains moving particles.

Internal energy includes motion and interactions

Internal energy is an energy store made up of two particle contributions:

The total kinetic energy associated with the random motion of the particles.
The total potential energy between the particles, associated with their arrangement and interactions.

These are totals for the whole system, not the energy of one selected particle. The potential-energy contribution matters as well as the motion: changing the particles' arrangement can change internal energy without raising temperature.

Temperature is related to an average; internal energy is a total

Worked comparison

100 g and 200 g of the same liquid at 30°C

The two samples have the same average random kinetic energy per particle because they are the same substance at the same temperature.

The 200 g sample contains about twice as many particles. Adding their kinetic energies therefore gives about twice the total random kinetic energy, although the temperature has not doubled.

Internal energy also includes the total potential energy between those particles. Matching temperatures alone does not establish matching internal energies, and the temperature reading does not give a numerical value for either sample's internal energy.

For a fixed amount of one substance that stays in the same state, warming increases average random kinetic energy and increases internal energy. When comparing different samples, also consider the amount of material, the substance and its state. Temperature alone is not a complete energy comparison.

Keep motion of the whole body separate

A trolley moving across a room has a kinetic store associated with that overall motion. Its particles also move randomly and interact with one another; those contributions form its internal store.

Making the whole trolley move faster does not automatically mean its temperature has risen. Conversely, a stationary block can gain internal energy while its centre remains at rest.

Include both internal-energy contributions. "Total energy of moving particles" leaves out the potential energy between particles. "Average kinetic energy" describes the temperature relationship, not the full internal-energy store.

Optional check Two samples of the same liquid, 100 g and 200 g, are both at 30 degrees C. Which statement follows from the particle model?

Measure the sample's temperature

Temperature may be represented by θ (theta) or T. The symbol θ commonly denotes a Celsius temperature in °C, while T commonly denotes a temperature in kelvin (K). These letters name the quantity; °C and K name the units. Always retain the stated scale and unit with a reading.

A thermometer measures temperature through a property that changes as its sensing region responds to the sample. Place and read it so that it represents the sample you intend to measure.

Choose a suitable range and resolution. A thermometer covering -10°C to 110°C can include the 20°C and 50°C readings above. With divisions every 1°C, the scale does not justify reporting many decimal places.
Immerse the sensing region correctly. Follow the instrument's immersion marking or instructions. A liquid-in-glass thermometer needs its bulb in the sample; do not leave the bulb mainly in the air above it.
Avoid contact with the vessel. Keep the sensing region clear of the base and sides, especially while the vessel is being heated. Gentle stirring, where suitable, can reduce temperature differences within a liquid.
Allow time for the response. For a sample held at a steady temperature, wait until the reading settles. If the sample is continuously warming, a slow thermometer can lag behind its changing temperature.
Read the scale properly. View the top of a liquid-in-glass thermometer's column at eye level to reduce parallax. Record the unit and the relevant time when following a change.

Measurement reasoning

Two readings of the same warming liquid

A thermometer touches the heated base of a beaker. That region may be hotter than the bulk liquid, so its reading can be too high for the intended liquid temperature. Moving the sensor into the liquid, away from the base, addresses the placement problem.

A second thermometer is correctly placed but responds slowly. While the liquid warms, its reading can be below the liquid's current temperature. Repeating the same timing does not remove this response lag; use a suitable sensor and account for its response time.

Repeated readings can reveal variation, but they do not correct a sensor touching the wrong object or an unsuitable response time. A finely divided display also does not guarantee that the measurement is accurate.

Next, changes of state show why internal energy can change while temperature remains constant.

Energy during changes of state

Internal energy includes total random particle kinetic energy and total potential energy between particles. Temperature relates to the average random kinetic energy.

A substance can gain or lose internal energy while its temperature stays constant during a change of state.

Consider a pure substance undergoing the stated transition at constant pressure. Its temperature remains at the transition temperature while the amounts in the two states change. The particles continue moving; constant temperature does not mean zero motion.

State changes and the direction of energy transfer

For a pure substance at fixed pressure, temperature stays constant during each stated transition. Energy moves into or out of the substance.

Melting and boiling transfer energy into the substance. Solidification and condensation transfer energy out. Each reverse process has the opposite energy-transfer direction.

Four processes, with two transfer directions

Melting: solid to liquid: Energy enters the substance. Particles become able to move past one another instead of remaining near fixed positions. Their arrangement and interactions change, increasing the potential-energy contribution to internal energy.
Solidification: liquid to solid: Energy leaves the substance. Particles settle into an arrangement in which they vibrate about fixed positions. The potential-energy contribution decreases. The released energy can increase internal stores of the surroundings.
Boiling: liquid to gas: Energy enters the substance. Particles become widely separated as the liquid changes to gas. Energy is needed to separate particles against their attractions, so their potential energy increases.
Condensation: gas to liquid: Energy leaves the substance. Particles become close together in a liquid, and their potential energy decreases. The energy transferred out can increase the surroundings' internal stores.

During each transition at the stated conditions, the average random kinetic energy remains unchanged because the temperature remains unchanged. The energy change is associated with the changing particle arrangement and potential energy.

Melting does not break the atoms or molecules into smaller particles. It changes how they are arranged and how freely they move relative to their neighbours. A liquid's particles are still close together; becoming widely separated is characteristic of the gas state.

Read a temperature plateau as a state change

The following idealised values describe an unspecified pure sample at a constant pressure. Its melting point is 50°C, and energy continues to enter throughout the six minutes. These are supplied model values, not measurements of a named material.

Temperature while energy continues to enter the sample
Time / min	Temperature / °C
0	20
1	35
2	50
3	50
4	50
5	65
6	80

Energy continues entering during the melting plateau

Supplied idealised data for an unspecified pure substance at constant pressure. Its melting point is 50 °C.

0-2 min: the solid warms from 20 to 50 °C.

2-4 min: solid changes to liquid at 50 °C. Energy transfer continues.

4-6 min: the liquid warms from 50 to 80 °C.

The temperature rises to 50°C, stays there from 2 to 4 min while melting occurs, then rises again as the liquid warms. Energy continues entering during the horizontal part of the graph.

0 to 2 min: the solid warms from 20°C to 50°C. Its average particle kinetic energy increases.
2 to 4 min: melting takes place at 50°C. The amount of liquid increases and the amount of solid decreases. Internal energy increases while average random kinetic energy stays unchanged.
After 4 min: the sample is liquid and its temperature rises. Average particle kinetic energy increases again.

Worked explanation

Why does the reading stay at 50°C?

At 3 min, the sample is in the melting interval. Continued energy input changes the particle arrangement and potential energy as more solid becomes liquid. It does not increase average random kinetic energy during this transition, so the temperature remains at 50°C.

The flat section does not show that the heater has stopped or that the particles have stopped moving. Temperature and total internal energy are different quantities.

Explain the reverse process

If energy is removed from the same liquid, it first cools to its solidification temperature. While it solidifies at the same fixed pressure, energy continues to leave and the amount of solid increases, but its temperature stays constant until the transition is complete.

The same reasoning applies to boiling and condensation at the boiling/condensation temperature for that pressure. Boiling requires continuing energy input while liquid becomes gas; condensation transfers energy out while gas becomes liquid. A constant temperature does not mean the transfer has ended.

Measure temperature and time consistently

Keep the thermometer's sensing region in the sample, clear of the heated vessel, and use the same timing origin for all readings. Read at the chosen intervals while recording whether the sample is solid, liquid or a mixture. Do not infer state only from a single temperature reading.

A thermometer that responds slowly can lag behind a rising sample temperature and round off a change in slope. Poor placement can measure a locally hotter region rather than the sample represented by the model. Repetition does not by itself fix either cause.

State the plateau conditions. This explanation concerns a pure substance undergoing a transition at fixed pressure. It does not claim that every mixture melts at one sharp temperature or that all warming must include a flat interval.

Optional check A pure sample is melting at a constant pressure. Its temperature stays at 50 degrees C while energy continues to enter. Which explanation is correct?

Revision summary

Connect the property to the particle model

Solid: Particles are close and vibrate near fixed positions. Forces keep them near those positions, giving a fixed shape and volume under ordinary conditions. Close spacing makes compression difficult.
Liquid: Particles are close and irregularly arranged; attractions keep them close while they move past one another. The liquid flows and changes shape but keeps nearly the same volume and is difficult to compress.
Gas: Widely separated particles move randomly through the available volume. Attractions are negligible for most of the time between collisions. Large spaces make compression easy compared with liquids and solids.

Particles may be atoms or molecules. A crystalline model's regular arrangement is not a claim about every solid. Gas expansion changes particle spacing, not the size of each molecule.

Temperature and measurement

Temperature symbols include θ (theta) and T, commonly used for Celsius and kelvin temperatures respectively. State the unit, °C or K; a symbol or number alone does not give a complete temperature reading.

A temperature rise means increased average random kinetic energy of all the particles. Individual speeds remain varied; solid particles vibrate. Ratios of Celsius readings are not particle-energy ratios.

Choose a thermometer with a suitable range and resolution. Immerse its sensing region correctly, keep it clear of the vessel, allow for response time and read an analogue scale at eye level. Repetition does not correct poor sensor placement or response lag.

Combined: internal energy

Internal energy contains the total kinetic energy of random particle motion and the total potential energy between particles. Temperature relates to an average, not that total. More of the same material can have more total random kinetic energy at the same temperature. Motion of the whole body is a separate kinetic store.

Combined: four changes of state

Melting: solid to liquid, energy enters.
Solidification: liquid to solid, energy leaves.
Boiling: liquid to gas, energy enters.
Condensation: gas to liquid, energy leaves.

For a pure substance undergoing the stated transition at fixed pressure, temperature stays constant while the proportions in each state change. The potential-energy contribution changes while average random kinetic energy remains unchanged. Particles keep moving, and energy transfer continues during the plateau.

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