What you'll learn
The particle model of matter is the unit of AQA GCSE Combined Science: Trilogy that uses one simple idea — that matter is made of particles whose arrangement and motion determine its behaviour — to explain density, changes of state, heating and the behaviour of gases. It is a unit where the same physical model answers a wide range of apparently unrelated questions, so understanding the model properly is worth far more than memorising individual facts. By the end you should be able to calculate density and describe how to measure it for regular solids, irregular solids and liquids, describe the particle arrangement in each state of matter, explain why a change of state is a physical change, distinguish internal energy from temperature, apply the specific heat capacity and specific latent heat equations, interpret a heating graph with its flat sections, and explain gas pressure in terms of particle collisions. This unit is assessed on Physics Paper 1 and includes the required practical on density.
Key terms and definitions
Density — the mass per unit volume of a substance, measured in kilograms per cubic metre
Internal energy — the total kinetic energy and potential energy of all the particles in a system
Change of state — a physical change in which a substance changes between solid, liquid and gas, with the mass conserved
Specific heat capacity — the energy required to raise the temperature of one kilogram of a substance by one degree Celsius
Specific latent heat — the energy required to change the state of one kilogram of a substance with no change in temperature
Latent heat of fusion — the specific latent heat for changing between a solid and a liquid
Latent heat of vaporisation — the specific latent heat for changing between a liquid and a vapour
Absolute zero — the temperature, at minus 273 degrees Celsius, at which particles have the least possible kinetic energy
Gas pressure — the force per unit area exerted on the walls of a container by colliding gas particles
Core concepts
Density and the particle model
Density is mass divided by volume. Working in kilograms and cubic metres gives density in kilograms per cubic metre, while grams and cubic centimetres give grams per cubic centimetre. Water has a density of 1,000 kilograms per cubic metre, or equivalently 1 gram per cubic centimetre, which is a useful benchmark.
The density of a material depends on how closely its particles are packed. Solids are usually densest because their particles touch and are arranged in a regular pattern. Liquids are slightly less dense because the particles, while still touching, are randomly arranged. Gases are far less dense because the particles are widely separated.
Measuring density
For a regular solid, measure the mass on a balance and calculate the volume from the dimensions using a ruler, then divide.
For an irregular solid, measure the mass on a balance and find the volume by displacement. The object is lowered into a eureka can filled to the spout, and the water displaced is collected in a measuring cylinder. The volume of water collected equals the volume of the object.
For a liquid, measure the mass of an empty measuring cylinder, pour in a known volume of the liquid, measure the mass again, and subtract to find the mass of the liquid alone. Forgetting to subtract the mass of the container is a standard error.
States of matter and changes of state
In a solid the particles are close together, in a regular arrangement, and vibrate about fixed positions. In a liquid the particles are still close together but randomly arranged and able to move past one another. In a gas the particles are far apart and move quickly in random directions.
A change of state is a physical change, not a chemical one. The particles themselves are unchanged; only their arrangement and motion differ. This means the change can be reversed, and the substance recovers its original properties.
Mass is conserved during a change of state. If 20 grams of ice melts, exactly 20 grams of water results.
Internal energy
Internal energy is the energy stored by the particles that make up a system. It is the total of the kinetic energy of the particles, which depends on how fast they move, and the potential energy of the particles, which depends on their separation and arrangement.
Heating a system increases its internal energy, and this produces one of two outcomes. Either the temperature of the system increases, because the particles gain kinetic energy and move faster, or the state changes, because the particles gain potential energy as the forces between them are overcome.
Both cannot happen at once, and that is the key to understanding heating graphs.
Specific heat capacity
When heating changes the temperature, the energy needed depends on the mass, the substance and the size of the temperature change. The change in thermal energy equals mass multiplied by specific heat capacity multiplied by temperature change.
Specific heat capacity is measured in joules per kilogram per degree Celsius, and it differs between substances. Water's value of about 4,200 is unusually high, which is why water is effective in heating systems and why it takes so long to boil a full kettle.
Specific latent heat
When heating changes the state, the temperature does not change at all while the change is happening. All the energy supplied goes into overcoming the forces between the particles rather than making them move faster.
The energy needed equals mass multiplied by specific latent heat. Specific latent heat is measured in joules per kilogram, with no temperature term, because there is no temperature change.
Two values are used. The specific latent heat of fusion applies to melting and freezing; the specific latent heat of vaporisation applies to boiling, evaporating and condensing. For any substance the latent heat of vaporisation is the larger, because separating particles completely requires more energy than merely allowing them to move past one another.
Heating and cooling graphs
A graph of temperature against time for a substance being heated steadily has a distinctive shape: sloping sections separated by horizontal plateaus.
The sloping sections are where the temperature is rising and the substance is in a single state. The steepness depends on the specific heat capacity: a substance with a low specific heat capacity heats quickly, giving a steep line.
The horizontal plateaus are where a change of state is occurring. The temperature stays constant even though energy is still being supplied, because the energy is going into the potential energy of the particles, breaking the forces between them, rather than into kinetic energy. The first plateau is melting and the second is boiling, and the longer plateau is boiling because the latent heat of vaporisation is larger.
Being able to explain why the plateau is flat, in terms of potential rather than kinetic energy, is the single most valuable explanation in this unit.
Gas pressure
The particles of a gas move in random directions at random speeds. When they collide with the walls of the container, each collision exerts a small force on the wall. The total force over an area gives the pressure, so gas pressure is the result of countless collisions.
The temperature of a gas is related to the average kinetic energy of its particles. Heating a gas therefore makes the particles move faster.
If a gas is heated in a sealed container of fixed volume, the particles move faster, so they collide with the walls more frequently and each collision exerts a greater force. Both effects increase the pressure. A full answer needs both the frequency and the force.
Absolute zero, at minus 273 degrees Celsius, is the temperature at which the particles have the least possible kinetic energy.
Worked examples
Example 1: Calculating density (3 marks)
A metal block has a mass of 540 grams and measures 5 centimetres by 4 centimetres by 2.5 centimetres. Calculate its density in grams per cubic centimetre.
The volume is 5 multiplied by 4 multiplied by 2.5, which gives 50 cubic centimetres. Density is mass divided by volume, which is 540 divided by 50, giving 10.8 grams per cubic centimetre. Since this is greater than water's 1 gram per cubic centimetre, the block would sink, which is a sensible result for a metal.
Example 2: A specific latent heat calculation (3 marks)
Calculate the energy needed to melt 0.35 kilograms of ice at 0 degrees Celsius. The specific latent heat of fusion of ice is 334,000 joules per kilogram.
The energy equals mass multiplied by specific latent heat, which is 0.35 multiplied by 334,000. This gives 116,900 joules, or about 117 kilojoules. Note that no temperature change appears in the calculation, because the ice stays at 0 degrees Celsius throughout the melting.
Example 3: Explaining a flat section on a heating graph (4 marks)
A substance is heated steadily. Explain why its temperature stays constant for a period even though energy is still being supplied.
During this period the substance is changing state. The energy supplied is being used to increase the potential energy of the particles by overcoming the forces of attraction between them, rather than increasing their kinetic energy. Since temperature depends on the average kinetic energy of the particles, and that is not increasing, the temperature remains constant. Once the change of state is complete, further energy increases the kinetic energy again and the temperature rises.
Common mistakes and how to avoid them
The most common error in this unit is treating a change of state as a chemical change. It is physical and reversible, and the particles themselves are unchanged.
Students frequently use the specific heat capacity equation when a change of state is occurring. If the temperature is constant, use specific latent heat; if the temperature is changing, use specific heat capacity. Checking which is happening before choosing the equation prevents this entirely.
In gas pressure explanations, many answers mention only that particles collide more often. The force of each collision also increases, and both are usually needed.
Another regular slip is confusing internal energy with temperature. Internal energy is the total kinetic and potential energy of all the particles; temperature relates only to the average kinetic energy.
Finally, in density practicals, forgetting to subtract the mass of the measuring cylinder when finding the mass of a liquid produces a density far too high. Always subtract the container.
Exam technique for "Physics: Particle Model of Matter"
Before starting any calculation, decide whether the temperature is changing. That one decision selects the correct equation and is where most marks in this unit are won or lost.
State units carefully. Density may be asked for in kilograms per cubic metre or grams per cubic centimetre, and the two differ by a factor of 1,000.
When explaining anything in this unit, refer to the particles explicitly — their arrangement, their separation, their speed, or the forces between them. Answers phrased only in terms of the substance as a whole rarely reach full marks.
For the required practical, be ready to describe the eureka can method for an irregular solid and to explain why the displaced water equals the object's volume.
Quick revision summary
Density is mass divided by volume, and depends on how closely particles are packed, so solids are densest and gases least dense. Regular solids are measured by dimensions, irregular solids by displacement, and liquids by subtracting the container's mass. Solids have particles vibrating in fixed regular positions, liquids have particles touching but randomly arranged and mobile, gases have widely separated fast-moving particles. Changes of state are physical and reversible, and mass is conserved. Internal energy is the total kinetic and potential energy of the particles. Heating either raises temperature, using mass times specific heat capacity times temperature change, or changes state, using mass times specific latent heat with no temperature change. Heating graphs show sloping sections where temperature rises and flat plateaus during changes of state, where energy goes to potential rather than kinetic energy. Gas pressure comes from particle collisions with the container walls, and heating a sealed gas raises pressure by making collisions both more frequent and more forceful.