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GCSE Physics · GCSEChapter 9 · The particle model, density and internal energy
GCSE · Chapter 9

The particle model, density and internal energy

By the end of this chapter you will be able to

  • Describe the three states of matter using the particle model
  • Calculate density from mass and volume, and rearrange the equation
  • Describe how to measure the density of a regular solid, an irregular solid and a liquid
  • Read a heating curve and explain the flat parts
  • Calculate the energy needed to melt or boil a mass of a substance

You should already know

  • Specific heat capacity and E = mc change in theta (Chapter 3)
  • Energy stores and transfers (Chapter 1)

Where this leads

  • Pressure in gases and liquids (Chapter 14)
  • Atoms and the nuclear model (Chapter 10)

GCSE Physics. Content follows the GCSE (9-1) subject content for England (Edexcel and AQA). Content references: Describe the arrangement, motion and energy of particles in solids, liquids and gases, Use density = mass / volume, in g/cm3 and kg/m3, Describe the practical to find the density of a regular solid, an irregular solid and a liquid, Explain internal energy as the kinetic and potential energy of the particles, and read a heating curve, Use E = m L to calculate the energy to change the state of a material (specific latent heat).

Exercise P  Do you remember?

1
FWhat is 540 divided by 200? Write the number.
2
FWhat is the volume of a box 5 cm long, 4 cm wide and 2 cm high? Write the number of cubic centimetres.
3
FWhat is the energy needed to warm 1 kg of water by 1 °C? Write the number of joules.
4
FWhat are the three states of matter? Write one: solid, liquid or gas.
5
FWhat is 1000 multiplied by 1000? Write the number.
9.1

States of matter and the particle model

GCSE
Describe the arrangement, motion and energy of particles in solids, liquids and gases
Video lesson: States of matter and the particle modelComing soon
Context. Ruby puts an ice cube in a glass. It melts, and the water later evaporates into the room. “Where does the ice go?” she asks. The particle model explains the three states of matter: solid, liquid and gas.

All matter is made of tiny particles. In a solid, the particles are close together in a regular pattern and vibrate in fixed positions. In a liquid, the particles are close but can move past each other. In a gas, the particles are far apart and move quickly in all directions. Gases can be compressed because there is a lot of space between the particles.

solidfixed, close, regularliquidclose, can move past each othergasfar apart, fast and random
The arrangement of particles in solids, liquids and gases
Energy storeWhat it isWhat happens when the substance is heated
kinetic (in particles)energy of the moving particlesthe temperature rises as the particles move faster
potential (in particles)energy stored by the forces between particlesit increases when a substance changes to a state with weaker forces, such as melting
Internal energy: the kinetic and potential energy of the particles

Key ideas

  • Solid: particles fixed in a regular pattern, vibrate only.
  • Liquid: particles close together, can move past each other, flow.
  • Gas: particles far apart, move quickly and randomly, can be compressed.
  • Changing state does not change the mass of the substance.
Worked example 9.1.1
In which state are the particles closest together and in a regular pattern? Write the state.

Method. Compare the three arrangements.

  1. Look. Solids have particles in a fixed, regular arrangement.
    regular
  2. Decide. So the solid is the state with particles closest in a regular pattern.
    solid
  3. Write the answer.
    solid

Check. ✓

Worked example 9.1.2
Why can a gas be compressed more easily than a liquid? Write one reason in one sentence. Accept any sentence that says there is a lot of space between the gas particles.

Method. Think about the space between the particles.

  1. Look. The gas particles are far apart.
    far apart
  2. Decide. So there is space to push them closer together.
    space
  3. Write the answer.
    Accept any sentence that says there is a lot of space between the gas particles.

Check. ✓

Worked example 9.1.3
When a solid is heated, its particles vibrate more. What happens to the temperature? Write rises or falls.

Method. More vibration means more kinetic energy.

  1. Look. The particles have more kinetic energy when they vibrate more.
    more kinetic
  2. Decide. Temperature is a measure of the average kinetic energy, so it rises.
    rises
  3. Write the answer.
    rises

Check. ✓

Watch out

Watch out: the particles themselves do not expand when a substance is heated. The gap between them changes, or they move more.

Exam tip

Exam tip. When describing particles, use the words “arrangement”, “motion” and “energy” in turn.

Exercise 9A  States and particles

1
FIn which state do the particles move freely and fill a container? Write the state.
2
FIn which state do particles vibrate in fixed positions? Write the state.
3
FIn which state are the particles close together but able to move past each other? Write the state.
4
FWhat happens to the mass of an ice cube when it melts? Write the word: increases, decreases or stays the same.
5
RGases can be compressed. Explain why, in one sentence. Accept any sentence that says the particles are far apart, so there is space to push them closer.
6
RLiquids cannot be compressed much. Explain why, in one sentence. Accept any sentence that says the particles are already close together, so there is little space to compress them.
7
FA solid is heated and its temperature rises. What happens to the kinetic energy of its particles: increases or decreases? Write the word.
8
PSName the state of matter in which the particles have the most kinetic energy of the three states, at the same temperature. Write the state.
9
RA pupil says “the particles in a solid stop moving.” Explain why this is wrong. Accept any answer that says the particles still vibrate about fixed positions.
10
RA balloon is filled with a gas. The temperature rises, and the balloon expands. Explain, in one sentence, using the particle model. Accept any sentence that says the particles move faster and hit the walls harder, so the balloon expands.
11
RDraw a simple particle diagram for a gas in a box, and say how many particles you drew. Write only the number of particles drawn, and accept any number of at least 6 widely spaced particles.
12
RIn a solid, the particles are in a regular pattern. Explain why a solid keeps its shape, in one sentence. Accept any sentence that says the particles are held in fixed positions by strong forces.
9.2

Density and measuring density

GCSE
Use density = mass / volume, in g/cm3 and kg/m3, Describe the practical to find the density of a regular solid, an irregular solid and a liquid
Video lesson: Density and measuring densityComing soon
Context. A pupil is given three objects and asked which is made of the densest material. She weighs each one on a balance and measures its size. The density is the mass divided by the volume, so she needs both.

Density is the mass of a material in each unit of volume. It is found from:

density = mass / volume, so mass = density x volume and volume = mass / density

Density is measured in g/cm3 or kg/m3. To change g/cm3 into kg/m3, multiply by 1000. A substance with a higher density has more mass in the same volume. Objects with a density less than water float.

MaterialDensity (g/cm3)Density (kg/m3)
water1.01000
ice0.92920
aluminium2.72700
iron7.97900
copper8.98900
Densities of some common materials (approximate values)

Required practical: density. Measure the mass of each object on a balance and record it in grams. For a regular solid (a block), measure its length, width and height with a ruler, and multiply to find the volume. For an irregular solid, use a measuring cylinder: note the water level, put the object in carefully, and note the new level. The difference is the volume of the object (displacement). For a liquid, find the mass of an empty measuring cylinder, pour in a known volume, and find the mass again. The mass of the liquid divided by its volume is its density.

02040608010050 cm3 (before)80 cm3 (after)stone: volume = 80 - 50 = 30 cm3
Finding the volume of an irregular solid by displacement

Key ideas

  • density = mass / volume. Units: g/cm3 (or kg/m3).
  • 1 g/cm3 = 1000 kg/m3.
  • Regular solid: volume = length x width x height.
  • Irregular solid: volume = the rise in the water level (displacement).
Worked example 9.2.1
A block has a mass of 540 g and a volume of 200 cm3. Calculate its density in g/cm3. Write the number.

Method. Use density = mass / volume.

  1. Take the numbers. Mass = 540 g and volume = 200 cm3.
    m = 540, V = 200
  2. Divide. Density = 540 / 200 = 2.7 g/cm3.
    540 / 200 = 2.7
  3. Write the answer.
    2.7 g/cm3

Check. 2.7 x 200 = 540 g. ✓

Worked example 9.2.2
An irregular stone has a mass of 75 g. The water level rises from 50 cm3 to 80 cm3 when it is added. Calculate its density in g/cm3. Write the number.

Method. Find the volume by displacement first.

  1. Volume. Volume = 80 - 50 = 30 cm3.
    80 - 50 = 30 cm3
  2. Density. Density = 75 / 30 = 2.5 g/cm3.
    75 / 30 = 2.5
  3. Write the answer.
    2.5 g/cm3

Check. 2.5 x 30 = 75 g. ✓

Worked example 9.2.3
A liquid has a mass of 80 g in a volume of 100 cm3. Convert the density into kg/m3. Write the number.

Method. Find the density in g/cm3 first, then multiply by 1000.

  1. Density. Density = 80 / 100 = 0.8 g/cm3.
    0.8 g/cm3
  2. Convert. 0.8 x 1000 = 800 kg/m3.
    0.8 x 1000 = 800
  3. Write the answer.
    800 kg/m3

Check. 800 kg/m3 is less than water, so it would float on water. ✓

Watch out

Watch out: the displacement volume is the difference between the two water levels, not the level after the object is added. Use the mass in grams with cm3 to get g/cm3.

Exam tip

Practical safety. Use ordinary lab apparatus at room temperature. Wipe up spills, and wear eye protection if the teacher asks you to.

Exercise 9B  Density calculations and the practical

1
FA block has a mass of 200 g and a volume of 100 cm3. Calculate its density. Write the number of g/cm3.
2
FA cube of metal has a volume of 40 cm3 and a density of 2.5 g/cm3. Calculate its mass. Write the number of grams.
3
FA liquid has a mass of 250 g and occupies 250 cm3. Calculate its density. Write the number of g/cm3.
4
FA material has a density of 3 g/cm3 and a volume of 12 cm3. Calculate its mass. Write the number of grams.
5
FA block has a mass of 96 g and a density of 8 g/cm3. Calculate its volume. Write the number of cm3.
6
PSA regular block measures 5 cm by 4 cm by 2 cm and has a mass of 320 g. Calculate its density. Write the number of g/cm3.
7
PSA stone has a mass of 45 g. When it is placed in a measuring cylinder, the water rises from 20 cm3 to 35 cm3. Calculate its density. Write the number of g/cm3.
8
PSConvert a density of 2.7 g/cm3 into kg/m3. Write the number.
9
PSA liquid has a mass of 60 g and a volume of 75 cm3. Calculate its density. Write the number of g/cm3.
10
PSIn the practical for a liquid, the empty measuring cylinder has a mass of 50 g. With 100 cm3 of liquid it has a mass of 150 g. Calculate the density. Write the number of g/cm3.
11
RExplain why a pupil should use the displacement method, rather than a ruler, to find the volume of a stone. Accept any answer that says the stone has an irregular shape, so its volume cannot be found from its length, width and height.
12
RWhich object floats in water: a block of density 0.6 g/cm3 or a block of density 2.7 g/cm3? Write 0.6 or 2.7.
13
RA pupil says “the density of a liquid is the same whatever the volume.” Is the pupil right? Write yes or no.
14
PSTwo blocks of the same material have masses of 100 g and 300 g. Which has the bigger volume: the 300 g block or the 100 g block? Write 300 or 100.
9.3

Internal energy and heating curves

GCSE
Explain internal energy as the kinetic and potential energy of the particles, and read a heating curve
Video lesson: Internal energy and heating curvesComing soon
Context. Mr Singh heats a beaker of water with a low-voltage heater. He plots the temperature against time. The graph is not a straight line: it has flat parts. What is happening during the flat parts?

The internal energy of a substance is the total kinetic energy and potential energy of its particles. When a substance is heated, its internal energy increases. If the temperature rises, the average kinetic energy of the particles increases. When the substance changes state (melts or boils), the energy goes into the potential energy of the particles, which pulls them apart, so the temperature stays constant during the change.

Heating curve for water (example)-20020406080100120temperature (deg C)time (minutes)meltingboilingsolid warming
Heating curve for water: flat parts at the melting point (0 °C) and the boiling point (100 °C)

Key ideas

  • Internal energy = kinetic + potential energy of the particles.
  • A rising temperature means the kinetic energy of the particles is rising.
  • During a change of state the temperature stays constant: energy goes into potential energy.
  • A heating curve has flat parts where the substance is melting or boiling.
Worked example 9.3.1
On the heating curve, what is the temperature of the flat part for melting water? Write the number in °C.

Method. Read the flat part at the start.

  1. Read. The first flat part is at 0 °C.
    0 °C
  2. Decide. So water melts at 0 °C.
    0 °C
  3. Write the answer.
    0 °C

Check. ✓

Worked example 9.3.2
During the flat part at 100 °C, what happens to the internal energy? Write increases or stays the same.

Method. Think about where the energy goes during boiling.

  1. Look. The energy goes into breaking the forces between particles, not into the kinetic store.
    potential store
  2. Decide. So the internal energy rises while the temperature stays at 100 °C.
    increases
  3. Write the answer.
    increases

Check. The internal energy increases during a change of state. ✓

Worked example 9.3.3
Why does the temperature stay constant during melting, even though energy is still being supplied? Write one reason in one sentence. Accept any sentence that says the energy goes into potential energy, separating the particles.

Method. Think about where the energy goes.

  1. Look. The energy is used to change the arrangement of the particles.
    arrangement
  2. Decide. So it goes into potential energy and not into a rise in temperature.
    potential energy
  3. Write the answer.
    Accept any sentence that says the energy goes into potential energy, separating the particles.

Check. ✓

Watch out

Watch out: the flat part does not mean no energy is being supplied. Energy is still going in, but it changes the state, not the temperature.

Exam tip

Exam tip. On a heating curve, a sloping part means the temperature rises; a flat part means a change of state.

Exercise 9C  Heating curves and internal energy

1
FOn a heating curve, what does a flat part show? Write the word: state or temperature.
2
FWhat is the melting point of water on the heating curve? Write the number in °C.
3
FWhat is the boiling point of water on the heating curve? Write the number in °C.
4
FInternal energy is the total of which two kinds of energy of the particles? Write two words.
5
PSDuring melting, is the potential energy of the particles increasing or decreasing? Write the word.
6
PSBetween 0 °C and 100 °C, the water is a liquid and its temperature rises. What is happening to the kinetic energy of the particles? Write the word.
7
RExplain why the internal energy of a substance increases during a flat part of a heating curve, in one sentence. Accept any sentence that says energy is supplied and goes into potential energy while the temperature is constant.
8
RA pupil says “the temperature of a substance stops rising when it is heated.” Explain why this is not true in general. Accept any answer that says the temperature stops rising only during a change of state.
9
PSOn a heating curve, a substance warms from 20 °C to 60 °C without a flat part. Is it changing state? Write yes or no.
10
FName the store that gains energy during melting and is not the kinetic store. Write the word.
9.4

Specific latent heat

GCSE
Use E = m L to calculate the energy to change the state of a material (specific latent heat)
Video lesson: Specific latent heatComing soon
Context. An ice cube at 0 °C melts into water at 0 °C. Energy goes in, but the temperature does not change. The energy needed is the specific latent heat.

The specific latent heat L of a substance is the energy needed to change the state of 1 kg of it, without a change of temperature. Its unit is J/kg. There are two values: the specific latent heat of fusion (for melting or freezing) and the specific latent heat of vaporisation (for boiling or condensing).

E = m x L

Key ideas

  • E = m x L, with m in kg and L in J/kg.
  • L is the energy to change state of 1 kg, with no temperature change.
  • Use the example values here: fusion of ice 330 000 J/kg; vaporisation of water 2 300 000 J/kg (rounded examples).
  • Energy for a temperature change uses E = m c change in theta; energy for a change of state uses E = m L.
Worked example 9.4.1
Calculate the energy needed to melt 0.5 kg of ice at 0 °C, using L = 330 000 J/kg. Write the number of joules.

Method. Use E = m x L.

  1. Take the numbers. m = 0.5 kg and L = 330 000 J/kg.
    m = 0.5, L = 330000
  2. Multiply. E = 0.5 x 330000 = 165000 J.
    0.5 x 330000 = 165000
  3. Write the answer.
    165000 J

Check. 165000 / 330000 = 0.5 kg. ✓

Worked example 9.4.2
Calculate the energy needed to boil 2 kg of water at 100 °C, using L = 2 300 000 J/kg. Write the number of joules.

Method. Use E = m x L.

  1. Take the numbers. m = 2 kg and L = 2 300 000 J/kg.
    m = 2, L = 2300000
  2. Multiply. E = 2 x 2300000 = 4600000 J.
    2 x 2300000 = 4600000
  3. Write the answer.
    4600000 J

Check. 4600000 / 2300000 = 2 kg. ✓

Worked example 9.4.3
A mass of 0.25 kg of a substance needs 75 000 J to melt. Find its specific latent heat. Write the number in J/kg.

Method. Rearrange to L = E / m.

  1. Rearrange. L = 75000 / 0.25.
    75000 / 0.25
  2. Divide. L = 300000 J/kg.
    75000 / 0.25 = 300000
  3. Write the answer.
    300000 J/kg

Check. 0.25 x 300000 = 75000 J. ✓

Watch out

Watch out: E = m L is for a change of state. Do not use E = m c Δθ for melting or boiling, and do not use L for a temperature change.

Exam tip

Exam tip. Ask yourself: is the temperature changing, or the state? Temperature change uses c; change of state uses L.

Exercise 9D  Specific latent heat

1
FCalculate the energy needed to melt 1 kg of ice, with L = 330 000 J/kg. Write the number of joules.
2
FCalculate the energy needed to boil 0.5 kg of water, with L = 2 300 000 J/kg. Write the number of joules.
3
FCalculate the energy needed to melt 2 kg of a substance with L = 150 000 J/kg. Write the number of joules.
4
PSA substance needs 600 000 J to melt 2 kg. Find the specific latent heat. Write the number in J/kg.
5
PSCalculate the mass of ice that can be melted by 99 000 J, with L = 330 000 J/kg. Write the number of kg.
6
PSHow much energy is needed to change 0.2 kg of water at 100 °C into steam at 100 °C, with L = 2 300 000 J/kg? Write the number of joules.
7
RExplain the difference between E = mcΔθ and E = mL, in one sentence. Accept any sentence that says the first is for a temperature change and the second is for a change of state at constant temperature.
8
PSIce at 0 °C is melted and the water is then warmed from 0 °C to 10 °C. Write which equation is used for the warming part: c or L.
9
PSCalculate the energy to melt 0.4 kg of ice, with L = 330 000 J/kg. Write the number of joules.
10
PSA heater supplies 3000 W to melt ice. How long does it take to supply 165 000 J? Write the number of seconds.
11
RExplain why steam at 100 °C can cause more harm than boiling water at 100 °C, in one sentence. Accept any sentence that says steam releases a large amount of energy as it condenses, due to the latent heat.

Chapter summary

SkillMethod
Particle arrangementSolid: regular, fixed; liquid: close, sliding; gas: far apart, random
Densitydensity = mass / volume; kg/m3 = g/cm3 x 1000
Measure densityRegular: ruler; irregular: displacement; liquid: mass difference over volume
Heating curveSloping: temperature rises; flat: change of state
Latent heatE = m x L; L in J/kg; no temperature change

Can you…?

  • I can describe the particle arrangement in each state
  • I can calculate density and convert g/cm3 to kg/m3
  • I can describe how to find the density of a regular solid, an irregular solid and a liquid
  • I can read a heating curve and explain the flat parts
  • I can use E = mL for a change of state

Key terms

density
mass per unit volume; density = mass / volume
internal energy
the total kinetic and potential energy of the particles of a substance
displacement
the volume of water pushed aside by an object
specific latent heat (L)
the energy needed to change the state of 1 kg without a temperature change, in J/kg
change of state
a change such as melting or boiling; the temperature stays constant during it

Exercise 9Z  Check-up

1
A block of mass 60 g has a volume of 20 cm3. Calculate its density. Write the number of g/cm3.
2
Calculate the mass of a 15 cm3 object of density 4 g/cm3. Write the number of grams.
3
Convert 1.5 g/cm3 into kg/m3. Write the number.
4
Which state of matter has particles far apart and moving quickly in all directions? Write the state.
5
During which part of a heating curve does the temperature stay constant? Write the word: melting or heating.
6
Calculate the energy needed to melt 0.5 kg of ice with L = 330 000 J/kg. Write the number of joules.
7
A measuring cylinder has 40 cm3 of water. A stone is added and the level reads 65 cm3. What is the volume of the stone? Write the number of cm3.
8
A stone of mass 50 g has a volume of 25 cm3. Calculate its density. Write the number of g/cm3.
9
Name the energy store that increases when a solid melts, apart from the kinetic store. Write the word.
10
Explain why a gas is easier to compress than a solid, in one sentence. Accept any sentence that says gas particles are far apart and there is more space between them.

Total 32 marks. Allow about 32 minutes.

Exercise 9X  Exam-style questions

1
FA block has a mass of 540 g and a volume of 200 cm3. Calculate its density. Write the number of g/cm3.[2 marks]
2
FA student measures the volume of an irregular stone using a measuring cylinder. The water level rises from 30 cm3 to 45 cm3. Calculate the volume of the stone. Write the number of cm3.[2 marks]
3
RDescribe the practical steps to find the density of a regular block with a balance and a ruler. Accept any answer with: measure the mass with a balance, measure length, width and height with a ruler, multiply for the volume, then divide mass by volume.[4 marks]
4
RDescribe how the particle model explains why a gas exerts pressure on the walls of a container. Accept any answer that says the particles move randomly and collide with the walls, exerting a force.[3 marks]
5
RA heating curve for a substance has a flat part at 50 °C. Explain what is happening during the flat part, using the idea of internal energy. Accept any answer that says the substance is changing state, and energy goes into potential energy, not temperature.[3 marks]
6
PSA pupil heats 0.2 kg of ice at 0 °C to melt it, with L = 330 000 J/kg. Calculate the energy needed. Write the number of joules.[2 marks]
7
PSA liquid of mass 0.8 kg has a volume of 1 000 cm3. Calculate its density in g/cm3, and then in kg/m3. Write two values, separated by a comma.[3 marks]
8
RA student wants to find the density of a liquid. Describe the method and the calculation, including how to find the mass of the liquid. Accept any answer that finds the mass of the empty cylinder, then with the liquid, subtracts, and divides by the volume.[4 marks]
9
RExplain why the temperature of a substance stays the same during a change of state, even though energy is supplied, and say what the energy is used for. Accept any answer that says the energy is used to change the arrangement or the potential energy of the particles.[4 marks]
10
PSA 0.5 kg block of ice at 0 °C is melted, and the water is then warmed to 20 °C. Calculate the total energy needed. Use L = 330 000 J/kg and c = 4200 J/kg °C. Write the number of joules.[5 marks]
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