Cambridge IGCSE Physics 0625

Chapter 2.1

Kinetic Particle Model of Matter

Detailed Core and Extended notes on states of matter, particle motion, Brownian motion, gas pressure, absolute temperature and the pressure–volume relationship.

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Syllabus coverage

Syllabus Checklist

Core You should be able to:

2.1.1 States of matter

  1. Know the distinguishing properties of solids, liquids and gases.
  2. Know the terms for changes in state between solids, liquids and gases.

2.1.2 Particle model

  1. Describe the particle structure of solids, liquids and gases in terms of particle arrangement, separation and motion, and represent these states using simple particle diagrams.
  2. Describe the relationship between particle motion and temperature, including the idea that there is a lowest possible temperature, approximately −273 °C, known as absolute zero, where particles have the least kinetic energy.
  3. Describe the pressure and changes in pressure of a gas in terms of the motion of its particles and their collisions with a surface.
  4. Know that the random motion of microscopic particles in a suspension is evidence for the kinetic particle model of matter.
  5. Describe and explain Brownian motion in terms of random collisions between microscopic particles in a suspension and particles of the surrounding liquid or gas.

2.1.3 Gases and the absolute scale of temperature

  1. Describe qualitatively, using particles, the effect on the pressure of a fixed mass of gas of:
    1. a change of temperature at constant volume
    2. a change of volume at constant temperature
  2. Convert temperatures between kelvin and degrees Celsius, and recall and use T (in K) = θ (in °C) + 273.

Extended Core plus Supplement:

2.1.1 States of matter

There are no separate Supplement points for this subsection.

2.1.2 Particle model

  1. Know that the forces and distances between particles, including atoms, molecules, ions and electrons, and the motion of the particles affect the properties of solids, liquids and gases.
  2. Describe gas pressure and changes in pressure in terms of forces exerted by particles colliding with surfaces, creating a force per unit area.
  3. Know that microscopic particles may be moved by collisions with light, fast-moving molecules, and correctly distinguish atoms and molecules from microscopic particles.

2.1.3 Gases and the absolute scale of temperature

  1. Recall and use pV = constant for a fixed mass of gas at constant temperature, including a graphical representation of this relationship.
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Essential language

Definitions

Particle

A small constituent of matter. Depending on the substance, its particles may be atoms, molecules or ions.

Kinetic energy

The energy an object or particle has because it is moving.

Absolute zero

The lowest possible temperature, approximately −273 °C or 0 K, where particles have the least possible kinetic energy.

Brownian motion

The random, irregular motion of microscopic particles suspended in a liquid or gas, caused by unequal collisions with surrounding molecules.

Gas pressure

Force per unit area produced when moving gas particles collide with the walls of their container.

Atom

The smallest particle of an element that retains the chemical properties of that element.

Molecule

A group of two or more atoms chemically bonded together.

Fixed mass of gas

A sealed quantity of gas in which no particles enter or leave during the investigation.

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Core

Core Notes

2.1.1 States of matter

Matter commonly exists as a solid, liquid or gas. These states can be distinguished by whether they have a fixed shape and a fixed volume.

State Shape Volume Ability to flow Compressibility
Solid Fixed shape Fixed volume Does not flow Very difficult to compress
Liquid Takes the shape of the container Fixed volume Flows Very difficult to compress
Gas Fills the container No fixed volume Flows Can be compressed

Changes of state

  • Melting: solid to liquid.
  • Freezing: liquid to solid.
  • Boiling or evaporation: liquid to gas.
  • Condensation: gas to liquid.
Fig. 1: Particle arrangements and changes between solid, liquid and gas.

2.1.2 Particle model

Solid

  • Particles are very close together in a regular arrangement.
  • Strong attractive forces hold the particles in fixed positions.
  • The particles cannot move from place to place, but they continually vibrate about fixed positions.
  • Because the particles remain in fixed positions, a solid has a fixed shape.
  • Because the particles are already closely packed, a solid has a fixed volume and is extremely difficult to compress.
  • Heating increases the kinetic energy of the particles, so they vibrate more vigorously.
Fig. 2: Particles in a solid.

Liquid

  • Particles are close together but are arranged irregularly.
  • Attractive forces keep the particles close, but the particles are not held in fixed positions.
  • The particles move randomly and slide past one another.
  • This movement allows a liquid to flow and take the shape of its container.
  • The particles remain close together, so a liquid has a fixed volume and is difficult to compress.
Fig. 3: Particles in a liquid.

Gas

  • Particles are widely separated and arranged randomly.
  • Attractive forces between particles are negligible except during collisions.
  • The particles move rapidly and randomly in every direction.
  • Particles collide with one another and with the walls of their container.
  • A gas has no fixed shape or volume because its particles move throughout the available space.
  • The large gaps between particles allow a gas to be compressed.
Fig. 4: Particles in a gas.

Particle motion and temperature

Temperature is related to the average kinetic energy of particles. When a substance is heated, its particles gain kinetic energy. Particles in a solid vibrate more vigorously, while particles in liquids and gases move faster.

When temperature decreases, the average kinetic energy decreases. Particle movement becomes slower, but particles do not normally stop moving.

Gas pressure

Gas particles move randomly and repeatedly collide with the walls of their container. Each collision exerts a force on the wall. The combined force of very many collisions, acting over the wall’s area, produces gas pressure.

If the temperature of a fixed mass of gas increases while its volume remains constant:

  1. The average kinetic energy of the particles increases.
  2. The particles move faster.
  3. They collide with the walls more frequently.
  4. Each collision produces a greater change in momentum.
  5. The force on the walls increases, so the pressure increases.

If the temperature decreases at constant volume, the particles move more slowly. Their collisions with the walls are less frequent and produce smaller forces, so the pressure decreases.

Evidence for the particle model

Microscopic smoke, dust or pollen particles suspended in a liquid or gas can be observed moving randomly. This motion provides evidence that the surrounding liquid or gas is made of rapidly moving particles.

Brownian motion

Brownian motion is the random, irregular movement of microscopic particles suspended in a liquid or gas. The suspended particles are much larger than the individual atoms or molecules of the surrounding fluid.

Surrounding molecules move rapidly and collide with each suspended particle from every direction. At any instant, the collisions are not perfectly balanced. The unequal forces make the suspended particle change speed and direction unpredictably.

Fig. 5: Random motion caused by unequal molecular collisions.

2.1.3 Gases and the absolute temperature scale

Temperature change at constant volume

When a fixed mass of gas is heated in a rigid sealed container, its volume cannot change. The particles gain kinetic energy and move faster. They collide with the container walls more frequently and each collision causes a larger momentum change. The force on the walls increases, so the pressure increases.

Volume change at constant temperature

If the volume of a fixed mass of gas increases while its temperature remains constant, the average particle speed remains unchanged. The particles travel farther between collisions with the walls, so collisions occur less frequently. The force exerted on the walls per unit area decreases, so the pressure decreases.

If the gas is compressed at constant temperature, particles travel a shorter distance between wall collisions. Collisions become more frequent, so pressure increases.

Converting Celsius and kelvin temperatures

The kelvin scale begins at absolute zero. A temperature difference of 1 K is the same size as a temperature difference of 1 °C.

  • Convert Celsius to kelvin by adding 273.
  • Convert kelvin to Celsius by subtracting 273.
  • Example: 25 °C + 273 = 298 K.
  • Example: 300 K − 273 = 27 °C.
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Equations and units

Key Equations

Celsius to kelvin

T (K) = θ (°C) + 273

T is absolute temperature in kelvin (K). θ is temperature in degrees Celsius (°C).

Gas pressure

p = F A

p is pressure in pascals (Pa), F is force in newtons (N), and A is area in square metres (m2).

Boyle’s law

pV = constant

For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume.

Changing pressure and volume

p1V1 = p2V2

Pressure units must be consistent with each other, and volume units must be consistent with each other.

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Supplement material

Extended Notes

These notes add the Supplement content. The Core notes above are not repeated.

Forces and distances between particles

The properties of a state depend on the distance between its particles, the forces between them and their motion.

  • Solids: particles are very close together and strong forces hold them near fixed positions. This produces a fixed shape and volume.
  • Liquids: particles remain close because attractive forces still act, but they have enough energy to move past one another. A liquid flows while retaining a fixed volume.
  • Gases: particles are widely separated. Forces between them are negligible except during collisions, so particles move freely and occupy the available space.

Heating increases particle kinetic energy. If particles gain enough energy to overcome some of the attractive forces, a solid may melt or a liquid may become a gas. Cooling reduces particle kinetic energy, allowing attractive forces to bring particles closer together.

Gas pressure in terms of force

When a gas particle strikes a wall, it changes direction and therefore changes momentum. A force is required to cause this momentum change. By Newton’s third law, the particle exerts an equal and opposite force on the wall.

Billions of collisions occur continuously. Their combined force divided by the surface area gives the pressure of the gas. More frequent collisions or larger momentum changes produce a greater force and therefore a greater pressure.

Fig. 6: A collision changes particle momentum and produces a force on the wall.

Microscopic particles, atoms and molecules

A microscopic suspended particle, such as a smoke or pollen particle, contains a very large number of atoms or molecules. It must not be confused with an individual atom or molecule.

The suspended particle is moved by unequal collisions with much lighter and faster-moving molecules of the surrounding gas or liquid. Individual molecules are too small to be seen with an ordinary microscope, but their effects on the larger suspended particles can be observed.

Boyle’s law

For a fixed mass of gas at constant temperature, pressure is inversely proportional to volume. This means that increasing the volume decreases the pressure, while decreasing the volume increases the pressure.

The condition of constant temperature is essential. If temperature changes, the average kinetic energy and speed of the particles also change, so pV will not necessarily remain constant.

Fig. 7: Initial and final pressure and volume quantities.

Graphical relationship

  • A graph of pressure against volume is a decreasing curve called a rectangular hyperbola.
  • A graph of pressure against 1/V is a straight line through the origin.
  • The straight-line graph shows that p ∝ 1/V.
Fig. 8: Graphical representations of Boyle’s law.

Worked example: compressing a gas

A fixed mass of gas is compressed at constant temperature from 340 cm3 to 40 cm3. Its initial pressure is 150 kPa. Calculate the final pressure.

Equation: p1V1 = p2V2

Substitution: 150 × 340 = p2 × 40

Rearrangement:

p2 = 150 × 340 40

Final answer: p2 = 1275 kPa = 1.275 × 106 Pa

The final pressure is greater because the gas has been compressed into a smaller volume.

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Exam practice

Practice Questions

Core3 marks

Question 1

Describe the arrangement and motion of particles in a liquid.

Core3 marks

Question 2

The temperature of a fixed mass of gas in a rigid container decreases. State and explain what happens to its pressure.

Core2 marks

Question 3

Convert 47 °C to kelvin.

Extended4 marks

Question 4

Explain, in terms of momentum, how gas particles produce pressure on a container wall.

Extended4 marks

Question 5

A gas occupies 600 cm3 at 90 kPa. It is compressed at constant temperature to 240 cm3. Calculate its new pressure.

Extended3 marks

Question 6

Explain why a smoke particle observed under a microscope moves randomly even though individual air molecules cannot be seen.

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Flashcards

Next topic 2.2 Thermal properties and temperature
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