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Cambridge IGCSE0625

Kinetic particle model of matter

Physics 0625 Chapter Notes

What this chapter covers

Kinetic particle model of matter - States of matterKinetic particle model of matter - Particle modelKinetic particle model of matter - Gases and the absolute scale of temperature
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In this chapter

  1. 1Solids
  2. 2Liquids and gases
  3. 3Changes of state
  4. 4Solids, liquids and gases
  5. 5Temperature and absolute zero
  6. 6Gas pressure from particle collisions
  7. 7Random motion of microscopic particles
  8. 8Forces and distances between particles
  9. 9Pressure as force per unit area
  10. 10Atoms, molecules and microscopic particles
  11. 11Gas pressure and temperature
  12. 12Gas pressure and volume
  13. 13Kelvin and degrees Celsius
  14. 14Pressure and volume at constant temperature
  15. 15Graphs of pressure and volume

1. Solids

In a solid, the particles are in a regular (uniform) arrangement.

They are closely packed and held in fixed positions. They vibrate about those positions.

Examiner insight

“Weaker answers referred to inter-molecular spacing, energy or stated that particles are stationary in a solid.”

Worked example 13 marks

Describe the arrangement, separation and motion of the particles in a solid.

  1. 1

    arrangement: regular / uniform [1]

  2. 2

    separation: closely / tightly packed [1]

  3. 3

    motion: vibrate about fixed positions [1]

2. Liquids and gases

A liquid has a fixed volume. It is able to flow and has no fixed shape. Its particles are close to each other and slide over each other.

In a gas, the particles are far apart and in variable positions. Their arrangement is irregular (random). They move rapidly, in random directions.

Compared with a liquid, gas particles are further apart, have greater kinetic energy and fill the container.

Examiner insight

“In the arrangement section, a few candidates confused gas particles with the particles in a liquid, saying that the particles take the shape of the container.” “A common ambiguous description of particle motion was to state that particles move freely.”

Worked example 12 marks

Describe, in terms of particles and their motion, two ways in which a gas differs from a liquid.

  1. 1

    gas particles are further apart OR fill the container [1]

  2. 2

    gas particles have greater kinetic energy [1]

3. Changes of state

Melting is solid to liquid. Solidification is liquid to solid.

Condensation is gas to liquid. Evaporation and boiling are both liquid to gas. In evaporation, the more energetic particles escape from the surface of the liquid.

Gas to solid and solid to gas are not required.

Examiner insight

“Some confusion between boiling and evaporation was seen here.”

Worked example 11 mark

A hot furnace heats some solid metal until the metal becomes liquid. Name the process by which a solid becomes a liquid.

  1. 1

    melting [1]

Recap

  • Solid: regular arrangement, closely packed, vibrating about fixed positions.
  • Liquid: fixed volume, able to flow, no fixed shape. Particles close, sliding over each other.
  • Gas: particles far apart, irregular arrangement, moving rapidly in random directions.
  • Melting: solid to liquid. Solidification: liquid to solid.
  • Condensation: gas to liquid. Evaporation and boiling: liquid to gas.
  • Evaporation: the more energetic particles escape from the surface.

4. Solids, liquids and gases

In a solid the particles are in a regular arrangement, closely packed, and vibrate about fixed positions.

In a liquid the particles are close to each other and slide over each other. A liquid has a fixed volume, flows and has no fixed shape.

In a gas the particles are far apart, in an irregular arrangement, and move randomly and rapidly.

Examiner insight

“Some candidates confused the motion of particles in a solid with the motion of particles in a liquid.” “A common ambiguous description of particle motion was to state that particles move freely.”

Worked example 13 marks

Describe the arrangement, separation and motion of the particles in a solid.

  1. 1

    arrangement: regular (uniform) [1]

  2. 2

    separation: close together (closely packed) [1]

  3. 3

    motion: vibrate about fixed positions [1]

5. Temperature and absolute zero

The hotter a substance is, the faster its particles move. When the temperature falls, the average kinetic energy of the particles decreases.

The lowest possible temperature is absolute zero, −273 °C. At absolute zero the particles have the least kinetic energy.

Examiner insight

“Other candidates were unable to link the decrease in temperature to a decrease in kinetic energy of particles.” “Common incorrect answers stated that water froze at this temperature, showing confusion between the scales of temperature.”

Worked example 12 marks

State the term for the lowest possible temperature.

State the value, in °C, of the lowest possible temperature.

  1. 1

    absolute zero [1]

  2. 2

    −273 °C [1]

6. Gas pressure from particle collisions

A gas has pressure because its particles move randomly and collide with the walls of the container.

If the temperature rises, the particles move faster. They collide more frequently and with more force, so the pressure increases. If the temperature falls, the pressure decreases.

If the same gas is squeezed into a smaller volume, the particles hit the walls more frequently and the pressure increases.

Examiner insight

“Some candidates recognised that the speed of the gas molecules decreased when the temperature was decreased; this was not linked to a reduced rate of collisions with the wall of the balloon.” “Many candidates scored marks by referring to collisions between molecules, but only the most able referred to collisions with the walls of the tyre.”

Worked example 13 marks

The temperature of the air inside the box increases.

State and explain, in terms of particles, the effect on the air pressure inside the box.

  1. 1

    statement: the air pressure increases [1]

  2. 2

    the air particles move faster [1]

  3. 3

    the particles collide more frequently with the box, or with more force [1]

7. Random motion of microscopic particles

Pollen grains in water and smoke particles in air are microscopic particles in a suspension. Their motion is random: they move in a jerky way and keep changing direction.

The invisible molecules of the liquid or gas are very small and move fast and randomly. They collide with (bombard) the microscopic particle and make it change direction.

This random motion is evidence for the kinetic particle model of matter.

Examiner insight

“Weaker candidates thought that the motion was a result of pollen grains colliding with other pollen grains.” “Many weaker candidates incorrectly believed that the smoke particles moved randomly because they are less dense than air, and therefore chose option B.”

Worked example 13 marks

Figure 4.1 shows the path of a pollen grain in a drop of water. The pollen grain is a microscopic particle.

Describe and explain the motion of the pollen grain.

  1. 1

    the motion of the pollen grain is random [1]

  2. 2

    invisible water particles move randomly [1]

  3. 3

    the water particles collide with (bombard) the pollen grain [1]

8. Forces and distances between particles

The forces and distances between particles, and the motion of the particles, affect the properties of solids, liquids and gases.

The force of attraction between the particles of a solid is greater than between the particles of a gas. It is therefore easier to increase the separation of gas particles.

Compared with the particles of a liquid, gas particles are further apart, fill the container, have greater kinetic energy and have less force between them.

Examiner insight

“The fact that it is therefore easier to increase the separation of gas molecules was almost always missed.” “A few candidates confused the terms separation and arrangement of particles.”

Worked example 12 marks

Describe, in terms of particles and their motion, two ways in which a gas differs from a liquid.

  1. 1

    gas particles are further apart (they fill the container) [1]

  2. 2

    gas particles have greater kinetic energy, or less force between them [1]

9. Pressure as force per unit area

Each particle that collides with a wall has a change of momentum. The collisions cause a force on the wall.

The pressure is the total force of the collisions per unit area of the surface.

p = F/A

Examiner insight

“Most weaker candidates recalled that the gas particles experience a change in momentum when they collide with the walls of a container, but many of these candidates thought that the resulting pressure was equal to force × area.” “Others did not refer either to the difference in force exerted or that a smaller momentum change occurred.”

Worked example 13 marks

Explain how the particles of helium gas in the balloon exert a pressure on the inside of the balloon.

  1. 1

    the particles move fast (they have high kinetic energy) [1]

  2. 2

    the particles collide with the walls of the balloon [1]

  3. 3

    the collisions cause a force on the walls (a change of momentum) [1]

10. Atoms, molecules and microscopic particles

Microscopic particles may be moved by collisions with light, fast-moving molecules.

Use the terms with care. Atoms or molecules are the particles of the liquid or gas. A pollen grain or a smoke particle is a microscopic particle: pollen grains are hit by water molecules.

Examiner insight

“Although most candidates knew that the pollen was moved by the water molecules, a large number did not make the correct distinction between particles and molecules and therefore chose option D.” “Although some candidates recognised that the pollen particles were moved by water particles, many thought that the water particles are more massive than the pollen particles.”

Worked example 11 mark

Very small pollen grains are suspended in water. A bright light shines from the side.

When looked at through a microscope, small specks of light are seen to be moving in a random, jerky manner.

What are the moving specks of light?

A pollen grains being hit by other pollen grains · B pollen grains being hit by water molecules · C water molecules being hit by other water molecules · D water molecules being hit by pollen grains

  1. 1

    B: pollen grains being hit by water molecules. [1]

Recap

  • Solid: regular, closely packed, vibrate. Liquid: close, slide over each other. Gas: far apart, random.
  • Higher temperature: faster particles, more kinetic energy. Absolute zero is −273 °C, where particles have least kinetic energy.
  • Gas pressure: particles collide with the walls, more often and harder when hotter.
  • Microscopic particles move randomly because molecules bombard them.
  • Extended: forces and distances between particles affect the properties of solids, liquids and gases.
  • Extended: pressure = force ÷ area.
  • Extended: pollen is a microscopic particle; water is made of molecules.

11. Gas pressure and temperature

The particles of a gas move fast and collide with the walls of the container. The collisions exert a force on the walls. Pressure = force ÷ area.

At constant volume, a rise in temperature makes the particles move faster. They collide with the walls more frequently and with greater force, so the pressure increases.

A fall in temperature does the opposite. The particles move more slowly and collide with the walls less frequently and with less force, so the pressure decreases.

Examiner insight

“Weaker candidates often stated that this would increase the collisions but a reference to the increased frequency of collisions was required for credit.” “Some weaker candidates only referred to the energy of the molecules increasing and did not specify that it was their KE that increased.”

Worked example 13 marks

A box contains small dust particles suspended in air. The temperature of the air inside the box increases.

State and explain, in terms of particles, the effect on the air pressure inside the box.

  1. 1

    statement: the air pressure increases [1]

  2. 2

    air particles move faster [1]

  3. 3

    particles collide more frequently with the box (or with more force) [1]

12. Gas pressure and volume

At constant temperature the particles keep the same average speed, so their kinetic energy does not change.

When the volume of a fixed mass of gas is reduced, the particles are closer together. They hit the walls more frequently, so the pressure increases.

When the volume is increased, the particles hit the walls less frequently and the pressure decreases.

Examiner insight

“The key idea that there were more frequent collisions (with the wall of the container) was rarely seen.” “Nearly half of the candidates thought that reducing the volume of a gas, at constant temperature, caused the average speed of the molecules to increase.”

Worked example 11 mark

A gas is trapped inside a cylinder which is sealed by a freely moving piston. The piston is slowly pushed in so that the volume of the gas is reduced, but the temperature does not change.

What happens to the kinetic energy of the gas particles and the rate at which they collide with the piston?

kinetic energy of particlesrate at which they collide with the piston
Ano changeno change
Bno changeincreases
Cincreasesno change
Dincreasesincreases
  1. 1

    B: no change in kinetic energy, and the collision rate increases [1]

13. Kelvin and degrees Celsius

To change degrees Celsius into kelvin, add 273. To change kelvin into degrees Celsius, subtract 273.

Write the unit in the answer: K for kelvin, °C for degrees Celsius.

T (in K) = θ (in °C) + 273

θ = T - 273

Examiner insight

“Most candidates did not convert degrees Celcius into kelvin correctly.”

Worked example 12 marks

A flame heats the air in a hot-air balloon. The temperature of the hot air above the flame is 120 °C.

Determine the value of 120 °C in kelvin.

  1. 1

    temperature in kelvin = temperature in °C + 273 [1]

  2. 2

    120 + 273 = 393 K [1]

14. Pressure and volume at constant temperature

For a fixed mass of gas at constant temperature, pV is constant. So p₁V₁ = p₂V₂.

Pressure and volume change in opposite directions. Halving the volume doubles the pressure.

Write the equation in symbols first, then substitute and rearrange. Use the pressures as given.

pV = constant

p₁V₁ = p₂V₂

V₂ = p₁V₁/p₂

Examiner insight

“A few candidates related pressure and volume as p1V1 = p2V2 and were then unable to rearrange their equation to make V2 the subject.” “A few candidates subtracted atmospheric pressure from either the pressure inside the tyre or from their calculated volume.”

Worked example 13 marks

Atmospheric pressure is 1.0 × 10⁵ Pa. A volume of 1.02 m³ of air at atmospheric pressure is pumped into a car tyre. The pressure of the air when it is inside the tyre is 2.6 × 10⁵ Pa.

Calculate the volume of the air when it is in the car tyre.

  1. 1

    pV = constant [1]

  2. 2

    V = (1.02 × 1.0 × 10⁵)/(2.6 × 10⁵) [1]

  3. 3

    = 0.39 m³ [1]

15. Graphs of pressure and volume

For a fixed mass of gas at constant temperature, a graph of p against V is a curve that falls as V rises. It is not a straight line.

A graph of p against 1/V is a straight line through the origin.

Examiner insight

“Although a high proportion of candidates knew that there was an inverse relationship between pressure and volume, many were not aware that the graph to show inverse proportion is a curve.” “Many, however, have the misconception that the evidence for this is simply that as the pressure increases, the volume decreases.”

Recap

  • Gas pressure comes from particles colliding with the walls of the container.
  • Constant volume, higher temperature: particles faster, more frequent and harder collisions, higher pressure.
  • Constant temperature, smaller volume: particles closer, more frequent collisions, higher pressure. Their speed does not change.
  • T (in K) = θ (in °C) + 273. Subtract 273 to go back.
  • Extended: pV = constant for a fixed mass of gas at constant temperature, so p₁V₁ = p₂V₂.
  • Extended: p against V is a curve. p against 1/V is a straight line through the origin.

End-of-chapter exercise

Test yourself on the whole chapter. Work through these before moving on.

  1. Describe the arrangement and the separation of the particles in a solid.2 marks
  2. Name the process by which a liquid changes to a solid.1 mark
  3. State whether a liquid has a fixed shape and whether it has a fixed volume.2 marks
  4. Name the change of state when a gas becomes a liquid.1 mark
  5. A student says that the particles in a gas vibrate about fixed positions. Correct the student.2 marks
  6. Describe two ways in which the particles in a gas differ from the particles in a liquid.2 marks
  7. A puddle of water dries on a warm day, well below its boiling point. Name the process and state which particles leave the surface.2 marks
  8. Steam touches a cold window and forms water droplets. Name the change of state. Describe how the separation and the freedom of movement of the particles change.3 marks
  9. A solar still makes drinking water from sea water. Sunlight warms the sea water, which does not boil. Water leaves its surface as a gas. The gas touches a cold glass lid and droplets of liquid form on the glass. (a) Name the two changes of state, in the order they happen. (b) A student describes the gas under the lid. For arrangement the student writes “the particles take the shape of the lid”. For motion the student writes “the particles move freely”. Write a correct description of the arrangement and of the motion. (c) State how the separation of the particles changes when the droplets form.5 marks
  10. A sealed tube holds one substance. The table describes its particles at three temperatures. (a) The tube is cooled from 200 °C to 20 °C. Name the two changes of state, in the order they happen. (b) State the temperature in the table at which the substance has a fixed volume and is able to flow. (c) A student describes the substance at 90 °C: “The particles are close to each other, so they vibrate about fixed points.” State which part of the description is wrong and correct it. | Temperature | Particles | | --- | --- | | 20 °C | close to each other, vibrate about fixed positions | | 90 °C | close to each other, slide over each other | | 200 °C | far apart, move rapidly in random directions |5 marks
  11. Describe how the particles of a liquid are arranged and how they move.2 marks
  12. Describe the arrangement, separation and motion of the particles in a gas.3 marks
  13. The diagrams show the particles of a substance in two states, X and Y. One state is a liquid. State which one and give one reason.2 marks
  14. State the lowest possible temperature in °C. State what is true about the kinetic energy of the particles at this temperature.2 marks
  15. A block of metal is cooled from 20 °C to −196 °C. (a) State what happens to the average kinetic energy of its particles. (b) Calculate how many °C the block is above the lowest possible temperature.3 marks
  16. A sealed syringe contains gas at constant temperature. The plunger is pushed in and the pressure increases. State what happens to the speed of the gas particles and explain why the pressure increases.2 marks
  17. Smoke particles in a box of air are seen through a microscope to move in a random, jerky way. Explain this motion.3 marks
  18. Explain, in terms of the forces between particles, why it is easier to increase the separation of the particles of a gas than of a solid.2 marks
  19. A sealed steel cylinder holds a fixed mass of gas. One end has an area of 150 cm². In a warm room the gas exerts a force of 3.0 kN on this end. On a cold night the force is 2.7 kN. The volume does not change. (a) Calculate the decrease in the pressure of the gas, in Pa. (b) Explain, in terms of particles and their momentum, why the force is smaller on the cold night.6 marks
  20. Tiny oil droplets are suspended in the air in a sealed glass cell. Through a microscope each droplet is a speck of light moving in a random, jerky way. The cell is warmed at constant volume. (a) A student writes: ‘The oil molecules move because heavier air molecules push them.’ Give two corrections. (b) State and explain what happens to the motion of the droplets. (c) Explain, in terms of force and momentum, what happens to the air pressure on the cell walls.7 marks
  21. A fixed mass of gas at constant temperature is compressed. State what happens to its pressure.1 mark
  22. A gas is sealed in a container. Explain, in terms of particles, how the gas exerts a pressure on the walls of the container.3 marks
  23. The temperature of a room is 20 °C. Calculate this temperature in kelvin.2 marks
  24. A gas is at a temperature of 350 K. Calculate this temperature in °C.2 marks
  25. A fixed mass of gas is trapped in a cylinder by a piston. The piston is pushed in slowly and the temperature stays the same. Explain, in terms of particles, why the pressure of the gas increases.3 marks
  26. The pressure of the air in a sealed car tyre falls on a cold night. The volume of the air does not change. Explain, in terms of particles, why the pressure falls.3 marks
  27. A sealed steel cylinder of gas is left outside. Its volume does not change. The temperature is −3 °C at night and 47 °C during the day. (a) Convert both temperatures to kelvin. (b) State when the gas pressure is higher. Explain your answer in terms of particles.5 marks
  28. A fixed mass of gas has a volume of 6.0 m³ at a pressure of 2.0 × 10⁵ Pa. It is compressed to 1.5 m³ at constant temperature. Calculate the new pressure.3 marks
  29. The graph shows how the pressure p of a fixed mass of air in a syringe varies with its volume V. (a) A student says the pressure falls by the same amount for every 20 cm³ rise in volume. Use values from the graph to show that this is wrong. (b) Use two points from the graph to show that the temperature of the air stayed constant. (c) The air is compressed to 15 cm³ at the same temperature. Calculate the new pressure.6 marks
  30. A diver breathes out an air bubble of volume 2.0 cm³. The pressure of the air in the bubble is 3.5 × 10⁵ Pa. The bubble rises to the surface, where the pressure of the air in it is atmospheric pressure, 1.0 × 10⁵ Pa. The mass and temperature of the air stay constant. (a) Calculate the volume of the bubble at the surface. (b) Calculate the pressure of the air in the bubble when its volume is 3.5 cm³. (c) Explain, in terms of particles, why the pressure decreases as the bubble rises. Include what happens to the speed of the particles.8 marks

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