Cambridge IGCSE · 0625

Physics

Thermal physics and waves — Topics 2-3

Name: ____________________Date: October 10, 2026

1.
A 0.50 kg metal block receives 9000 J of energy and its temperature rises by 40 °C. Calculate its specific heat capacity.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses E = mcΔT. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Rearranges to c = E/(mΔT). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Substitutes 9000/(0.50×40). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Develop this part of the answer: Obtains 450 J/(kg °C). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Use the temperature change, not the final temperature.
Marking points
- Uses E = mcΔT.
- Rearranges to c = E/(mΔT).
- Substitutes 9000/(0.50×40).
- Obtains 450 J/(kg °C).
Examiner tip: Use the temperature change, not the final temperature.
2.
A water wave travels at 1.8 m/s with wavelength 0.60 m. Calculate its frequency and state what happens to frequency when the wave enters shallower water.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses v = fλ. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Rearranges to f = v/λ. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains f = 3.0 Hz. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Develop this part of the answer: States that frequency remains unchanged in shallower water. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The source fixes the frequency; speed and wavelength change at the boundary.
Marking points
- Uses v = fλ.
- Rearranges to f = v/λ.
- Obtains f = 3.0 Hz.
- States that frequency remains unchanged in shallower water.
Examiner tip: The source fixes the frequency; speed and wavelength change at the boundary.
3.
A 2.0 kg block of ice at 0 °C is heated until it fully melts, absorbing 668 000 J. Calculate the specific latent heat of fusion of ice.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses E = mL. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Rearranges to L = E/m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains L = 334 000 J/kg. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Latent heat calculations involve no temperature change (the temperature stays at 0 °C throughout melting) — do not confuse this with specific heat capacity.
Marking points
- Uses E = mL.
- Rearranges to L = E/m.
- Obtains L = 334 000 J/kg.
Examiner tip: Latent heat calculations involve no temperature change (the temperature stays at 0 °C throughout melting) — do not confuse this with specific heat capacity.
4.
Explain, using the kinetic particle model, why the pressure of a fixed mass of gas increases when it is heated at constant volume.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that heating increases the average kinetic energy (speed) of the gas particles. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that faster particles collide with the container walls more frequently. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that faster particles also collide with greater force (momentum change) per collision, so both effects increase the pressure exerted on the walls. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: A complete kinetic-model explanation should mention both increased collision frequency and increased force per collision, not just one.
Marking points
- States that heating increases the average kinetic energy (speed) of the gas particles.
- States that faster particles collide with the container walls more frequently.
- States that faster particles also collide with greater force (momentum change) per collision, so both effects increase the pressure exerted on the walls.
Examiner tip: A complete kinetic-model explanation should mention both increased collision frequency and increased force per collision, not just one.
5.
Describe, in terms of particle arrangement and movement, the difference between a solid and a gas.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that in a solid, particles are closely packed in a fixed, regular arrangement and only vibrate about fixed positions. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that in a gas, particles are far apart with no fixed arrangement, moving freely and randomly at high speed. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that this difference explains why a gas can be easily compressed while a solid cannot. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Always describe both arrangement (spacing/order) and movement for full marks in kinetic particle theory questions.
Marking points
- States that in a solid, particles are closely packed in a fixed, regular arrangement and only vibrate about fixed positions.
- States that in a gas, particles are far apart with no fixed arrangement, moving freely and randomly at high speed.
- States that this difference explains why a gas can be easily compressed while a solid cannot.
Examiner tip: Always describe both arrangement (spacing/order) and movement for full marks in kinetic particle theory questions.
6.
A sound wave has frequency 500 Hz and travels at 340 m/s through air. Calculate its wavelength.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses v = fλ. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Rearranges to λ = v/f. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains λ = 0.68 m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The wave equation v = fλ applies to all wave types, including sound and light, though the value of v differs for each medium.
Marking points
- Uses v = fλ.
- Rearranges to λ = v/f.
- Obtains λ = 0.68 m.
Examiner tip: The wave equation v = fλ applies to all wave types, including sound and light, though the value of v differs for each medium.
7.
Distinguish between a transverse wave and a longitudinal wave, giving one example of each.
[2 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that in a transverse wave, the particle oscillation (or field oscillation) is perpendicular to the direction of energy transfer, e.g. light or a water wave. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that in a longitudinal wave, the particle oscillation is parallel to the direction of energy transfer, e.g. sound. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Remember: transverse = perpendicular (crosses the direction of travel), longitudinal = parallel/along (compressions and rarefactions in the direction of travel).
Marking points
- States that in a transverse wave, the particle oscillation (or field oscillation) is perpendicular to the direction of energy transfer, e.g. light or a water wave.
- States that in a longitudinal wave, the particle oscillation is parallel to the direction of energy transfer, e.g. sound.
Examiner tip: Remember: transverse = perpendicular (crosses the direction of travel), longitudinal = parallel/along (compressions and rarefactions in the direction of travel).
8.
Describe an experiment to demonstrate the reflection of a water wave from a straight barrier in a ripple tank, and state the relationship between the angle of incidence and the angle of reflection.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: Describes generating plane (straight) water waves in a ripple tank using a vibrating bar, directed at a straight barrier placed in the water. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: Describes observing the reflected wave pattern from above (e.g. using a stroboscope or by viewing shadows). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that the angle of incidence equals the angle of reflection. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The law of reflection (angle of incidence = angle of reflection) applies identically to water waves, light and sound.
Marking points
- Describes generating plane (straight) water waves in a ripple tank using a vibrating bar, directed at a straight barrier placed in the water.
- Describes observing the reflected wave pattern from above (e.g. using a stroboscope or by viewing shadows).
- States that the angle of incidence equals the angle of reflection.
Examiner tip: The law of reflection (angle of incidence = angle of reflection) applies identically to water waves, light and sound.
9.
Explain why a difference in temperature is required for thermal energy to transfer between two objects by conduction, and state the direction of transfer.
[2 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that thermal energy always transfers from the region/object at higher temperature to the region/object at lower temperature. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that if there is no temperature difference between two objects in contact, there is no net thermal energy transfer between them. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Thermal energy transfer stops (net transfer becomes zero) once the two objects reach thermal equilibrium at the same temperature.
Marking points
- States that thermal energy always transfers from the region/object at higher temperature to the region/object at lower temperature.
- States that if there is no temperature difference between two objects in contact, there is no net thermal energy transfer between them.
Examiner tip: Thermal energy transfer stops (net transfer becomes zero) once the two objects reach thermal equilibrium at the same temperature.
10.
A wave passes from deep water into shallow water and its speed decreases. Explain what happens to its wavelength, and state what happens to its frequency.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that the frequency of the wave remains unchanged, since it is set by the source generating the wave. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Work through this mathematical step: States that since v = fλ and v decreases while f stays constant, the wavelength must decrease proportionally. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: Explains that this decrease in wavelength as waves enter shallower water is what causes waves to bend (refract) when approaching a shoreline at an angle. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Frequency is always fixed by the source and never changes when a wave changes medium — only speed and wavelength change together, in the same proportion.
Marking points
- States that the frequency of the wave remains unchanged, since it is set by the source generating the wave.
- States that since v = fλ and v decreases while f stays constant, the wavelength must decrease proportionally.
- Explains that this decrease in wavelength as waves enter shallower water is what causes waves to bend (refract) when approaching a shoreline at an angle.
Examiner tip: Frequency is always fixed by the source and never changes when a wave changes medium — only speed and wavelength change together, in the same proportion.
11.
Explain, in terms of density, how a convection current transfers thermal energy in a fluid that is heated from below.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that the fluid nearest the heat source is heated and expands. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that this heated fluid becomes less dense than the surrounding cooler fluid. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that the less dense (warmer) fluid rises, while cooler, denser fluid sinks to take its place. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Develop this part of the answer: States that this circulating movement of fluid (a convection current) transfers thermal energy through the fluid. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Convection requires a fluid (liquid or gas) that can flow — it cannot occur in a solid, since the particles cannot circulate.
Marking points
- States that the fluid nearest the heat source is heated and expands.
- States that this heated fluid becomes less dense than the surrounding cooler fluid.
- States that the less dense (warmer) fluid rises, while cooler, denser fluid sinks to take its place.
- States that this circulating movement of fluid (a convection current) transfers thermal energy through the fluid.
Examiner tip: Convection requires a fluid (liquid or gas) that can flow — it cannot occur in a solid, since the particles cannot circulate.
12.
State how the colour and texture of a surface affect the rate at which it emits infrared radiation, and state which type of surface is the best emitter.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that dark, matte (dull) surfaces emit infrared radiation faster than light, shiny surfaces at the same temperature. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that dark, matte surfaces are also the best absorbers of infrared radiation, while light, shiny surfaces are the best reflectors. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that a dark, matte black surface is the best emitter (and absorber) of infrared radiation. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The same property (dark and matte) makes a surface both a good emitter and a good absorber of infrared radiation — the two go together.
Marking points
- States that dark, matte (dull) surfaces emit infrared radiation faster than light, shiny surfaces at the same temperature.
- States that dark, matte surfaces are also the best absorbers of infrared radiation, while light, shiny surfaces are the best reflectors.
- States that a dark, matte black surface is the best emitter (and absorber) of infrared radiation.
Examiner tip: The same property (dark and matte) makes a surface both a good emitter and a good absorber of infrared radiation — the two go together.
13.
State three factors that increase the rate of evaporation of a liquid, and explain why evaporation causes cooling of the remaining liquid.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that increasing the temperature increases the rate of evaporation. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that increasing the surface area increases the rate of evaporation. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that increasing air movement over the surface, or decreasing humidity, increases the rate of evaporation. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Develop this part of the answer: Explains that the fastest-moving (most energetic) particles escape from the surface, leaving behind particles with lower average kinetic energy, so the average temperature of the remaining liquid decreases. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Evaporative cooling explains why sweating cools the body: the most energetic water molecules escape as vapour, lowering the average energy (temperature) of the remaining liquid on the skin.
Marking points
- States that increasing the temperature increases the rate of evaporation.
- States that increasing the surface area increases the rate of evaporation.
- States that increasing air movement over the surface, or decreasing humidity, increases the rate of evaporation.
- Explains that the fastest-moving (most energetic) particles escape from the surface, leaving behind particles with lower average kinetic energy, so the average temperature of the remaining liquid decreases.
Examiner tip: Evaporative cooling explains why sweating cools the body: the most energetic water molecules escape as vapour, lowering the average energy (temperature) of the remaining liquid on the skin.
14.
Distinguish between boiling and evaporation.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that boiling occurs at a fixed temperature (the boiling point) throughout the whole liquid, while evaporation occurs at any temperature and only at the liquid's surface. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that boiling requires a continuous energy supply and occurs rapidly with bubble formation throughout the liquid, while evaporation is a slower process. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that both processes involve a change of state from liquid to gas. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: A puddle drying up on a warm day is evaporation (below boiling point, surface only); water bubbling in a kettle is boiling (at a fixed temperature, throughout the liquid).
Marking points
- States that boiling occurs at a fixed temperature (the boiling point) throughout the whole liquid, while evaporation occurs at any temperature and only at the liquid's surface.
- States that boiling requires a continuous energy supply and occurs rapidly with bubble formation throughout the liquid, while evaporation is a slower process.
- States that both processes involve a change of state from liquid to gas.
Examiner tip: A puddle drying up on a warm day is evaporation (below boiling point, surface only); water bubbling in a kettle is boiling (at a fixed temperature, throughout the liquid).
15.
A fixed mass of gas at constant volume has a pressure of 100 kPa at a temperature of 27 °C. Calculate its pressure when the temperature is increased to 127 °C.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Converts both temperatures to kelvin: T₁ = 27 + 273 = 300 K, T₂ = 127 + 273 = 400 K. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: States the pressure law at constant volume: P₁/T₁ = P₂/T₂. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Substitutes 100/300 = P₂/400. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Develop this part of the answer: Obtains P₂ ≈ 133 kPa. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Gas law calculations always require temperature to be converted to kelvin first — using Celsius directly gives an incorrect ratio.
Marking points
- Converts both temperatures to kelvin: T₁ = 27 + 273 = 300 K, T₂ = 127 + 273 = 400 K.
- States the pressure law at constant volume: P₁/T₁ = P₂/T₂.
- Substitutes 100/300 = P₂/400.
- Obtains P₂ ≈ 133 kPa.
Examiner tip: Gas law calculations always require temperature to be converted to kelvin first — using Celsius directly gives an incorrect ratio.
16.
State the order, from least to greatest, in which solids, liquids and gases expand for the same rise in temperature, and describe how this property is used in a bimetallic strip.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that, for the same temperature rise, solids expand the least, then liquids, then gases expand the most. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that a bimetallic strip is made of two different metals with different rates of expansion, bonded together. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that when heated, the strip bends because one metal expands more than the other, e.g. used in a thermostat to break an electrical circuit at a set temperature. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Different rates of expansion between materials, not the expansion itself, is what makes a bimetallic strip bend — a strip of a single metal would not bend when heated.
Marking points
- States that, for the same temperature rise, solids expand the least, then liquids, then gases expand the most.
- States that a bimetallic strip is made of two different metals with different rates of expansion, bonded together.
- States that when heated, the strip bends because one metal expands more than the other, e.g. used in a thermostat to break an electrical circuit at a set temperature.
Examiner tip: Different rates of expansion between materials, not the expansion itself, is what makes a bimetallic strip bend — a strip of a single metal would not bend when heated.
17.
A ray of light travelling from air into glass has an angle of incidence of 40° and an angle of refraction of 25°. Calculate the refractive index of the glass.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses refractive index n = sin(angle of incidence) ÷ sin(angle of refraction). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes sin(40°) ÷ sin(25°). Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: Obtains n ≈ 1.52. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Light bends towards the normal when entering a denser medium (like glass from air), so the angle of refraction is always smaller than the angle of incidence in this direction.
Marking points
- Uses refractive index n = sin(angle of incidence) ÷ sin(angle of refraction).
- Substitutes sin(40°) ÷ sin(25°).
- Obtains n ≈ 1.52.
Examiner tip: Light bends towards the normal when entering a denser medium (like glass from air), so the angle of refraction is always smaller than the angle of incidence in this direction.
18.
A glass has a refractive index of 1.5. Calculate the critical angle of the glass, and explain how total internal reflection at angles greater than the critical angle allows light to travel along an optical fibre.
[4 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses sin(critical angle) = 1 ÷ refractive index. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes 1 ÷ 1.5 = 0.667. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: Obtains critical angle ≈ 42°. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Develop this part of the answer: Explains that light travelling inside the optical fibre strikes its walls at an angle greater than the critical angle, so it undergoes total internal reflection repeatedly and is confined within the fibre, allowing it to travel along its length with minimal loss. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Total internal reflection only occurs when light travels from a denser to a less dense medium at an angle greater than the critical angle — both conditions are required.
Marking points
- Uses sin(critical angle) = 1 ÷ refractive index.
- Substitutes 1 ÷ 1.5 = 0.667.
- Obtains critical angle ≈ 42°.
- Explains that light travelling inside the optical fibre strikes its walls at an angle greater than the critical angle, so it undergoes total internal reflection repeatedly and is confined within the fibre, allowing it to travel along its length with minimal loss.
Examiner tip: Total internal reflection only occurs when light travels from a denser to a less dense medium at an angle greater than the critical angle — both conditions are required.
19.
List the regions of the electromagnetic spectrum in order of increasing wavelength, starting with gamma rays, and state one practical use of X-rays.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States the correct order: gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves, radio waves. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that all regions of the electromagnetic spectrum travel at the same speed in a vacuum, but differ in wavelength and frequency. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States a valid use of X-rays, e.g. medical imaging of bones, or security scanning at airports. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Every region of the electromagnetic spectrum is a transverse wave that can travel through a vacuum at the same speed (the speed of light) — they differ only in wavelength and frequency.
Marking points
- States the correct order: gamma rays, X-rays, ultraviolet, visible light, infrared, microwaves, radio waves.
- States that all regions of the electromagnetic spectrum travel at the same speed in a vacuum, but differ in wavelength and frequency.
- States a valid use of X-rays, e.g. medical imaging of bones, or security scanning at airports.
Examiner tip: Every region of the electromagnetic spectrum is a transverse wave that can travel through a vacuum at the same speed (the speed of light) — they differ only in wavelength and frequency.
20.
State what is meant by diffraction, and describe how the amount of diffraction of water waves passing through a gap changes as the gap width is decreased, for a constant wavelength.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that diffraction is the spreading out of waves as they pass through a gap or around an obstacle. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that diffraction increases (the waves spread out more) as the gap width is decreased. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that diffraction is most noticeable when the gap width is comparable to (approximately equal to) the wavelength of the wave. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Diffraction happens for all wave types, but is only noticeable when the gap or obstacle size is similar to the wavelength — this is why sound (long wavelength) diffracts around doorways much more obviously than light (short wavelength).
Marking points
- States that diffraction is the spreading out of waves as they pass through a gap or around an obstacle.
- States that diffraction increases (the waves spread out more) as the gap width is decreased.
- States that diffraction is most noticeable when the gap width is comparable to (approximately equal to) the wavelength of the wave.
Examiner tip: Diffraction happens for all wave types, but is only noticeable when the gap or obstacle size is similar to the wavelength — this is why sound (long wavelength) diffracts around doorways much more obviously than light (short wavelength).
21.
A ship's echo sounder sends an ultrasound pulse towards the seabed. The reflected pulse returns to the ship after 0.80 s. Calculate the depth of water beneath the ship, given that the speed of sound in water is 1500 m/s.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: States that the pulse travels to the seabed and back, so depth = (speed × time) ÷ 2. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Substitutes (1500 × 0.80) ÷ 2. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Obtains depth = 600 m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Always halve the total travel time (or distance) in echo calculations, since the recorded time covers the round trip there and back, not just the one-way distance.
Marking points
- States that the pulse travels to the seabed and back, so depth = (speed × time) ÷ 2.
- Substitutes (1500 × 0.80) ÷ 2.
- Obtains depth = 600 m.
Examiner tip: Always halve the total travel time (or distance) in echo calculations, since the recorded time covers the round trip there and back, not just the one-way distance.
22.
Describe an experiment to determine the specific heat capacity of a metal block using electrical heating, stating the key measurements needed.
[4 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that an electrical heater is inserted into a hole in the metal block, with a thermometer used to measure the initial temperature. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Work through this mathematical step: States that the heater is switched on for a measured time, with the current and potential difference recorded to calculate the electrical energy supplied, using E = IVt. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Develop this part of the answer: States that the final temperature of the block is recorded, so the temperature rise can be found. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Work through this mathematical step: States that the specific heat capacity is then calculated using c = E ÷ (mΔT), where m is the mass of the block. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
6. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: Insulating the block reduces heat loss to the surroundings during the experiment, which would otherwise make the calculated specific heat capacity too high.
Marking points
- States that an electrical heater is inserted into a hole in the metal block, with a thermometer used to measure the initial temperature.
- States that the heater is switched on for a measured time, with the current and potential difference recorded to calculate the electrical energy supplied, using E = IVt.
- States that the final temperature of the block is recorded, so the temperature rise can be found.
- States that the specific heat capacity is then calculated using c = E ÷ (mΔT), where m is the mass of the block.
Examiner tip: Insulating the block reduces heat loss to the surroundings during the experiment, which would otherwise make the calculated specific heat capacity too high.
23.
State three characteristics of the image formed by a plane mirror.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that the image is the same size as the object. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that the image is virtual (it cannot be formed on a screen). Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that the image is laterally inverted, and appears the same distance behind the mirror as the object is in front of it. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: A virtual image is one that light rays only appear to come from — no light actually passes through the image location, so it cannot be captured on a screen.
Marking points
- States that the image is the same size as the object.
- States that the image is virtual (it cannot be formed on a screen).
- States that the image is laterally inverted, and appears the same distance behind the mirror as the object is in front of it.
Examiner tip: A virtual image is one that light rays only appear to come from — no light actually passes through the image location, so it cannot be captured on a screen.
24.
Describe an experiment that shows sound cannot travel through a vacuum, and state what this shows about the nature of sound waves.
[3 marks] · no calculator
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. Break the command into its requested parts. For each part, connect a relevant fact or observation to the conclusion it supports. Describing what happens and explaining why it happens are different tasks.
2. Develop this part of the answer: States that an electric bell is suspended inside a bell jar connected to a vacuum pump, and switched on so it can be heard ringing. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
3. Develop this part of the answer: States that as air is gradually pumped out of the jar, the sound becomes fainter until it can no longer be heard, even though the bell can still be seen ringing. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
4. Develop this part of the answer: States that this shows sound is a mechanical wave that requires a medium (particles) to travel through, unlike light, which can travel through a vacuum. Show which detail or principle supports it and how it addresses the command; equivalent supported wording is acceptable.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: This experiment is the classic evidence that sound, unlike light or other electromagnetic waves, must have particles to vibrate — it cannot travel through empty space.
Marking points
- States that an electric bell is suspended inside a bell jar connected to a vacuum pump, and switched on so it can be heard ringing.
- States that as air is gradually pumped out of the jar, the sound becomes fainter until it can no longer be heard, even though the bell can still be seen ringing.
- States that this shows sound is a mechanical wave that requires a medium (particles) to travel through, unlike light, which can travel through a vacuum.
Examiner tip: This experiment is the classic evidence that sound, unlike light or other electromagnetic waves, must have particles to vibrate — it cannot travel through empty space.
25.
A kettle supplies 45 200 J of energy to boil away 0.020 kg of water at 100 °C. Calculate the specific latent heat of vaporisation of water.
[3 marks]
Answer explanation
Draft walkthroughs are based on marking guidance, not independently verified derivations.
1. List the given quantities and the requested unknown. Choose the relation that connects them, state any required assumptions, then substitute before rounding. Preserve exact expressions when the task asks for an exact result.
2. Work through this mathematical step: Uses E = mL. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
3. Work through this mathematical step: Rearranges to L = E ÷ m. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
4. Work through this mathematical step: Substitutes 45 200 ÷ 0.020 to obtain L = 2.26 × 10⁶ J/kg. Write the intermediate operation, keep the units consistent where applicable, and check the relation against the quantities given in the question.
5. Check the complete task again, including restrictions, units, precision and supporting evidence when relevant. Specific caution: The specific latent heat of vaporisation is always much larger than the specific latent heat of fusion for the same substance, since far more energy is needed to fully separate particles into a gas than to break the rigid structure of a solid.
Marking points
- Uses E = mL.
- Rearranges to L = E ÷ m.
- Substitutes 45 200 ÷ 0.020 to obtain L = 2.26 × 10⁶ J/kg.
Examiner tip: The specific latent heat of vaporisation is always much larger than the specific latent heat of fusion for the same substance, since far more energy is needed to fully separate particles into a gas than to break the rigid structure of a solid.