OxfordAQA International GCSE Physics: Kinetic theory, specific heat and latent heat, conduction, convection and expansion (9203) – Revision Notes

These revision notes condense sections 3.4.1 and 3.4.2 of the OxfordAQA International GCSE Physics (9203) specification, for exams from May/June 2018. Read the full study guide for explanations, then try the practice questions. Check your progress on the checklist, see the course hub and use the free diagnostics to find gaps.

Key definitions

• Specific heat capacity: the energy that warms 1 kg of a substance by 1 °C.
• Specific latent heat of fusion (LF): the energy that melts 1 kg of solid at constant temperature.
• Specific latent heat of vaporisation (LV): the energy that vaporises 1 kg of liquid at constant temperature.
• Evaporation: the escape of the fastest particles from the surface of a liquid, at any temperature below the boiling point.
• Convection: energy transfer in a fluid by the rising of warmer, less dense fluid.

Equations and units

Quantity	Equation	Units
Energy to change temperature	E = m c Δθ	J, kg, J/kg °C, °C
Energy to change state	E = m L	J, kg, J/kg
Surface area to volume (cube)	6s² / s³ = 6 / s	per unit length

Rearrangements: c = E / (m Δθ), Δθ = E / (m c), m = E / L, L = E / m. If a heater of power P runs for time t, then E = P t.

Particle model summary

	Solid	Liquid	Gas
Gaps between particles	None	None	Large
Order	Lattice	Disordered	Disordered
Motion	Vibrating	Sliding past	Fast, free
Forces	Strong	Weaker	Almost none
Energy	Lowest	Middle	Highest

At a change of state the energy changes the separation of the particles, not their speed, so temperature stays constant.

Method in steps: energy calculations

1. Write down which stages happen (warming, melting, warming, boiling).
2. Use E = m c Δθ for each warming stage and E = m L for each change of state.
3. Convert grams to kilograms and minutes to seconds.
4. Add the stages. Finish with the unit and a sensible rounding.

Worked reminder. Energy to raise 0.30 kg of copper (c = 390 J/kg °C) from 25 °C to 85 °C: E = 0.30 × 390 × 60 = 7020 J = 7.0 × 10³ J.

Worked reminder. A 1.8 kW heater provides energy for 90 s to a liquid at its boiling point, evaporating 0.075 kg. Find LV. E = 1800 × 90 = 162 000 J LV = 162 000 / 0.075 = 2.16 × 10⁶ J/kg, so about 2.2 × 10⁶ J/kg.

Worked reminder (three stages). Energy to warm 0.50 kg of ice from −10 °C to 0 °C (c = 2100 J/kg °C), melt it (LF = 3.34 × 10⁵ J/kg), then warm the water to 30 °C (c = 4200 J/kg °C): Stage 1: 0.50 × 2100 × 10 = 10 500 J Stage 2: 0.50 × 3.34 × 10⁵ = 167 000 J Stage 3: 0.50 × 4200 × 30 = 63 000 J Total = 240 500 J = 2.4 × 10⁵ J. The melting stage is the largest, even though the temperature does not change during it.

Temperature-time graphs

• Sloping section: one state, temperature changing. Energy raises the kinetic energy of the particles.
• Flat section: a change of state, temperature constant. Energy changes the potential energy between particles.
• For constant power the gradient of a sloping section depends on m c. A smaller specific heat capacity gives a steeper line.
• The boiling flat usually lasts longer than the melting flat, because LV is bigger than LF.
• Reading a graph: name the state in each section, say what the particles are doing, and say what the energy is doing.
• Cooling curve: same shape in reverse. The flat part is where the substance freezes or condenses.
• Pure substance: sharp flat step. With impurities: lower melting point, higher boiling point, change over a range.

Stearic acid cooling practical

• Melt the acid in a boiling tube in hot water, remove, insert thermometer or sensor.
• Record temperature at regular intervals (for example every 30 s).
• Plot temperature against time. Expect a fall, a plateau at the freezing point (close to 69 °C), then a fall.
• Safety: eye protection, hot water, no direct flame, clamp the tube.
• Improve reliability: repeat, stir gently while liquid, read the thermometer at eye level.

Conduction, convection, evaporation

• Conduction in a metal: vibrating particles pass energy on, and free electrons move through the lattice carrying energy, so metals are good conductors.
• Insulators: no free electrons; gases have widely spaced particles, so energy transfers slowly.
• Convection: warmed fluid expands, particles move apart, density falls, fluid rises; cooler denser fluid sinks and replaces it. Only in liquids and gases.
• Evaporation cooling: fastest particles leave, so the average kinetic energy of those left falls. The liquid cools.
• Faster evaporation: higher temperature, larger surface area, moving air, drier air.
• Condensation: vapour particles lose energy and become liquid, giving energy to the surroundings.

Rate of energy transfer by heating

• Larger surface area compared with volume means faster transfer.
• Better conducting material in contact means faster transfer.
• Dull, dark surfaces transfer faster than shiny ones.
• Bigger temperature difference means faster transfer, so the cooling graph is steep at first and flattens.
• Cube of side 1 cm: 6 per cm. Cube of side 3 cm: 6 / 3 = 2 per cm. Tripling the side cuts the ratio to a third.
• A small, thin object has a high ratio and cools quickly; a large, round object has a low ratio and cools slowly.
• Cooling fins have a large surface area. Large ears help animals lose energy in hot places; small ears and compact bodies keep energy in cold places.

Expansion

• Heated particles vibrate with larger amplitude and spread slightly further apart.
• Hazard: bridges and roofs need expansion joints or rollers.
• Use: bi-metallic strip. Two metals expand by different amounts, so the strip bends; the metal that expands more is on the outside of the bend. In a thermostat the bend opens a contact.

Must-know distinctions

• Evaporation vs boiling: evaporation is from the surface at any temperature below the boiling point; boiling is throughout the liquid at the boiling point.
• Specific heat capacity vs latent heat: the first changes temperature, the second changes state with no temperature change.
• Fusion vs vaporisation: solid to liquid (smaller L) vs liquid to gas (larger L).
• Conduction vs convection: vibrations and electrons in solids vs movement of the fluid itself.

Quick self-test

1. Calculate the energy needed to warm 0.75 kg of water from 20 °C to 80 °C (c = 4200 J/kg °C).
2. What mass of ice at 0 °C does 1.0 × 10⁵ J melt (LF = 3.34 × 10⁵ J/kg)?
3. What mass of water at 100 °C does 6.8 × 10⁵ J turn to steam (LV = 2.26 × 10⁶ J/kg)?
4. A 0.40 kg steel block (c = 480 J/kg °C) receives 9600 J. What is its temperature rise?
5. An 80 W heater melts 0.12 kg of wax at its melting point (L = 2.1 × 10⁵ J/kg). How long does it take?
6. Why does the temperature stay constant while a substance boils?
7. Why are metals better conductors than plastics?
8. Why does sweating cool the body?
9. Why does warm air rise?
10. Which metal in a bi-metallic strip is on the outside of the bend?

Answers

1. E = 0.75 × 4200 × 60 = 189 000 J (1.9 × 10⁵ J).
2. m = 1.0 × 10⁵ / 3.34 × 10⁵ = 0.30 kg.
3. m = 6.8 × 10⁵ / 2.26 × 10⁶ = 0.30 kg.
4. Δθ = 9600 / (0.40 × 480) = 50 °C.
5. E = 0.12 × 2.1 × 10⁵ = 25 200 J, t = 25 200 / 80 = 315 s.
6. The energy supplied separates the particles instead of speeding them up, so the average kinetic energy does not change.
7. Metals have free electrons that carry energy through the material; plastics do not.
8. The fastest particles leave the sweat, so the average kinetic energy of the remaining sweat falls and energy is taken from the skin.
9. Warm air expands, so its particles are further apart, its density is lower, and it floats up through cooler air.
10. The metal that expands more.

Where marks are usually lost

• Writing “the particles get hotter” or “bigger” instead of “move faster” or “vibrate more”.
• Using E = m c Δθ for the melting or boiling stage of a question.
• Leaving mass in grams or time in minutes.
• Not giving the unit, or giving J when the answer is clearly kJ.
• Saying heat “rises” instead of explaining density and particle spacing.
• Describing convection in a solid.
• For evaporation, saying only “the liquid cools” without the loss of the fastest particles.
• Forgetting that a flat part of a graph is a change of state, not “no energy being supplied”.
• Reading a cooling curve as heating, or vice versa.

Official syllabus

These notes are aligned to sections 3.4.1 and 3.4.2 of the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards, published by OxfordAQA.