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

This guide covers sections 3.4.1 (Kinetic theory) and 3.4.2 (Energy transfers and particle motion) of the OxfordAQA International GCSE Physics (9203) specification, for exams from May/June 2018. The qualification is untiered, so everything here is for every candidate. Use the OxfordAQA International GCSE Physics hub to see the rest of the course and tick topics off on the printable checklist. When you finish reading, test yourself with the revision notes and the practice questions, and find weak spots with the free diagnostics.

What the specification asks for

Section	You must be able to
3.4.1 a	Use kinetic theory to explain solids, liquids and gases; recognise, use and compare particle diagrams
3.4.1 b	Define specific heat capacity and use E = m c Δθ
3.4.1 c, d	Define specific latent heat of vaporisation and of fusion; use E = m L
3.4.1 e	Explain that impurities affect melting and boiling points
Required practical	Investigate cooling curves for stearic acid
Throughout 3.4	Explain the shape of a temperature-time graph through changes of state
3.4.2 a	Explain conduction (including free electrons) and convection using particles
3.4.2 b	Explain evaporation, its cooling effect, and what affects its rate; condensation
3.4.2 c, d	Explain how the rate of energy transfer by heating depends on size, material, surface and temperature difference
3.4.2 e	Explain expansion as a hazard and as a use (bi-metallic strip thermostat)

States of matter and particle diagrams (3.4.1 a)

All matter is made of particles that are always moving. The three states differ in how far apart the particles are, how strongly they hold on to each other and how much energy they have.

	Solid	Liquid	Gas
Arrangement	Touching, in a regular pattern	Touching, no pattern	Far apart, random
Movement	Vibrate in place	Slide past each other	Dart about in straight lines between collisions
Forces between particles	Strong	Weaker	Almost none
Energy of particles	Least	More	Most
Shape and volume	Keeps its shape and volume	Pours to fit the container, same volume	Spreads to fill any container

In a particle diagram, draw circles of equal size. A solid is a tidy lattice of touching circles. A liquid is a jumbled group of touching circles with no pattern. A gas is a few circles with large gaps. To match a diagram to a description, check spacing, pattern and the number of circles.

Heating a substance gives its particles more energy, so they move or vibrate faster. At a change of state the energy goes into pulling particles apart, not into speeding them up.

Specific heat capacity (3.4.1 b)

Specific heat capacity is the energy needed to warm each kilogram of a substance by 1 °C.

E = m c Δθ

E is energy transferred in joules (J), m is mass in kilograms (kg), c is specific heat capacity in J/kg °C, and Δθ is the temperature change in °C. A high c means a lot of energy is needed for each degree, so the substance warms slowly and cools slowly.

Worked example 1. A pan holds 0.85 kg of oil with c = 2000 J/kg °C. How much energy raises it from 18 °C to 74 °C?

Δθ = 74 − 18 = 56 °C E = 0.85 × 2000 × 56 = 95 200 J = 95 kJ (2 significant figures, to match 0.85)

Worked example 2 (finding c). A 0.50 kg metal block is heated by a 60 W heater for 300 s and its temperature rises by 36 °C.

E = P t = 60 × 300 = 18 000 J c = E / (m Δθ) = 18 000 / (0.50 × 36) = 1000 J/kg °C

Some of the heater’s energy escapes to the surroundings, so the energy that really warms the block is less than 18 000 J. The calculated c is therefore larger than the true value. Lagging the block reduces the error.

Specific latent heat (3.4.1 c and d)

At a change of state the temperature stays constant while energy is still supplied or removed.

• Specific latent heat of fusion, LF: the energy that melts 1 kg of a solid, turning it to liquid at constant temperature.
• Specific latent heat of vaporisation, LV: the energy that turns 1 kg of a liquid into vapour at constant temperature.

E = m L

L is in J/kg. For freezing or condensing, the same amount of energy is released. For water, take LF = 3.34 × 10⁵ J/kg and LV = 2.26 × 10⁶ J/kg (values supplied here; questions will normally give them).

Worked example 3. Energy to melt 0.35 kg of ice already at 0 °C: E = 0.35 × 3.34 × 10⁵ = 116 900 J = 1.2 × 10⁵ J (2 s.f.)

Reverse it: 5.0 × 10⁴ J melts m = E / L = 5.0 × 10⁴ / 3.34 × 10⁵ = 0.15 kg.

Worked example 4. A 2.5 kW kettle element boils away 0.25 kg of water already at 100 °C. Ignoring losses, how long does it take? E = 0.25 × 2.26 × 10⁶ = 565 000 J t = E / P = 565 000 / 2500 = 226 s = 230 s (2 s.f.)

Worked example 5 (two stages). Energy to warm 0.40 kg of water from 20 °C to 100 °C and then boil away 0.10 kg of it. Use c = 4200 J/kg °C. Stage 1: 0.40 × 4200 × 80 = 134 400 J Stage 2: 0.10 × 2.26 × 10⁶ = 226 000 J Total = 360 400 J = 3.6 × 10⁵ J

Always split a problem at each state change, and use E = m c Δθ only where the substance is staying in one state.

Temperature-time graphs and the effect of impurities

Heat a solid at a steady rate and the graph has five parts.

Part	What is happening	Energy goes into
Rising line	Solid warming	Kinetic energy of vibrating particles
Flat	Melting	Pulling particles out of the lattice
Rising line	Liquid warming	Kinetic energy of moving particles
Flat	Boiling	Separating particles completely
Rising line	Gas warming	Kinetic energy of gas particles

The flat sections are at the melting point and the boiling point. The boiling flat lasts longer than the melting flat, since LV is much larger than LF. For the same power, a steeper line means a smaller m c, since the gradient is P / (m c). Solid ice warms faster than liquid water of the same mass because its specific heat capacity is about half as large.

A cooling curve is the reverse. The temperature falls, flattens while the substance condenses or freezes (energy is released by the forming bonds and passes to the surroundings), then falls again.

Impurities (3.4.1 e). A pure substance melts and boils at one fixed temperature. An impurity lowers the melting point and raises the boiling point, and the change of state happens over a range of temperatures instead of a sharp flat step. Salt on an icy road works because salty water freezes below 0 °C.

Required practical: cooling curves for stearic acid

1. Warm a boiling tube of stearic acid in a beaker of hot water until it is fully liquid (above its melting point of about 69 °C).
2. Lift the tube out, stand it in a clean beaker or clamp it, and place a thermometer or temperature sensor in the liquid.
3. Record the temperature every 30 seconds until it is well below the melting point.
4. Plot temperature against time.

The curve falls, stays flat at the freezing point while the acid solidifies, then falls again. Hazards: hot water and hot liquid, so wear eye protection, clamp the tube and do not heat the acid in a flame. Draw a smooth line of best fit through the points.

Conduction and convection (3.4.2 a)

Conduction in solids. Heated particles vibrate more and pass vibrations to neighbours, so energy moves along the material. In a metal, free electrons also carry energy. They move through the lattice, collide with particles and share energy quickly, which is why metals are good conductors. Non-metals have no free electrons, so they are poorer conductors, and gases are poor conductors because the particles are far apart and collide rarely. Trapped air makes good insulation.

Convection happens in fluids (liquids and gases). The fluid in a heated region has particles that move apart, so it expands and becomes less dense. It rises. Cooler, denser fluid sinks to take its place, setting up a convection current. Convection cannot happen in a solid because the particles cannot flow.

Evaporation and condensation (3.4.2 b)

Particles in a liquid have a range of speeds. At the surface, the fastest particles can escape as vapour. The ones that leave carry away a lot of energy, so the average kinetic energy of the remaining liquid falls: the liquid cools. This is why sweating cools you.

Evaporation is faster when:

• the liquid is warmer;
• the surface area is larger;
• there is a draught or wind to remove the vapour;
• the air is drier.

Evaporation happens at any temperature below the boiling point and only at the surface. Condensation is the reverse: vapour particles lose energy, slow down and become liquid, transferring energy to their surroundings.

Rate of energy transfer by heating (3.4.2 c and d)

An object transfers energy faster when:

• it has a larger surface area compared with its volume;
• it is made from a better conducting material;
• the surface it touches is a good conductor or is dull and dark rather than shiny.

Surface area to volume ratio. A cube with edge s has surface area 6s² and volume s³.

Side	Surface area	Volume	Area / volume
2 cm	24 cm²	8 cm³	3.0 per cm
5 cm	150 cm²	125 cm³	1.2 per cm

The smaller cube has more surface for its volume, so it loses energy faster per kilogram. Applications: cooling fins on a computer processor or engine have a large area to lose energy quickly. Animals in cold climates tend to have small ears and compact bodies to keep energy in; animals in hot climates, such as desert hares, have large ears to lose energy.

Temperature difference (3.4.2 d). The bigger the temperature difference between an object and its surroundings, the faster the rate of energy transfer by heating. A drink in a 20 °C room cooled like this:

Time (min)	0	5	10	15	20
Temperature (°C)	80	62	51	44	39
Difference from room (°C)	60	42	31	24	19
Fall in next 5 min (°C)	18	11	7	5

The fall slows as the difference shrinks, so the graph is a curve that flattens.

Expansion (3.4.2 e)

Most substances expand when heated. Particles vibrate with larger amplitude and push each other slightly further apart. Hazards: bridges and roofs need expansion gaps or rollers so they do not buckle. Useful: the bi-metallic strip.

A bi-metallic strip joins two metals, such as brass and iron, which expand by different amounts. When heated, the metal that expands more gets longer and the strip bends, with the more-expanding metal on the outside of the curve. In a thermostat the strip bends away from a contact when the room is warm enough, breaking the circuit and switching off the heater. When the room cools, the strip straightens and the circuit closes again.

Common errors

• Saying temperature rises during melting or boiling. It stays constant; the energy changes particle separation.
• Using E = m c Δθ across a change of state.
• Saying “heat rises”. Hot fluid rises because it is less dense.
• Saying free electrons conduct in non-metals.
• Describing evaporation as the whole liquid getting hotter.

See also energy transfers and Sankey diagrams and the infrared radiation guide.

Official syllabus

This guide is 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.