OxfordAQA International GCSE Physics: Energy transfers, efficiency, Sankey diagrams, resources (9203)

This guide follows the OxfordAQA International GCSE Physics (9203) specification, for exams May/June 2018 onwards. It covers sections 3.2.2 (energy transfers, conservation and dissipation of energy) and 3.2.3 (energy resources). The qualification is untiered, so everything here is for every candidate. Work, kinetic energy and gravitational potential energy (3.2.1) are used as tools and are explained in the Energy study guide.

Other pages for this topic: revision notes and practice questions. Course pages: OxfordAQA IGCSE Physics hub and the printable checklist. To find your weak spots first, try the free diagnostics.

What this unit covers

Section	What you need to be able to do
3.2.2 a	Say that a system is an object or group of objects, and that energy is transferred when it changes. Identify when and where energy is transferred, using kinetic, gravitational potential and elastic potential energy.
3.2.2 b	Describe the simple pendulum as oscillating motion with energy transferred between kinetic and gravitational potential energy.
3.2.2 c	State that energy can be transferred usefully, stored or dissipated, and cannot be created or destroyed.
3.2.2 d	Explain that only part of the energy is usefully transferred and the rest is dissipated, stored in less useful ways (“wasted”).
3.2.2 e	Explain that friction and air resistance dissipate energy by heating the surroundings.
3.2.2 f	Calculate efficiency from energy or from power, as a decimal or a percentage.
3.2.2 g	Draw and interpret Sankey diagrams.
3.2.3 a-b	Choose fuels using storage, energy content and safety. Know that some energy goes to the surroundings and some fuels are more efficient than others.
3.2.3 c	Compare energy sources used nationally and globally: renewability and the environmental impact of extraction, use and disposal.
3.2.3 d	Describe wave, solar and geothermal power, with advantages and drawbacks, and be aware of other examples.

3.2.2 a: Systems and energy transfers

A system is an object or a group of objects. Energy is transferred whenever the system changes. To identify a transfer, name the system, then say where the energy was before and after.

Change	Energy before	Energy after
A stretched elastic band is released and launches a paper ball	Elastic potential energy in the band	Kinetic energy of the ball (and a little dissipated by heating)
A diver steps off a high board	Gravitational potential energy	Kinetic energy
A ball rolls up a ramp	Kinetic energy	Gravitational potential energy
A compressed spring pushes a toy car	Elastic potential energy	Kinetic energy

Always name the type of energy. Energy is never “used up”.

3.2.2 b: The simple pendulum

A pendulum is a small mass (the bob) on a string. Pull it aside and release it.

• At the highest point of each swing the bob is momentarily at rest. It has maximum gravitational potential energy and zero kinetic energy.
• As it swings down, gravitational potential energy is transferred to kinetic energy.
• At the lowest point it has maximum kinetic energy and minimum gravitational potential energy, so it moves fastest here.
• As it rises on the other side, kinetic energy is transferred back to gravitational potential energy.

If no energy were dissipated, the swing would continue for ever to the same height. In practice air resistance and friction at the pivot dissipate a little energy on every swing, so each swing is slightly lower until the pendulum stops.

Worked example 1. A bob of mass 0.25 kg is released from rest 0.080 m above its lowest point. Use g = 9.8 N/kg. (a) Find its maximum speed if no energy is dissipated. (b) After one swing it reaches only 0.074 m on the far side. How much energy was dissipated?

(a) GPE at release = mgh = 0.25 x 9.8 x 0.080 = 0.196 J
    At the lowest point all of this is kinetic energy (nothing dissipated).
    1/2 x m x v^2 = 0.196  ->  v^2 = (2 x 0.196) / 0.25 = 1.568
    v = 1.25 m/s (3 s.f.)

(b) GPE at 0.074 m = 0.25 x 9.8 x 0.074 = 0.1813 J
    Dissipated = 0.196 - 0.1813 = 0.0147 J  (about 7.5% of the starting energy)

The missing 0.0147 J has warmed the air and the pivot slightly.

3.2.2 c-e: Conservation, useful energy and dissipation

Conservation: energy can be transferred usefully, stored or dissipated, but it cannot be created or destroyed. The total energy at the end of a change equals the total at the start.

• Usefully transferred energy ends up where you wanted it (the light from a lamp, the kinetic energy of a lifted load).
• Stored energy sits in a store such as gravitational potential, elastic potential or the chemical store of a fuel.
• Dissipated energy is spread into the surroundings and stored in less useful ways, usually as thermal energy in the surroundings. This is often called “wasted” energy.

Only part of the energy is usually transferred usefully. The rest is dissipated, so the useful output is always less than the input.

Friction and air resistance are forces that dissipate energy by heating the surroundings. When you rub your hands together, friction warms them. Brake pads rubbing on a wheel turn a vehicle’s kinetic energy into thermal energy.

Worked example 2. A van of mass 1500 kg brakes to rest from 12 m/s. How much energy is dissipated, and by what process?

Kinetic energy before = 1/2 x m x v^2 = 0.5 x 1500 x 12^2 = 108 000 J (108 kJ)
Final kinetic energy = 0
Energy dissipated = 108 000 J, by friction in the brakes (and between tyres and road),
which heats the brakes and the surroundings.

3.2.2 f: Efficiency

Efficiency compares the useful output with the total input. The specification gives two forms:

efficiency = useful energy out / total energy in      (x 100% for a percentage)
efficiency = useful power out  / total power in       (x 100% for a percentage)

You may be asked for the answer as a decimal or as a percentage, so read the question. Efficiency has no unit. Because some energy is always dissipated, efficiency is less than 1 (less than 100%).

Worked example 3 (power, decimal). A motor takes in 150 W and delivers 93 W of useful power.

efficiency = 93 / 150 = 0.62   (62%)
Wasted power = 150 - 93 = 57 W

Worked example 4 (rearranging). A device is 40% efficient and gives 270 J of useful energy. How much energy was supplied?

0.40 = 270 / input  ->  input = 270 / 0.40 = 675 J
Dissipated = 675 - 270 = 405 J

Worked example 5 (comparing devices). An LED lamp takes in 9.0 W and gives out 2.7 W of light. A filament lamp takes in 60 W and gives out 3.0 W of light.

LED:      2.7 / 9.0 = 0.30 (30%)
Filament: 3.0 / 60  = 0.050 (5.0%)

The LED is six times as efficient, so it dissipates far less energy for the same light.

Lubrication, insulation and streamlining raise efficiency by reducing dissipation.

3.2.2 g: Sankey diagrams

A Sankey diagram shows how the input energy is redistributed. The rules:

1. The arrow width is drawn in proportion to the energy (or power) it carries, using a stated scale.
2. The input arrow is on the left. Useful output continues straight on. Dissipated energy branches off, usually upwards or downwards.
3. The widths of the output arrows add up to the width of the input arrow, because there is no net change to the total energy.
4. Label every arrow with its type of energy and its value.

Worked example 6. A petrol engine transfers 80 kJ of chemical energy from fuel in a short interval. It gives 20 kJ of useful kinetic energy and 4 kJ as sound. The rest is dissipated as thermal energy. Draw the diagram on a scale of 1 mm for 2 kJ and find the efficiency.

Thermal energy = 80 - 20 - 4 = 56 kJ
Widths: input 80/2 = 40 mm
        kinetic (useful) 20/2 = 10 mm
        sound 4/2 = 2 mm
        thermal 56/2 = 28 mm        (10 + 2 + 28 = 40, so the arrows balance)
Efficiency = 20/80 = 0.25 (25%)

To interpret a diagram, measure each width, divide by the scale, and compare the useful arrow with the input arrow.

3.2.3 a-b: Fuels

A fuel is a useful store of energy. Fuels are chosen according to several factors:

• Ease of storage: solids and liquids are easy to store. Gases need pressurised tanks, which adds cost and risk.
• Energy content: the energy released per kilogram (or per unit volume). A fuel with a high energy content gives the same energy from a smaller mass, which matters for vehicles and aircraft.
• Safety: how easily it ignites, whether it gives off toxic fumes, and whether it is explosive or poisonous.

When a fuel is burnt, some energy is transferred to the surroundings (hot exhaust gases, warm equipment) rather than to the job you want. Some fuels and burners are more efficient than others.

Worked example 7. A boiler burns 2.0 kg of a fuel with energy content 30 MJ/kg. The water gains 33 MJ. Find the efficiency.

Energy released = 2.0 x 30 = 60 MJ
Efficiency = 33 / 60 = 0.55 (55%)
Energy to the surroundings = 60 - 33 = 27 MJ

3.2.3 c: National and global energy sources

Sources fall into groups.

Group	Examples	Key points
Fossil fuels (non-renewable)	Coal, oil, natural gas	Reliable and concentrated, but burning releases carbon dioxide, which contributes to global warming. Coal can also release sulfur dioxide (acid rain). Extraction damages land (mining) or sea (oil spills).
Nuclear fuel (non-renewable)	Uranium	No carbon dioxide from the reactor, but mining, and radioactive waste that needs safe storage for a very long time.
Renewable	Wind, hydroelectric, tidal, wave, solar, geothermal, biofuels	Replenished on a human timescale, so they do not run out. Each has its own environmental cost.

A renewable resource is replaced naturally as fast as it is used. A non-renewable resource is being used up much faster than nature forms it, so supplies fall. Environmental impact arises at extraction (mining, drilling, building), use (emissions, noise, appearance) and disposal (waste, worn-out panels).

3.2.3 d: Renewable technologies

Wave power. Floating or fixed devices are moved by waves, and this motion drives a generator.

• Advantages: no fuel needed, no carbon dioxide while running, and suitable for coastal countries.
• Drawbacks: output depends on sea conditions, equipment must survive storms and salt water, so it is costly to build and repair, and it may disturb marine life and shipping.

Solar power. Solar cells transfer light directly to electrical energy. Solar collectors can also use sunlight to heat water.

• Advantages: no fuel, no emissions while running, and it works on a small scale (one house).
• Drawbacks: no output at night, less in cloud, large areas for large outputs, and manufacture and disposal of panels have an environmental cost.

Geothermal power. Heat from hot rocks underground is used to make steam that turns turbines, or to heat water directly.

• Advantages: steady output day and night, and no fuel to buy.
• Drawbacks: only practical where hot rock is accessible, drilling is costly, and some sites release underground gases.

Worked example 8 (solar output). A panel of area 12 m² receives sunlight at a rate of 450 W for each square metre and is 18% efficient.

Power input = 12 x 450 = 5400 W
Useful power out = 0.18 x 5400 = 972 W (about 970 W)

Common errors

• Writing “energy is lost” or “used up”. Say it is dissipated to the surroundings (usually as thermal energy).
• Giving an efficiency above 1 (or 100%). It is always below that.
• Dividing input by output instead of output by input.
• Drawing Sankey arrows where the outputs do not add up to the input.
• Saying renewable sources have no environmental impact. Every source has some.

Official syllabus

OxfordAQA International GCSE Physics (9203) specification, Version 5.2, for exams May/June 2018 onwards, published by OxfordAQA. Sections 3.2.2 and 3.2.3.