The big idea: Energy is never destroyed, only transferred (this is conservation of energy). Some goes where we want it — the rest is wasted or degraded.
Where the wasted energy goes
- Your phone gets warm while it charges, and a car engine roars and heats up.
- In both, some energy ends up somewhere useless (heat, sound) instead of doing the job.
- It is usually wasted as thermal energy (heat).
- It isn't gone — it has just spread out and become useless.
Useful energy
- goes where you want it
- e.g. light from a lamp
- e.g. kinetic energy from a motor
- e.g. gravitational PE lifting a load
Wasted (degraded) energy
- goes where you don't want it
- almost always thermal energy (heat)
- also sound, in moving parts
- spread out → can't be reused
A Sankey diagram is a picture of this split.
Reading a Sankey diagram
- One wide arrow comes in (the total energy).
- It branches into a useful arrow and one or more wasted arrows.
- The width of each arrow shows how much energy goes that way — wider means more.
- Because energy is conserved, the widths of the branches always add up to the width of the input arrow.
| Lamp gets 100 J in | Energy (J) | Where it goes |
|---|---|---|
| Useful | 25 J | light — what we want |
| Wasted | 75 J | thermal energy (the lamp gets hot) |
| Total out | 100 J | = total in (energy is conserved) |
Here is the lamp from the table, drawn as a Sankey diagram:
Spot it — the wasted branch is heat: On almost every Sankey diagram, the energy that branches off is thermal energy (heat).
The useful arrow and the wasted arrow(s) together must add back up to the input — nothing is ever missing.
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Efficiency measures how good a system is at sending energy to the useful place rather than wasting it. It is the useful fraction of what you put in — and it is given in the data booklet.
- efficiency — the useful fraction of the energy supplied (no unit; often written as a %)
- the energy (or power) transferred to where you actually want it (J, or W for power)
- the total energy (or power) supplied to the system (J, or W for power)
Efficiency is a fraction — never more than 1: Because the useful output can never be bigger than the total input, efficiency is always between 0 and 1 (0% to 100%).
To turn it into a percentage, multiply by 100. An answer over 100% means a mistake — usually mixing up 'useful' and 'total'.
An electric motor is supplied with 500 J of electrical energy. It transfers 400 J to useful kinetic energy, and the rest becomes thermal energy. Find its efficiency.
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Energy density of fuels
When a fuel is burned, the energy it releases depends on how much fuel there is. Two ways to compare fuels:
| Quantity | Meaning | Unit |
|---|---|---|
| Energy density | Energy released per unit volume of fuel: E ÷ V | J m⁻³ |
| Specific energy | Energy released per unit mass of fuel: E ÷ m | J kg⁻¹ |
| Fuel | Energy density | Specific energy |
|---|---|---|
| Petrol | about 3.4 × 1010 J m⁻³ | about 4.6 × 107 J kg⁻¹ |
| Liquid hydrogen | about 8.5 × 109 J m⁻³ | about 1.4 × 108 J kg⁻¹ |
Volume or mass?: Liquid hydrogen releases about three times more energy per kilogram than petrol, but about four times less per cubic metre: a hydrogen tank must be much bigger.
Volume of fuel needed = energy needed ÷ energy density.
A generator must supply 17 GJ of useful energy. It is 25 % efficient and burns a fuel of energy density 34 GJ m⁻³. Estimate the volume of fuel needed. (1 GJ = one thousand million joules)
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How this is tested — energy transfers and efficiency show up as qualitative and simple-number questions:
Paper 1A
- Read a Sankey diagram.
- Identify the useful/wasted branch, or find the efficiency from the arrow values.
Paper 2
- Describe what happens to the wasted energy (it becomes thermal energy).
- Or do an energy-accounting calculation.
The classic trap: Never say energy is 'lost' or 'used up' — it is conserved, only transferred to a less useful store (heat). The Sankey branches must add up to the input.
Reading a Sankey diagram: Input arrow = total energy supplied. It splits into a useful arrow and a wasted arrow.
efficiency = useful arrow ÷ input arrow, and useful + wasted = input (energy is conserved).
Drawing a Sankey diagram: Input arrow on the left; the useful branch runs straight on; wasted branches bend away.
Draw the widths to scale, label every arrow with its energy form and amount, and check the branches add up to the input.
Energy accounting — every joule is accounted for
- Total energy in = the width of the input arrow
- Useful out = the branch going where you want it
- Wasted out = the branch(es) going to thermal energy (heat)
- Useful + wasted = total in — the branches always add back up
- efficiency = useful ÷ total, written as a fraction or a %
Animated graph
Watch the graph build step by step in study mode.
A Sankey diagram for an electric kettle shows 2000 J of electrical energy supplied, of which 1700 J is transferred usefully to the water. (a) Find the kettle's efficiency. (b) Find how much energy is wasted, and state what form it takes.
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