The big idea: Energy is never created or destroyed — it is only transferred from one store to another (this is conservation of energy).
But in any real machine, some of it is transferred to a place we don't want — usually as thermal energy (heat). We call that energy wasted or degraded.
It isn't gone — it has just spread out as heat 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: one wide arrow comes in (the total energy), and 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) |
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.
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'.
Worked example — efficiency of a motor
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.
Solution
- Start with the given formula:
- Put in the numbers (useful out = 400 J, total in = 500 J):
- Work it out, then multiply by 100 for a percentage:
Final answer
efficiency = 0.80 (80%). The wasted energy is 500 − 400 = 100 J, lost as thermal energy.
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How this is tested: Energy transfers and efficiency show up as qualitative and simple-numbers questions.
- Paper 1A: read a Sankey diagram — identify the useful branch, the wasted branch, or work out 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.
Classic trap: saying energy is 'lost' or 'used up'. It is conserved — it is 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).
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 %
IB-style question — (a) efficiency from a Sankey diagram
A Sankey diagram for an electric kettle shows 2000 J of electrical energy supplied. Of this, 1700 J is transferred usefully to thermal energy in the water; the rest heats the kettle body and the surroundings. Find the efficiency of the kettle.
Solution
- Read the two arrows: total in = 2000 J, useful out = 1700 J. Start with the given formula:
- Put in the numbers (useful = 1700 J, total = 2000 J):
- Work it out, then × 100 for a percentage:
Final answer
efficiency = 0.85 (85%).
IB-style question — (b) the wasted energy
For the same kettle, find how much energy is wasted, and state what form it takes.
Solution
- Energy is conserved, so wasted = total in − useful out:
- Work it out:
Final answer
300 J is wasted, as thermal energy (heat) spread into the kettle body and the surroundings — it is not destroyed, just transferred to a useless store.