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1.5.7Motion, Forces and Energy

Efficiency — Cambridge IGCSE Co-ordinated Sciences 0654 - Physics Revision Notes & Topical Questions

5 min read 9 parts Lesson 30 of 36

📚 Cambridge IGCSE Co-ordinated Sciences 0654 - Physics Hub / Topical Revision
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Part 1 of 7What efficiency means

No real device transfers all of its input energy into the store we want. Efficiency compares the useful energy output with the total energy input. It tells us what fraction of the energy supplied is put to good use.

1
efficiency = useful energy transferred by the device ÷ total energy supplied to the device
2
It can also be written with power in place of energy, provided both powers are measured over the same time:
3
efficiency = useful power output ÷ total power input
4
The result is a number between 0 and 1, or a percentage if multiplied by 100%.
  • Efficiency has no unit because it is a ratio of two quantities in the same unit.

Part 2 of 7Why efficiency is always less than 100%

Energy is conserved, so input energy = useful output + wasted output. Because friction, electrical resistance and sound production always dissipate some energy, the wasted part is never exactly zero in a real machine. An efficiency of more than 100% would suggest energy had been created, which is impossible. A value of 1 or 100% is an idealised limit.

Part 3 of 7Typical figures and causes

An incandescent filament lamp transfers about 5 to 10% of its input as light; the rest is thermal. An LED lamp does far better, around 40% or more. A modern gas boiler can reach 90%. A petrol car engine typically manages about 25 to 30%. An electric motor can exceed 80 to 90%.

Sources of waste include:

1
friction between moving parts, which heats them;
2
electrical resistance in wires and components;
3
air resistance;
4
sound produced by moving parts;
5
heat escaping from hot surfaces through poor insulation.

Part 4 of 7Improving efficiency

Each source of waste suggests a fix.

1
Lubricate moving parts to reduce friction.
2
Use thicker, shorter wires to lower resistance.
3
Streamline shapes to cut air resistance.
4
Insulate hot appliances and buildings.
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Replace filament lamps with LED lamps.
6
Be careful with explanations: increasing efficiency means a larger fraction of the energy goes to the useful store, not that the energy input is automatically smaller or the output bigger.

Part 5 of 7Calculating with efficiency

If you know any two of useful output, total input and efficiency you can find the third by rearranging.

Calculating with efficiency
Often the wasted energy is easier to find from the energy accounting: wasted = total input − useful output.
Always state the answer as a decimal or a percentage and be sure the numerator and denominator use the same units and the same time interval.
In the Edexcel course the equation is given as efficiency = (useful energy transferred by the device ÷ total energy supplied to the device) × 100%,
  • so you will usually be asked to quote a percentage.

Part 6 of 7Efficiency in practice and in exam questions

Questions on efficiency often supply a Sankey diagram or a statement such as "for every 100 J supplied, 30 J is transferred as light".

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Read off the useful part first, then divide by the total.
2
When two devices do the same job, the more efficient one wastes less energy for the same useful output, which means lower running costs.
3
For example, an LED lamp and a filament lamp that both give 5 W of light: the LED may need only 12 W of input whereas the filament lamp needs 100 W.
4
Over 1000 hours the LED uses 12 kWh and the filament lamp 100 kWh, so the LED saves 88 kWh.

Efficiency is not the same as power.

1
A powerful machine is not necessarily efficient, and a low-power machine may waste a large fraction of its input.
2
A small motor can be more efficient than a large engine.
3
When comparing, quote both the useful and the total quantities.
4
Remember also that wasted energy is not "lost": it is still energy, usually thermal, in the surroundings,
  • and any claim of a device above 100% efficiency would imply energy was created from nothing,
  • which conflicts with conservation of energy.

Part 7 of 7Worked examples

  1. A motor takes 500 J of electrical energy in 10 s and lifts a load, gaining 350 J of GPE. Calculate the efficiency and the wasted energy.

  2. An LED lamp has a power input of 8.0 W and is 40% efficient. Find the useful light power output and the wasted power.

  3. A machine is 25% efficient and wastes 900 J. What was the total input energy?

Key terms

TermMeaning
EfficiencyFraction (or percentage) of input energy transferred to a useful store.
Useful outputThe energy or power that does what the device is designed for.
Wasted energyEnergy transferred to stores that are not useful.
PowerEnergy transferred per second, measured in watts.
Sankey diagramDiagram showing useful and wasted energy as arrows of proportional width.

Avoid these mistakes

1
Quoting efficiency in joules or watts. It is a ratio with no unit.
2
Dividing input by output instead of output by input, which gives values above 1.
3
Giving an efficiency of more than 100%, which would break conservation of energy.
4
Mixing power and energy in the same ratio, for example 350 J ÷ 50 W.
5
Saying wasted energy "disappears"; it goes to the thermal store of the surroundings.

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