Efficiency
Most devices waste some of the energy supplied to them. Efficiency measures the fraction of input energy (or input power) that ends up doing the intended job.
📖Definition
Efficiency $= \dfrac{\text{useful output energy}}{\text{total input energy}} \times 100%$
(or replace energy with power — the ratio is the same).
You can express efficiency as a decimal (0.75) or a percentage (75%). Always state which.
✦Worked example— Worked examples
Example 1. A 60 W light bulb produces 6 W of useful light, the rest dissipated as heat.
- Efficiency $= 6 / 60 = 0.10 = 10%$.
Example 2. A motor uses 5000 J of electrical energy to lift a load that gains 4000 J of GPE.
- Efficiency $= 4000 / 5000 = 0.80 = 80%$.
Example 3. A gas boiler delivers 36 kW of thermal energy to water from 45 kW of input chemical energy.
- Efficiency $= 36 / 45 = 0.80 = 80%$.
Common efficiencies
| Device | Approximate efficiency |
|---|---|
| Petrol engine | 25–30 % |
| Filament lamp | 5 % |
| LED lamp | 30 % |
| Coal-fired power station | 35 % |
| Gas-fired power station | 50–60 % |
| Wind turbine | 35–45 % |
| Solar PV cell | 20 % |
| Modern condensing boiler | 90 % |
These illustrate why LED bulbs are far more efficient than filaments, and why no energy conversion is 100% in practice.
Improving efficiency
Reducing wasted transfers raises efficiency. The same techniques as P1.5 apply:
- Mechanical — lubrication, ball bearings, streamlining.
- Thermal — insulation, lagging hot pipes, double glazing.
- Electrical — thicker wires, higher transmission voltage.
- Light — replace filament lamps with LEDs.
Some inefficiency is unavoidable: in heat engines, the second law of thermodynamics sets a maximum theoretical efficiency that depends on temperature differences. You don't need this formula at GCSE, but you should know that energy "wasted as heat" is part of why no real engine reaches 100%.
Calculations involving wasted energy
If a device has efficiency $\eta$, then:
Useful energy $= \eta \times$ input energy. Wasted energy $= (1 - \eta) \times$ input energy.
So a 25% efficient car engine wastes 75% of its fuel energy as heat in the engine, exhaust and brakes.
A "Sankey diagram" view
Sankey diagrams show energy flow as arrows whose width is proportional to the energy. The useful output is one arrow; wasted energies branch off. The total input width = total output width — conservation in pictorial form. You may be asked to label or interpret one in the exam.
✦Worked example— Worked example — combining
A 1500 W kettle takes 4 minutes to boil 1.0 kg of water from 20 °C to 100 °C. Assume specific heat capacity = 4200 J/kg °C.
- Energy used $= 1500 \times 240 = 360{,}000$ J.
- Useful energy $= mc\Delta\theta = 1.0 \times 4200 \times 80 = 336{,}000$ J.
- Efficiency $= 336{,}000 / 360{,}000 = 0.93 = 93%$.
That's why kettles are nearly the most efficient electrical heaters — almost all the input ends up in the water.
Common pitfalls
- Confusing decimal with percentage — 0.85 is not 85% of 100, it is 85% expressed as a decimal.
- Mixing energy and power. Use one or the other consistently.
- Forgetting useful and wasted must add to the input.
- Calculating efficiency above 100% — check arithmetic; you've probably swapped numerator and denominator.
➜Try this— Quick check
A car engine takes 4000 J of chemical energy and produces 1000 J of kinetic energy. Find its efficiency. Where does the rest go?
- Efficiency = 1000 / 4000 = 25%.
- Wasted: 3000 J — in the thermal stores of engine, exhaust, brakes; sound to surroundings.
AI-generated · claude-opus-4-7 · v3-deep-physics