Useful energy and wasted energy
A machine changes energy from one form to another. A fan changes electrical energy into movement. A car engine changes chemical energy in fuel into movement.
The energy we want is called useful energy. The rest is wasted energy. Most wasted energy becomes heat. Some becomes sound.
Wasted energy is not destroyed. The law of conservation of energy says energy cannot be made or destroyed. So:
energy in = useful energy out + wasted energy out
Wasted energy spreads into the air around us. Spread-out heat is very hard to use again.
How to calculate efficiency
Efficiency tells us what fraction of the energy in becomes useful.
Efficiency = useful energy out ÷ total energy in × 100 %
You can also use power (energy each second): efficiency = useful power out ÷ total power in × 100 %.
- Efficiency has no unit. It is a fraction or a percentage.
- It is always less than 100 % for real machines, because some energy always turns into heat (from friction, electrical resistance or hot gases).
Typical efficiencies
- Filament bulb: about 5 %
- LED bulb: about 30–50 %
- Petrol car engine: about 20–30 %
- Solar panel: about 15–22 %
- Large electric motor: about 85–95 %
- Coal power station: about 33–40 %
Sankey diagrams
A Sankey diagram is an arrow picture of energy flow. The arrow width shows how much energy there is.
- The thick arrow on the left is the energy in.
- A straight arrow carries on to the right: useful energy.
- Arrows bend down: wasted energy.
Widths must add up: the in-arrow is as wide as all the out-arrows together. This shows energy conservation.
Saving energy and sustainability
Most electricity in the world still comes from burning coal, oil and gas. Using less energy means less fuel burnt, less carbon dioxide and lower bills.
Two ways to save energy
- Use efficient devices: LED bulbs, star-rated fridges, inverter air conditioners, efficient motors and electric trains.
- Waste less: switch off lights and fans, do not leave chargers on standby, use daylight, cycle or walk short trips, insulate roofs and walls so heat does not leak.
Energy that is cheap to save is often called the "first fuel". Saving 1 unit is usually cheaper than making 1 new unit.
Waste heat can be useful
Some power stations send their hot water to heat nearby homes (combined heat and power). This raises the overall efficiency.
Try it: find the waste at home
- Touch (carefully, after a minute) an old bulb, an LED bulb, a phone charger and a laptop base. Hot = energy being wasted as heat.
- List three devices. Guess their efficiency. Then check the 3D and the list above.
- Find a star-rating label on a fridge or AC. Count the stars. More stars = less waste.
Key formulas and definitions
- Efficiency = (useful energy out ÷ total energy in) × 100 %
- Efficiency = (useful power out ÷ total power in) × 100 %
- Energy in = useful energy out + wasted energy out
- Useful energy out = efficiency × energy in
- Energy in J (joule), power in W (watt); 1 W = 1 J/s
Worked examples
1. A motor takes in 500 J and gives out 400 J of useful kinetic energy. Find its efficiency.
Efficiency = 400 ÷ 500 × 100 = 80 %.
2. A bulb uses 60 J each second and gives 3 J of light. Find the wasted energy and the efficiency.
Wasted = 60 − 3 = 57 J. Efficiency = 3 ÷ 60 × 100 = 5 %.
3. A solar panel is 20 % efficient. Sunlight brings it 1000 J each second. How much electrical energy comes out each second?
Useful out = 0.20 × 1000 = 200 J each second, so the output power is 200 W.
4. An LED gives 10 W of light and is 40 % efficient. What power does it take in?
Input = useful ÷ efficiency = 10 ÷ 0.40 = 25 W.
Common mistakes
- Dividing the wrong way: it is useful ÷ input, never input ÷ useful. The answer must be less than 100 %.
- Saying wasted energy is "destroyed" or "lost forever". It still exists, mostly as heat spread in the surroundings.
- Forgetting to multiply by 100 when the question asks for a percentage.
- Thinking a more powerful device is more efficient. Power is how fast energy is used; efficiency is how much of it is useful.