No machine turns all its input energy into what you want. The rest is wasted: it is dissipated, usually into the thermal store of the surroundings, where it spreads out and is no longer useful.

efficiency = useful output energy transfer ÷ total input energy transfer
efficiency = useful power output ÷ total power input

Efficiency has no unit. It is a decimal from 0 to 1; multiply by 100 for a percentage. Recall both forms: they are not on the sheet for AQA, Edexcel or OCR.

1. A motor is supplied with 800 J and transfers 600 J as kinetic energy.
2. efficiency = 600 ÷ 800 = 0.75
3. as a percentage: 0.75 × 100 = 75%
4. wasted = 800 − 600 = 200 J

To find the input, divide by the efficiency: a 60% efficient pump giving 0.3 kW useful needs 0.3 ÷ 0.6 = 0.5 kW. If your input is smaller than your output, you multiplied.

A Sankey diagram shows the energy as arrows. The width of each arrow stands for the amount of energy. Energy is conserved, so the outputs add up to the input.

Efficiency here: 60 ÷ 100 = 0.6, or 60%.

• Lubrication (oil, grease) reduces friction in moving parts, so less energy is dissipated by heating.
• Streamlining reduces air resistance.
• Thermal insulation reduces the rate of energy transfer by heating. A material with a low thermal conductivity lets energy through slowly by conduction; a thicker layer slows it more.

So a house loses energy more slowly if its walls are thick and made of materials with a low thermal conductivity (foam in the cavity, fibre in the loft). A pan base wants the opposite: copper's high thermal conductivity gets energy to the food fast.

Wrap beakers of hot water in different materials (or different numbers of layers), start them all at the same temperature, and record the temperature every few minutes.

• Independent variable: the material (or number of layers).
• Dependent variable: the temperature after a set time (or the temperature drop).
• Control variables: volume of water, starting temperature, beaker size, the time.

Plot temperature against time for each beaker. The better insulator gives the curve that falls more slowly.

Always compare drops, not end temperatures, if the starting temperatures were not quite the same.