What efficiency measures

1. Every device receives an input energy transfer, the total energy supplied to it, from a battery, the mains, a fuel or a moving object.
2. Part of the input is the useful output energy transfer, the energy that goes where the device was designed to send it.
3. The rest is wasted energy, which is dissipated, usually into the thermal energy stores of the device and its surroundings.
4. Because energy is conserved, the useful output and the wasted energy always add up to the input, so $wasted\; energy=input\; energy-useful\; output\; energy$.
5. Efficiency compares the useful output with the input, and it shows what fraction of the energy supplied does the job.
6. The equation is $efficiency=\frac{useful\; output\; energy\; transfer}{input\; energy\; transfer}$, with both energies measured in joules.
7. Both energies must be in the same unit, because the units cancel and efficiency itself has no unit.
8. Efficiency can be given as a decimal between $0$ and $1$, or as a percentage by multiplying the decimal by $100$, so $0.65$ is the same as $65\%$.
9. The useful output can never be larger than the input, so efficiency can never be greater than $1$ or $100\%$.
10. In every real device some energy is dissipated, so the efficiency is always less than $1$ or $100\%$.
11. Because power is energy transferred per second, efficiency can also be calculated from $\frac{useful\; power\; output}{total\; power\; input}$, as long as both powers are for the same device over the same time.

Typical efficiencies

1. Electric kettle: about $90\%$, because the element sits in the water it is heating.
2. Large electric motor: up to about $90\%$, with the rest dissipated by resistance in the coils and friction in the bearings.
3. Petrol car engine: about $25\%$, because most of the energy from the fuel leaves as hot exhaust gases and by heating the engine.
4. Filament lamp: about $5\%$, because most of the energy is transferred by heating the surroundings instead of by light.
5. A device with a high efficiency wastes only a small fraction of its input, while a device with a low efficiency dissipates most of the energy supplied to it.
6. Comparing efficiencies tells you which of two devices wastes the smaller fraction of its input, which is not the same as which one wastes less energy in total.

Calculating efficiency

1. First decide what the device is for, because that decides which output counts as useful.
   1. For a lamp the useful output is energy transferred by light, but for an electric heater it is energy transferred by heating.
2. Write down the useful output energy and the input energy, checking that both are in joules.
3. Divide the useful output by the input to get the efficiency as a decimal.
4. Multiply by $100$ only if the question asks for a percentage, and add the $\%$ sign.
5. The equation can be rearranged to find a missing energy, giving $useful\; output=efficiency\times input$ and $input=\frac{useful\; output}{efficiency}$.
6. A percentage efficiency must be turned back into a decimal before you rearrange, so $40\%$ becomes $0.40$.
7. Round the final answer to a sensible number of significant figures, usually the same as the data in the question.

Efficiency from a Sankey diagram

1. A Sankey diagram shows energy transfers as arrows, and the width of each arrow is proportional to the energy it represents.
2. The input energy enters as one wide arrow on the left.
3. The useful output continues straight on, and each wasted transfer branches off and usually curves downwards.
4. The widths of all the output arrows add up to the width of the input arrow, which is the conservation of energy shown as a picture.
5. When the diagram is drawn on squared paper, each square stands for a fixed amount of energy, so counting squares across an arrow gives its energy.
6. The efficiency is the width of the useful arrow divided by the width of the input arrow, so a useful arrow half as wide as the input shows an efficiency of $0.5$ or $50\%$.
7. A device with a high efficiency has a wide useful arrow and narrow wasted arrows.