Efficiency measures how much of the input does the job you wanted
Definition
Efficiency
The fraction of the energy or power supplied to a device that is transferred to the useful output, the rest being dissipated to the surroundings.
- Every device is given an input, delivers a useful output, and wastes the remainder. Efficiency is simply the size of the useful share.
- Nothing is destroyed in the process. The wasted portion is transferred to the internal energy store of the surroundings, usually through friction, air resistance or hot exhaust gases, and is spread too thinly to be recovered.
- A device with a high efficiency wastes little of what it is given. A filament lamp wastes most of its input by heating the room, while an LED lamp transfers far more of it usefully as light.
- Efficiency can never be greater than 100%100\%100%. Getting more energy out than you put in would break the principle of the conservation of energy.
- Efficiency can never be exactly 100%100\%100% in practice either, because no real machine escapes friction, and no hot object escapes losing energy to cooler surroundings.
- Reducing waste is therefore mostly about attacking the mechanism: lubricating bearings to cut friction, streamlining shapes to cut air resistance, and insulating hot parts to cut unwanted heating.
Example
- A hairdryer is supplied with 2000 J2000\ \text{J}2000 J of energy each second. It transfers 1900 J1900\ \text{J}1900 J to the internal store of the moving air and 100 J100\ \text{J}100 J to the kinetic store of the air.
- If the purpose of the hairdryer is to warm the air, the useful output is 1900 J1900\ \text{J}1900 J and the efficiency is high.
- The useful output depends on what the device is for, so the same energy transfer can count as useful in one device and wasted in another.
Calculating efficiency from energy or from power
Definition
Efficiency equations
Efficiency is calculated from energy or from power, and multiplying by 100100100 turns the fraction into a percentage.
% efficiency=useful energy outputtotal energy input×100% \%\ \text{efficiency} = \frac{\text{useful energy output}}{\text{total energy input}} \times 100\% % efficiency=total energy inputuseful energy output×100% % efficiency=useful power outputtotal power input×100% \%\ \text{efficiency} = \frac{\text{useful power output}}{\text{total power input}} \times 100\% % efficiency=total power inputuseful power output×100%- The two forms are interchangeable. Use the energy version when the question gives you joules, and the power version when it gives you watts.
- Efficiency is a ratio of two quantities with the same unit, so it has no unit of its own.
- Left as a fraction it runs from 000 to 111; multiplied by 100100100 it runs from 0%0\%0% to 100%100\%100%. Either form is acceptable as long as you say which you have given.
- The total input is everything supplied to the device, not just the part that ends up useful. Dividing the useful output by the wasted energy is the classic wrong move.
- Because energy is conserved, total input=useful output+wasted energy\text{total input} = \text{useful output} + \text{wasted energy}total input=useful output+wasted energy, which lets you find any one of the three from the other two.
- For a chain of stages, work out each stage separately. The overall efficiency is smaller than any single stage, because every stage takes its own cut.
Common Mistake
- Efficiency has no unit. Writing "65% J65\%\ \text{J}65% J" or "0.65 W0.65\ \text{W}0.65 W" loses the mark.
- Divide by the total input, not by the wasted energy and not by the useful output.
- An efficiency above 100%100\%100% always means an arithmetic error, because it would break conservation of energy.
- Energy is never lost. Say it is wasted or dissipated to the surroundings.
- Convert both quantities to the same unit before dividing, particularly when one is given in kilojoules or kilowatts.
Exam technique
- Write the equation in words before substituting. That single line usually carries a method mark.
- Underline the useful output in the question. Deciding what counts as useful is the actual skill being tested, and it depends on the purpose of the device.
- If the question gives the input and the wasted energy, subtract to get the useful output before dividing.
- Say whether your answer is a fraction or a percentage, and give it to two or three significant figures.
Self review
- Explain what is meant by the efficiency of an energy transfer.
- Write both efficiency equations.
- A lamp is supplied with 60 J60\ \text{J}60 J and transfers 9 J9\ \text{J}9 J usefully as light. Calculate its percentage efficiency.
- State where the wasted energy in that lamp ends up.
- Explain why no device can have an efficiency greater than 100%100\%100%.
