What efficiency means

A device or process usually transfers energy in more than one way. Some of the input energy is transferred in the useful way, and some is dissipated to less useful stores, often warming the surroundings or producing sound.

The word useful is not fixed forever; it depends on the intended purpose. In a lamp, the useful output is light. In an electric motor lifting a load, the useful output is the increase in gravitational potential energy of the load. In a kettle, thermal energy transferred to the water is useful, but thermal energy transferred from the kettle to the surrounding air is not.

Efficiency is a ratio, so it has no unit. A high efficiency means a large fraction of the input is useful. A low efficiency means a large fraction is dissipated in unwanted ways.

For normal GCSE efficiency calculations:

• as a decimal, efficiency is between 0 and 1
• as a percentage, efficiency is between 0% and 100%
• a decimal of 0.65 is the same as 65%
• an answer greater than 1 or greater than 100% usually means the useful output and total input have been swapped

Calculating efficiency from energy

Use the energy equation when the question gives energy transfers in joules, kilojoules or another energy unit. The useful output energy transfer and total input energy transfer must be in the same unit before you divide.

This is a recall-and-apply equation. Learn the exact structure: useful output goes on the top, total input goes on the bottom.

If a drill has an electrical input energy transfer of 500 J and transfers 320 J usefully to the kinetic energy store of the drill bit:

As a percentage:

The same answer can be written as 0.64 or 64%, depending on what the question asks for. Do not write "0.64%" unless the answer is meant to be 0.0064 as a decimal.

If the question gives percentage efficiency and you need to calculate an energy, convert the percentage to a decimal first. For example, 40% becomes 0.40.

For a device that is 40% efficient and gives a useful output energy transfer of 1200 J:

Calculating efficiency from power

Power is the rate of energy transfer. If a question gives input power and useful output power, use the power version of the efficiency equation.

This is also a recall-and-apply equation. Use watts with watts, kilowatts with kilowatts, or convert first so the units match.

For example, a lamp has a total electrical input power of 12 W and a useful light output power of 2.4 W:

As a percentage:

The energy and power equations give the same kind of answer because power is energy transferred per second. Use the equation that matches the data you are given. If the question gives energy, use energy. If it gives power, use power.

Checking and rearranging answers

Efficiency questions are often simple ratios, but the wording can still be slippery. A good calculation habit is to identify three things before substituting:

• what the intended useful output is
• whether the numbers are energy transfers or powers
• whether the required answer is a decimal, a percentage, a useful output, or a total input

For rearranging, start from the same equation each time. Suppose a pump transfers 900 J usefully and has an efficiency of 0.30:

So:

If you are finding useful output instead:

For example, a device with efficiency 0.80 and total input energy transfer 1500 J has:

Common mistakes to avoid:

• using the wasted energy as the useful output
• dividing total input by useful output, which can give an impossible efficiency above 1
• mixing energy and power in the same fraction
• forgetting to convert a percentage to a decimal before rearranging
• adding a unit to efficiency, even though efficiency has no unit

After a calculation, ask whether the answer makes physical sense. A motor with 500 W input cannot have 800 W useful output in an ordinary efficiency question, because that would mean more useful power leaves than total power enters.

Increasing efficiency (Higher tier)

Higher-tier students must also be able to describe ways to increase the efficiency of an intended energy transfer.

Increasing efficiency means increasing the fraction:

That can be done by increasing the useful output for the same input, or by reducing unwanted transfers so less input energy is dissipated.

A full description should link the design change to the unwanted transfer it reduces. For example:

• Lubricating moving parts reduces friction, so less energy is dissipated by heating at the contact surfaces.
• Using thermal insulation around a hot water tank reduces energy transfer to the surroundings, so a larger fraction of the input energy remains useful for heating the water.
• Streamlining a vehicle reduces drag, so less energy is transferred to thermal stores of the air and vehicle while it moves.
• Using an LED instead of a filament lamp increases the fraction of electrical energy transferred usefully as light, with less energy dissipated by heating the surroundings.

The best answer is specific to the intended transfer. If the intended output is heating a room, then thermal energy transferred into the room is useful. If the intended output is moving a machine part, then thermal energy produced by friction is usually unwanted.

Efficiency cannot usually be made 100% in real devices because some energy is still dissipated in unwanted ways. The aim is to make the useful transfer a larger fraction of the total input.

That cause-and-effect link is what turns a vague improvement into a physics answer.