Efficiency = useful ÷ total × 100%
Efficiency . It is always ≤ 100% — no device outputs more useful energy than it receives. The denominator is the total output (= total input, by conservation), not just the useful or wasted part. Wasted energy usually dissipates as thermal energy, sometimes sound or light. Unit: % (or a decimal 0–1 if the ×100% is dropped).
Sankey diagrams and improving efficiency
A Sankey diagram uses arrow widths proportional to energy: the input arrow splits into a thick useful output and thinner wasted (usually thermal/sound) outputs; total width is conserved. Improve efficiency by reducing waste: lubrication (less friction/heat), thermal insulation (less heat loss — lagging, double glazing), LED lighting (filament lamps waste ~92% as heat), and streamlining (less air resistance).
Drawn from real examiner reports.
Wrong denominator in the efficiency formula
The spec formula uses total energy output in the denominator. Because energy is conserved, total output = total input, so the number is the same — but quote it as "total energy output" to secure the formula mark. Worse: putting only the wasted output (not the total) in the denominator is simply wrong. Substitute the total, never just the wasted part.
Not identifying the useful output
The biggest efficiency error is putting the total output in both numerator and denominator, giving 100% every time. Many candidates also cannot spot which output is useful — for a turbine it is the blades' kinetic energy, not the total wind energy. Only the useful output goes on top; if you cannot identify it, the efficiency step is lost.
November 2024 Paper 2P Q7(b)(ii) — the examiner stated that significant numbers of candidates did not evaluate the kinetic energy correctly and, critically, many did not recognise it as the useful energy output, so could not access the efficiency calculation marks.
Efficiency over 100% or 0.75% mix-up
As a decimal, efficiency lies between 0 and 1; as a percentage, between 0% and 100%. Two slips: inverting the fraction (200 J / 150 J = 1.33, i.e. more useful out than in — impossible); and forgetting ×100%, then writing 0.75 as "0.75%". Report either 0.75 (ratio) or 75% (percentage), never mix them. If your answer exceeds 100%, you inverted it.
Not dividing % by 100 for useful output
To find the useful output from a percentage efficiency, divide by 100 first: useful (efficiency) total. For 35% of 2400 J that is J, not J. Skipping the is a very common slip.
(general exam technique)
Dropping the % or leaving units unconverted
Convert units before substituting (e.g. cm → m for any distance), and be clear whether the final efficiency is wanted as a decimal or a percentage — 0.80 and 80% are the same value but only one carries the % sign. Losing the % (or writing 0.80%) is a unit error that costs the final mark.
(general exam technique)
Multiplying when finding total input
To find the total input from efficiency and useful output, divide: total useful (efficiency). A common slip is to multiply instead ( J), which gives less than the useful output — impossible, since the total must exceed the useful part. Check total > useful.
(general exam technique)
Show structured working (ECF marks)
Efficiency questions are often multi-step. Scaffold: (1) write the formula; (2) label and calculate the useful output; (3) substitute; (4) give the unit (% or ratio). Structured working still earns the formula and substitution marks even if the useful-output value is wrong.
Ask what the device is for
Before any calculation, ask "what is this device for?" — that output is the useful energy. A lamp: light. A motor: kinetic energy. A heater: thermal energy. Circle it, then everything else is wasted. This step unlocks the whole efficiency calculation.
Sanity-check: 0–100%, total > useful
Always sanity-check the final efficiency: it must sit between 0 and 100% (or 0 and 1). If it comes out above 100%, you have inverted the fraction or used the wasted output. If you are finding the total input, it must be larger than the useful output.
Draw Sankey arrows to scale, label all
For a Sankey diagram, draw arrow widths to scale with the energy values, label the input and every output with value and type (useful vs wasted), send the wasted (thermal) arrow downward, and check outputs sum to the input. Equal-width arrows lose the proportionality mark.
where useful energy output is the energy transferred in the desired form (e.g. kinetic energy (KE) from a motor, light from a lamp) and total energy output = total energy input (by conservation of energy). Efficiency has no unit when expressed as a decimal ratio; it carries the unit % when multiplied by 100.
Rearrangements you must know:
Define efficiency (give the two-element mark-scheme form).
An electric motor is supplied with 200 J of electrical energy. It transfers 150 J as kinetic energy to a load. The remaining energy is dissipated as thermal energy and sound.
Calculate the efficiency of the motor. Give your answer as a percentage.
