Supplement (Extended) content
IGCSE 0625 · Section 1.7 · Extended

How much actually does the job.

No device turns all the energy it is given into the energy you want; some always slips away, usually as heat. Efficiency measures the fraction that does the useful job, and a Sankey diagram draws that split to scale, the useful flow carrying on, the wasted flow peeling away.

The Key Idea

Efficiency = useful energy output ÷ total energy input (× 100%). Equivalently, efficiency = useful power output ÷ total power input (× 100%). On a Sankey diagram the width of each arrow is proportional to the energy it carries.

SECTION 01

A Sankey drawn to scale.

Set the total energy going into a device and how much of it does the useful job. The Sankey diagram redraws to scale: the useful flow carries straight on, the wasted flow peels away as heat, and the two always add back to the input. Efficiency is the useful fraction. Try the real devices to see why a filament lamp wastes most of its energy while an LED keeps nearly all of it, and switch between energy and power to confirm the ratio is the same.

SECTION 02

Do not mix energy and power.

Keep both terms the same kind

Efficiency is a ratio of two quantities of the same kind. Use useful energy over total energy, or useful power over total power, never an energy divided by a power. Both forms give the same fraction, which has no unit and can be written as a percentage. Mixing the two, or putting wasted energy on top, is the usual slip.

Worked Example

An electric motor is supplied with 500 J of electrical energy and transfers 350 J usefully to the kinetic store of a load. Find its efficiency and the energy wasted.

Step 1 · Efficiency efficiency = useful ÷ total = 350 ÷ 500 = 0.70
Step 2 · As a percentage 0.70 × 100 = 70 %
Step 3 · Energy wasted 500 − 350 = 150 J (transferred to the thermal store)
Practice this topic →
Six original Cambridge-style questions.
Calculating efficiency from energy or power, finding wasted energy, reading a Sankey diagram, and using the correct matching quantities. Attempt each, then reveal the worked solution.