Efficiency and Sankey diagrams

What is efficiency?

When energy is transferred by a device, only some of it ends up in the useful form. The rest is wasted — usually as heat into the surroundings, or as sound.

Efficiency = useful energy transferred ÷ total energy supplied

The answer is a fraction between 0 and 1, often multiplied by 100 to give a percentage:

Efficiency (%) = (useful energy out ÷ total energy in) × 100

You can use either energy (J) or power (W) — both give the same ratio.

Efficiency = useful power out ÷ total power in

Sankey diagrams

A Sankey diagram shows energy transfers visually. The width of each arrow is proportional to the amount of energy.

• A wide arrow goes in (total input).
• A narrower useful arrow continues forward.
• A side arrow shows wasted energy (often heat).

For an old filament lamp: 100 J in → 10 J light (useful) + 90 J heat (wasted). The wasted-heat arrow on the Sankey is nine times wider than the useful-light arrow.

Reducing wasted energy

• Lubrication of moving parts reduces friction and so reduces wasted heat.
• Insulation (loft, cavity wall, double glazing) reduces heat transfer out of buildings.
• Aerodynamic shape reduces air resistance on cars, so less work is done against drag.
• LED bulbs waste far less energy as heat than filament bulbs (90% useful vs 10%).

Why efficiency is never 100%

The second law of thermodynamics dictates that some energy is always dissipated to the surroundings (most often as thermal energy in colder objects). Friction, electrical resistance and air drag are unavoidable in real systems. Even electric heaters (which are ~100% efficient if you only want heat) waste no energy in principle, but useful-energy machines (motors, lamps, generators) cannot reach 100%.

Edexcel exam tip

Read the question carefully — Edexcel often gives the wasted energy and asks for efficiency. You must subtract first: useful = total − wasted, then divide. Always state the unit (% or no unit if a fraction).