IGCSE Physics / Energy transfers
Sankey diagrams
Edexcel International GCSE Physics (4PH1), chapter 14: Energy transfers, specification point 4.5. Free lesson.
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A Sankey diagram shows how energy is transferred, with arrow widths in proportion to the amount of energy. It helps you identify useful and wasted outputs, check conservation of energy and calculate efficiency.
What a Sankey diagram shows
A Sankey diagram is an arrow that splits to show where the input energy goes. Each arrow's width is in proportion to the energy it carries. The useful output continues straight on, while wasted energy bends away. The output arrows add up to the input because energy is conserved. A filament lamp receives 100 J of electrical energy. It transfers 10 J usefully as light and wastes 90 J by heating the surroundings. An electric motor receives 500 J electrically. It transfers 300 J to its kinetic store, 150 J to heating the surroundings and 50 J to sound. The outputs total 500 J.
How to draw a Sankey diagram to scale
Choose a scale before drawing. On squared paper, the scale tells you how many squares wide each arrow should be. Draw the input arrow to represent the total energy, then split it into useful and wasted outputs. Label every arrow with the energy transfer and its amount in joules.
How to calculate wasted energy and efficiency
The outputs must add up to the input. If there is one unknown output, subtract the known output from the input to find it. Efficiency is the percentage of the input energy transferred usefully. Efficiency = useful energy output ÷ total energy input × 100%. For the motor, the useful output is 300 J from a 500 J input, so its efficiency is 60%.
Why arrow widths matter
Arrow width is what lets you compare the amounts of energy visually, so it must match the values shown. For example, a 90 J arrow is nine times wider than a 10 J arrow. Arrows drawn at arbitrary widths make the diagram incorrect, even if the labels are right. Check that the widths are in proportion to the energy carried. Check that the output energies add up to the input.