Sankey Diagrams (Oxford AQA IGCSE Combined Science Double Award)

Revision Note

Sankey Diagrams

  • Sankey diagrams can be used to represent energy transfers or energy flow in a system

    • Sankey diagrams are characterised by arrows that split to show the proportions of the energy transfers taking place

  • The different parts of the arrow in a Sankey diagram represent the different energy transfers:

    • The left-hand side of the arrow (the flat end) represents the energy transferred into the system

    • The straight arrow pointing to the right represents the energy that ends up in the desired store; this is the useful energy output

    • The arrows that bend away represent the wasted energy

Features of a Sankey diagram

Features of a Sankey diagram, for IGCSE & GCSE Physics revision notes
Total energy in, useful energy out, and wasted energy are shown on a Sankey diagram
  • The width of each arrow is proportional to the amount of energy being transferred

  • The law of conversation of energy states that:

Total energy in = total energy out 

Total energy in = Useful energy out + Wasted energy

  • A Sankey diagram for a modern efficient light bulb will look very different from that for an old filament light bulb

  • A more efficient light bulb has less wasted energy

    • This is shown by the smaller arrow downwards representing the heat energy

Comparing Sankey diagrams for a filament and an energy efficient bulb

A Sankey diagram for an energy efficient bulb shows a total input energy of 100 J with 75 J transferred by radiation and 25 J transferred by heating. A second Sankey diagram for a filament bulb shows an input energy of 100 J with only 10 J transferred by radiation and 90 J transferred by heating, for IGCSE & GCSE Physics revision notes
Filament bulbs have a much greater proportion of wasted energy than modern energy efficient bulbs

Worked Example

An electric motor is used to lift a weight. The diagram represents the energy transfers in the system.

A Sankey diagram showing an input energy of 500 J with 120 J transferred to the weight, and the remaining energy labelled as wasted energy, for IGCSE & GCSE Physics revision notes

Calculate the amount of wasted energy.

Answer:

Step 1: State the conservation of energy equation

total space energy space in space equals space useful space energy space out space plus space wasted space energy

Step 2: Rearrange the equation for the wasted energy

wasted space energy space equals space total space energy space in space minus space useful space energy space out

Step 3: Substitute the values from the diagram

wasted space energy space equals space 500 space minus space 120

wasted space energy space equals space 380 space straight J

Examiner Tip

  • Drawing good Sankey diagrams takes practice

  • It can be difficult to create a diagram that is to scale

  • Start by planning your diagram using graph paper and a ruler:

    • How many squares or mm wide will you make the input arrow?

    • How many squares or mm wide will the useful energy out arrow need to be?

    • How many squares or mm wide must the wasted arrow be?

  • Next, start drawing the diagram one step at a time:

    • Draw the left-hand side of the arrow, along with the line going across the top

    • Next add the useful energy out arrow, making sure it is the correct width

    • Now carefully mark the start and end of the wasted arrow – make sure your marks are the correct distance apart

    • Finally join the markings together, finishing the wasted energy arrow

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