Sankey Diagrams (DP IB Physics: SL): Revision Note
Sankey Diagrams
Sankey diagrams are used to represent energy transfers
The arrow in a Sankey diagram represents the transfer of energy:
The end of the arrow pointing to the right represents the energy that ends up in the desired store (the useful energy output)
The end(s) that point(s) down represents the wasted energy
Total energy in, wasted energy and useful energy out shown on a Sankey diagram
The width of each arrow is proportional to the amount of energy going to each store
As a result of the conversation of energy:
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 downward, representing energy transferred by heating
Sankey diagram for modern vs. old filament light bulb
Worked Example
An electric motor is used to lift a weight. The diagram represents the energy transfers in the motor.
Determine the amount of wasted energy.
Answer:
Step 1: State the conservation of energy
Energy cannot be created or destroyed, it can only be moved from one store to another
This means that:
Total energy in = Useful energy out + Wasted energy
Step 2: Rearrange the equation for the wasted energy
Wasted energy = Total energy in – Useful energy out
Step 3: Substitute the values from the diagram
500 – 120 = 380 J
Worked Example
A small electric car is driven by a 120 watt motor.
The useful power output of the motor is measured to be 33 W. 36 W of power is wasted on friction losses and a further 36 W is wasted on traction losses.
Further power is lost by the electric car during operation. This situation is shown in the diagram below.
Determine the remaining power loss for the electric car when it is operating.
Answer:
Step 1: State the conservation of energy
Energy cannot be created or destroyed, it can only be moved from one store to another
This also applies to power
This means that:
Total power in = Useful power out + Friction losses + Traction losses + Wasted power
Step 2: Rearrange the equation for the wasted power
Wasted power = Total power in – (Useful power out + Friction losses + Traction losses)
Step 3: Substitute the values from the diagram
120 – (33 + 36 + 36) = 15 W
Examiner Tips and Tricks
Drawing good Sankey diagrams takes practice.
Start by planning your diagram:
How wide are you going to make the input arrow?
How wide will the 'useful energy out' arrow need to be?
How wide must the 'wasted energy' 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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