IB DP Physics: SL复习笔记8.1.2 Sankey Diagrams

Sankey Diagrams

  • Diagrams are used to represent energy transfers
    • These are sometimes called Sankey diagrams
  • 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

8-1-2-sankey-diagram-demonstration_sl-physics-rn

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 downwards representing the heat energy

Sankey-comparison

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.3.1.3-WE-Sankey-Question-image

How much energy is wasted?

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. While 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.

8-1-2-we-sankey-diagram_sl-physics-rn

Determine what is the remaining power loss for the electric car when operating?

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 other losses

Step 2: Rearrange the equation for the wasted power

Wasted power other losses = Total power in – (Useful power out + Friction losses + Traction losses)

Step 3: Substitute the values from the diagram

120 – (33 + 36 + 36) = 15 W

Exam Tip

  • 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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