Worksheet: Sankey Diagrams

In this worksheet, we will practice correctly drawing and interpreting Sankey diagrams for processes that involve the transfer of energy.

Q1:

The image shows a Sankey diagram for a light bulb that is supplied with 100 J of energy, where 80 J of energy is wasted as heat. What is the useful energy output of the bulb?

Q2:

The image shows a Sankey diagram for a fluorescent light. What is the input power of the fluorescent light?

Q3:

The image shows a Sankey diagram of a 100 W light bulb.

What does 1 square of the diagram represent?

How much energy is wasted as heat by the light bulb?

What is the efficiency of the light bulb?

  • A70%
  • B50%
  • C30%
  • D20%
  • E10%

Q4:

The image shows a Sankey diagram for a 1.7 kW kettle turned on for 3 minutes.

Is the majority of the energy supplied to the kettle wasted or transferred usefully?

  • AThe majority of the energy is wasted.
  • BThe majority of the energy is transferred usefully.

What is the efficiency of the kettle?

  • A0%
  • B10%
  • C100%
  • D90%
  • E50%

Q5:

The image shows a Sankey diagram for a light bulb that has been drawn incorrectly. In which of the following ways has the diagram been drawn incorrectly?

  1. The value represented by one square of the diagram is not consistent.
  2. 1 square of a Sankey diagram should always represent 1 watt or 1 joule.
  3. Sankey diagrams can only be used for energy, not power.
  4. The two output arrows both represent 20 W, but they are of different widths.
  5. The total output power is not equal to the total input power.
  • Aa, c, and e
  • Be, b, and c
  • Ca, b, and e
  • Da, d, and e
  • Ed, b, and c

Q6:

Diagram (a) is a Sankey diagram of a 1.8 kW kettle. Diagram (b) is a Sankey diagram of an 80 W light bulb.

Which device is more efficient?

  • AThe kettle
  • BThe light bulb

What is the efficiency of the kettle?

  • A 5 0 %
  • B 2 0 %
  • C 1 0 %
  • D 1 0 0 %
  • E 9 0 %

What is the efficiency of the light bulb?

  • A 2 0 %
  • B 1 0 %
  • C 2 5 %
  • D 7 0 %
  • E 8 0 %

Q7:

The image shows Sankey diagrams for four different processes.

Which process is the most efficient?

  • A(d)
  • B(c)
  • C(b)
  • D(a)

Which process is the least efficient?

  • A(b)
  • B(c)
  • C(d)
  • D(a)

Q8:

The image shows a Sankey diagram for a process. Which of the following statements correctly describes why this process is not physically possible?

  • AThis process is inefficient. In order to be physically possible, processes need to have an efficiency greater than 50%.
  • BThe output energy is greater than the input energy. This process would create energy. Since energy cannot be created or destroyed, this process is not physically possible.

Q9:

The image shows a Sankey diagram for a car motor that is supplied with 2,400 J of energy, where 480 J of the energy is converted into useful kinetic energy. How much energy is wasted?

Q10:

The image shows a Sankey diagram for a process. Which of the following statements correctly describes why this process is not physically possible?

  • AReal physical processes always have efficiencies less than 50%. This process would have an efficiency greater than 50%.
  • BAll of the input energy of this process is the recycled energy, but the useful output energy is greater than zero. This process appears to create energy, but since energy cannot be created or destroyed, it is not physically possible.
  • CEnergy cannot be recycled in a physical process.
  • DOnce started, this process could continue indefinitely, but since there is no initial input energy, it cannot be started.

Q11:

The image shows a Sankey diagram for a steam locomotive. Coal in a boiler is used to heat water to turn it into steam. The steam is then used to drive pistons that turn the wheels. In this process, some of the input energy is converted to the kinetic energy of the train, some is lost as heat, and some of the heat is recycled.

What does 1 square represent in the diagram shown?

How much energy is lost as heat?

How much energy is recycled?

The diagram shows the energy usage per second for the train to maintain a constant speed of 40 mph. What input energy is needed for the train to maintain this constant speed?

Coal has an energy density of about 30 MJ/kg. How much coal needs to be combusted per minute in order to keep the train moving at 40 mph? Assume that all of the energy in the coal is transferred to the steam.

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