Energy Efficiency and Sankey Diagrams
In 2018, ARENA funded an audit showing NSW schools waste $120 million in electricity yearly, Sankey diagrams make that waste visible in one picture.
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Q1 · You switch on a light bulb that uses 100 W of electricity. Do you think all of that power turns into light, or does some of it go elsewhere? What makes you think that?
Q2 · If you had a diagram showing energy flowing into a device and out again, what would you need to draw to show that energy is conserved? How would you show which output is "useful" and which is "wasted"?
Key Relationships, This Lesson
● Know
- What a Sankey diagram is and what it represents
- That arrow width is proportional to energy
- How to read energy values from a Sankey diagram
● Understand
- Why Sankey diagrams visually prove conservation of energy
- How to calculate efficiency from a Sankey diagram
- Why some arrows are much wider than others
● Can do
- Read energy values and efficiency from any Sankey diagram
- Construct a simple Sankey diagram from given data
- Compare devices using Sankey diagrams to justify conclusions
Wrong: "The arrows in a Sankey diagram show the direction of energy, but the widths don't really matter."
Right: The widths are the whole point of a Sankey diagram. Each arrow's width is drawn to scale so you can instantly see how much energy goes to each output, a wider arrow means more energy.
Wrong: The widths are the entire point. If you ignore widths, you lose the quantitative information. A Sankey diagram without proportional widths is just a flow chart, not a Sankey diagram.
Right: Arrow widths encode the energy quantities, without them, a Sankey is just an unlabelled flow diagram. Always draw and read arrow widths to scale; they are what make Sankey diagrams scientifically useful.
Wrong: "Waste energy in a Sankey diagram is shown as a smaller arrow because it is less important."
Right: The width of the waste arrow simply shows how much energy is wasted, in an inefficient device, the waste arrow is often the widest of all. Width reflects quantity, not importance.
Wrong: In many Sankey diagrams, the waste arrow is actually the widest. For a coal power station, the waste arrow (thermal energy) is nearly twice as wide as the useful output arrow (electrical energy). Waste energy is not "less important", it is the largest portion of the energy flow.
Right: For most real devices, the waste arrow is wider than the useful output arrow, visually showing how much energy is lost. A coal power station's Sankey diagram is dominated by waste thermal energy, this is exactly the kind of inefficiency engineers are working to reduce.
Hold an old incandescent bulb near your palm for five seconds, the heat is overwhelming, yet the room is barely lit. That heat is wasted energy, and the fraction wasted tells you how inefficient the device is. Efficiency measures how well a device converts input energy into the form we actually want, calculated as useful output divided by total input, expressed as a percentage.
Low efficiency does not mean energy disappears, it means energy transforms into unwanted forms, usually heat. An old incandescent bulb is only about 5% efficient because 95% of the electricity becomes thermal energy rather than light. Modern LEDs achieve 20-30% efficiency, which is why they use far less power for the same brightness.
A car engine might be 25% efficient. For every 100 J of chemical energy in the petrol, only 25 J becomes useful kinetic energy. The other 75 J heats the engine, exhaust and surroundings. The energy is conserved but mostly wasted.
The Australian Energy Council notes that replacing all household incandescent bulbs with LEDs could reduce lighting energy use by over 70% nationwide. Efficiency improvements are often the cheapest way to cut emissions.
What to write in your book
- Efficiency = (useful energy output) ÷ (total energy input) × 100%
- No machine is 100% efficient, some energy is always wasted
- Sankey diagrams show energy flows with arrow widths
An incandescent light bulb converts 5% of electrical energy into light. What percentage becomes thermal energy?
How close was your prediction?
Nice calibration, your intuition is good for this kind of problem.
Good, being surprised is the point. This answer is worth remembering.
Sankey diagrams are visual tools that represent energy flows. A wide arrow enters from the left showing total input energy. This arrow then splits: one branch continues rightward representing useful output, while other branches drop downward showing wasted energy. The width of each branch is proportional to the amount of energy it carries.
The key rule of a Sankey diagram is conservation: the sum of all outgoing arrows must exactly equal the incoming arrow. If you draw a Sankey diagram for a coal power station, the useful electrical energy arrow is a thin stream compared to the thick waste heat arrow heading downward.
A Sankey diagram for a 60 W incandescent bulb shows a 60 W input arrow splitting into a 3 W light arrow (useful, going right) and a 57 W heat arrow (wasted, going down). The widths are in the ratio 3:57, making the waste visually obvious.
What to write in your book
- Sankey arrows are drawn to scale, wider means more energy
- The input arrow equals the sum of all output arrows
- Useful outputs point forward; wasted outputs point downward
- Incandescent bulb
- LED bulb
- Car engine
- Coal power station
- Electric motor
- ~90% efficient
- ~25% efficient
- ~33% efficient
- ~25% efficient
- ~5% efficient
Improving efficiency is one of the most powerful ways to reduce energy costs and environmental damage. Unlike building new power stations, efficiency gains often require only better technology or smarter design. A more efficient fridge uses less electricity to keep your food cold. Better insulation means less heating in winter.
Some systems actually achieve very high efficiency. Electric motors can convert over 90% of electrical energy into kinetic energy. The waste is minimal because there are no combustion steps creating unavoidable heat losses. When the useful output is heat, like in an electric heater, the efficiency approaches 100%.
Combined-cycle gas turbines used in modern power stations capture waste heat from the first engine to drive a second turbine. This raises overall efficiency from about 35% to nearly 60%, meaning less fuel for the same electricity.
The Sun Cable project planned for Australia's Northern Territory aims to export solar energy to Singapore via undersea cables. Efficiency of generation, transmission and conversion is critical to making such long-distance energy trade economically viable.
What to write in your book
- Improving efficiency saves money and reduces environmental impact
- Combined heat and power plants capture waste heat for useful purposes
- Efficiency is different from effectiveness, a heater is 100% efficient at making heat
Copy Into Your Books
▼Sankey Diagram Essentials
- Arrow width ∝ energy amount
- One input arrow on the left
- Output arrows on the right
- Total width in = total width out
- Always label with value + unit + energy form
Construction Steps
- 1. Identify input, useful, waste values
- 2. Choose a scale (e.g., 1 cm = 100 J)
- 3. Calculate widths: value ÷ scale
- 4. Draw input arrow on left
- 5. Draw output arrows on right
- 6. Add title and state the scale
Australian Efficiencies (Sankey-friendly)
- Hydro: ~90% useful (widest green arrow)
- Wind: ~45% useful
- Coal: ~35% useful
- Solar PV: ~20% useful
- LED: ~20% useful
- Incandescent: ~5% useful (thinnest green arrow)
Reading a Sankey
- Efficiency = (useful width ÷ input width) × 100
- Waste = input − useful
- Wider waste arrow = less efficient device
- Compare devices using same input energy
Interpreting Sankey Diagrams
1 A Sankey diagram for a device shows an input arrow of 8 cm width representing 800 J, a useful output arrow of 3 cm, and a waste arrow of 5 cm. What is the efficiency of this device?
2 Look at the comparative Sankey diagrams in Figure 2. For the same 1,000 J input, how many times more useful energy does the wind turbine produce compared to the incandescent bulb? Show your calculation.
3 A student draws a Sankey diagram with an input arrow of 6 cm and a useful output arrow of 6 cm, with no waste arrow. Explain why this diagram must be incorrect for a real device, and redraw it correctly assuming 30% efficiency with a scale of 1 cm = 100 J.
4 The Snowy Hydro scheme has turbines that are approximately 90% efficient. Using a scale of 1 cm = 200 J, construct a Sankey diagram for 1,000 J of gravitational potential energy input. State the width of each arrow and describe what the waste energy becomes.
Design Your Own Sankey
At the start of this lesson you were told that a standard incandescent bulb converts only about 5% of its electricity into visible light, the other 95% escapes as heat. You were asked what an honest Sankey diagram of your whole school's energy use would look like.
Now that you can read and draw Sankey diagrams, sketch that idea in your head: which arrows would be widest? Did this lesson change what you think about energy efficiency?
Q1. 6. A device is supplied with 600 J of energy and is 40% efficient. Using a scale of 1 cm = 50 J, construct a Sankey diagram. State the width of each arrow and show your scale calculation.
1 mark for correct scale calculation. 1 mark for correct widths (input 12 cm, useful 4.8 cm or approximately 5 cm, waste 7.2 cm or approximately 7 cm). 1 mark for correctly labelled diagram with title and energy forms.Q2. 7. The following two Sankey diagrams are drawn for two different light bulbs, both with 200 J of electrical energy input:
1 mark for describing the diagrams (Bulb X has very narrow useful arrow, Bulb Y has wider useful arrow). 1 mark for calculating both efficiencies (5% and 20%). 1 mark for explaining why Bulb Y saves energy. 1 mark for linking to cost reduction through reduced total energy use.Q3. 8. A politician claims: "We should stop building wind farms because they are only 45% efficient. We should build more coal power stations instead because we already know how to build them." Use Sankey diagram reasoning, the concept of efficiency, and what you know about energy forms to evaluate this claim. Consider both the efficiency percentages and the nature of the waste energy from each source.
1 mark for constructing or describing Sankey diagrams for both sources. 1 mark for noting that coal waste is thermal pollution and CO₂ emissions. 1 mark for noting that wind waste is just kinetic energy dissipation (no pollution). 1 mark for explaining that efficiency is only one factor, fuel source and environmental impact matter. 1 mark for a balanced conclusion.Model answers (click to reveal)
Comprehensive Answers
▼Activity 1, Interpreting Sankey Diagrams
1. Efficiency: Useful = 3 cm, Input = 8 cm. Efficiency = (3 ÷ 8) × 100 = 37.5% (or approximately 38%).
2. Comparison: Wind useful = 450 J. Incandescent useful = 50 J. Ratio = 450 ÷ 50 = 9 times more useful energy from wind.
3. Incorrect No real device is 100% efficient, so there must be a waste arrow [1 mark]. At 30% efficiency with 600 J input: useful = 600 × 0.30 = 180 J. Waste = 600 − 180 = 420 J. Scale 1 cm = 100 J: input = 6 cm, useful = 1.8 cm, waste = 4.2 cm [1 mark]. The student's diagram violates conservation of energy by showing no waste [1 mark].
4. Snowy Hydro: Scale 1 cm = 200 J. Input = 1,000 ÷ 200 = 5 cm. Useful = 1,000 × 0.90 = 900 J → 900 ÷ 200 = 4.5 cm. Waste = 1,000 − 900 = 100 J → 100 ÷ 200 = 0.5 cm. The waste energy becomes thermal energy through friction in turbines, generators, and water turbulence [1 mark].
Activity 2, Design Your Own Sankey
Accept any reasonable device with plausible estimates. Example, Electric kettle: Input ≈ 2,000 W electrical. Useful output ≈ 1,800 W thermal in water (90% efficient). Waste ≈ 200 W thermal to kettle body and air. Scale: 1 cm = 200 W. Input = 10 cm, useful = 9 cm, waste = 1 cm [2 marks for correct construction]. Explanation: The diagram shows the kettle is quite efficient because the useful arrow is almost as wide as the input arrow. Improvement: better insulation around the kettle body to reduce the waste arrow width [2 marks for evaluation].
Multiple Choice
1. BArrow width is proportional to energy amount. This is the defining feature of a Sankey diagram.
2. CEfficiency = (useful width ÷ input width) × 100 = (4 ÷ 10) × 100 = 40%. The scale cancels out because both widths use the same scale.
3. AUseful = 400 × 0.25 = 100 J. Waste = 400 − 100 = 300 J. Waste width = 300 ÷ 50 = 6 cm. Option B is the useful width. Option C is the input width. Option D is incorrect.
4. DDevice B's wider useful arrow means more input energy becomes useful work. Option A reverses the logic. Option B confuses total energy with efficiency. Option C is true but D is the most complete correct answer.
5. BInput = 1,000 ÷ 200 = 5 cm. Useful = 500 ÷ 200 = 2.5 cm. Waste = 500 ÷ 200 = 2.5 cm. The student made the input 6 cm (wrong) and waste 3.5 cm (wrong). Option A is false. Option C misunderstands the efficiency. Option D is false, Sankey diagrams are ideal for power stations.
Short Answer Model Answers
Q6 (3 marks): Useful = 600 × 0.40 = 240 J. Waste = 600 − 240 = 360 J [1 mark]. Scale 1 cm = 50 J: input = 600 ÷ 50 = 12 cm. Useful = 240 ÷ 50 = 4.8 cm (or ≈ 5 cm). Waste = 360 ÷ 50 = 7.2 cm (or ≈ 7 cm) [1 mark]. Diagram must show one input arrow labelled "600 J" and two output arrows labelled "240 J useful" and "360 J waste", with title and scale stated [1 mark].
Q7 (4 marks): Bulb X efficiency = (10 ÷ 200) × 100 = 5% [0.5 mark]. Bulb Y efficiency = (40 ÷ 200) × 100 = 20% [0.5 mark]. Bulb X very narrow green useful arrow (1 cm if scale 1 cm = 10 J), very wide red waste arrow (19 cm) [0.5 mark]. Bulb Y wider green useful arrow (4 cm), narrower red waste arrow (16 cm) [0.5 mark]. The school should choose Bulb Y because it produces four times as much light from the same input energy, meaning fewer bulbs or less power needed for the same brightness [1 mark]. This reduces electricity costs because less total energy is consumed, even though both use 200 J in the diagram, in reality Bulb Y could use less power to produce equivalent light [1 mark].
Q8 (5 marks): Coal Sankey: 1,000 J input → 350 J useful electrical + 650 J waste thermal + CO₂ emissions [0.5 mark]. Wind Sankey: 1,000 J input → 450 J useful electrical + 550 J waste kinetic energy dissipated into air [0.5 mark]. The politician's claim ignores that coal waste includes carbon dioxide (a greenhouse gas) and other pollutants, while wind waste is just dissipated kinetic energy with no chemical pollution [1 mark]. Efficiency alone is misleading, coal at 35% produces 650 J of waste per 1,000 J, and that waste includes climate-altering emissions. Wind at 45% produces 550 J of waste, but that waste is harmless air movement [1 mark]. Furthermore, coal requires continuous fuel (mining, transport, burning), while wind uses a free, renewable resource. The initial construction cost of wind is higher, but operating costs are lower and environmental impact is dramatically smaller [0.5 mark]. Conclusion: The claim is flawed because it uses efficiency in isolation. A balanced energy policy must consider efficiency, waste type, fuel source, environmental impact, and long-term sustainability [0.5 mark].
Marking Criteria Summary
Q6 (3 marks): (1) Correct scale calculation. (2) Correct widths. (3) Labelled diagram with title.
Q7 (4 marks): (1) Describes both diagrams. (2) Calculates both efficiencies. (3) Explains energy savings. (4) Links to cost reduction.
Q8 (5 marks): (1) Sankey for both. (2) Coal waste = pollution. (3) Wind waste = harmless. (4) Efficiency not the only factor. (5) Balanced conclusion.
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