Every second, the Loy Yang Power Station in Victoria's Latrobe Valley burns coal containing enough energy to power a small city. But where does all that energy actually go? A Sankey diagram shows the answer in a single glance — wide arrows for lots of energy, narrow arrows for little energy, and every joule accounted for from left to right.
A typical smartphone charger draws about 10 watts from the wall socket. The phone battery stores roughly 7 watts of that as chemical energy. The remaining 3 watts become thermal energy that warms the charger and the phone.
Before reading on, sketch a simple diagram showing this energy flow. Draw one arrow going in (labelled "electrical energy from wall, 10 W") and two arrows coming out (one labelled "stored in battery" and one labelled "waste thermal energy"). Make the width of each arrow roughly proportional to the energy it represents. Do not worry about perfect proportions — just get the idea down. You will compare your sketch to a proper Sankey diagram at the end of the lesson.
📚 Core Content
Wrong: "The arrows in a Sankey diagram show the direction of energy, but the widths don't really matter."
Right: 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.
Wrong: "Waste energy in a Sankey diagram is shown as a smaller arrow because it is less important."
Right: 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.
Imagine you could see energy flowing like water through pipes. A Sankey diagram is exactly that — a visual map of energy flow where the "pipes" are arrows, and the width of each arrow tells you how much energy is flowing through it. The wider the arrow, the more energy.
Sankey diagrams have three essential features:
The most powerful feature of a Sankey diagram is that the total width of all arrows going in equals the total width of all arrows going out. This is conservation of energy made visible. You can literally see that no energy has disappeared — it has just been redistributed between useful output and waste.
Figure 1 — Sankey diagram for a typical Australian coal-fired power station
Look at the diagram above. The input arrow (blue, left) is the widest because it represents all 1,000 joules of chemical energy in the coal. The useful output arrow (green, top right) is narrow — only 350 joules becomes electricity. The waste arrow (red, bottom right) is the widest of all — 650 joules of thermal energy escapes into the atmosphere through cooling towers and exhaust gases.
This single diagram tells the entire story of why coal power is inefficient. More than half the energy in every lump of coal is wasted before it ever reaches a light switch.
Drawing a Sankey diagram is not art class — it is mathematical communication. Follow these steps and you will produce diagrams that are clear, accurate, and worth full marks.
Identify your values
Write down the energy input, useful output, and waste energy. Check that input = useful + waste. If not, recalculate.
Choose a scale
Pick a scale that fits your page. For example: 1 cm = 100 J or 1 mm = 10 J. The scale must work for all three values.
Calculate arrow widths
Divide each energy value by your scale. Example: if input = 800 J and scale = 1 cm = 100 J, input width = 8 cm.
Draw the input arrow
Draw one wide arrow on the left. Label it with the energy value, unit, and energy form (e.g., "800 J chemical energy").
Draw the output arrows
Draw two (or more) arrows on the right. The sum of their widths must equal the input arrow width. Label each with value, unit, and energy form.
Add a title and scale
Every Sankey diagram needs a descriptive title and a stated scale. Without these, the diagram cannot be interpreted.
An LED bulb is supplied with 100 J of electrical energy. It produces 20 J of light energy and 80 J of thermal energy. Construct a Sankey diagram using a scale of 1 cm = 10 J.
Input = 100 J. Useful = 20 J. Waste = 80 J. Check: 20 + 80 = 100 ✓
Scale: 1 cm = 10 J. Input width = 100 ÷ 10 = 10 cm. Useful width = 20 ÷ 10 = 2 cm. Waste width = 80 ÷ 10 = 8 cm.
Draw a 10 cm wide arrow on the left labelled "100 J electrical energy". Draw a 2 cm arrow on the top right labelled "20 J light energy (useful)". Draw an 8 cm arrow on the bottom right labelled "80 J thermal energy (waste)". Title: "Sankey diagram for an LED bulb (scale: 1 cm = 10 J)".
Marking tip: In an exam, showing your scale calculation earns method marks even if your drawing is slightly inaccurate. Always show the working.
Australia's energy mix is diverse — from ancient coal plants in Victoria to cutting-edge solar farms in the outback. Here is how each major source would look as a Sankey diagram, all using the same input energy for easy comparison.
Figure 2 — Comparative Sankey diagrams (all with 1,000 J input)
Look at the incandescent bulb diagram. The useful output arrow is barely visible — a thin sliver representing just 50 joules of light from 1,000 joules of input. The waste arrow dominates the diagram. Now compare it to the LED bulb: the useful output arrow is four times wider, and the waste arrow is noticeably narrower. This is why replacing incandescent bulbs with LEDs is one of the fastest ways to reduce household energy use.
The Snowy Mountains Hydroelectric Scheme contains 16 major dams, 7 power stations, and 145 kilometres of tunnels through the Great Dividing Range. Its turbines are approximately 90% efficient — among the highest of any power source in Australia. A Sankey diagram of Snowy Hydro would show an impressively wide useful output arrow, which is why hydroelectric power has been the backbone of Australian renewable energy since 1974.
World-record swimmer Cate Campbell generates about 400 watts of useful power in the pool. A Sankey diagram of her energy use would show roughly 1,600 watts of chemical energy from food entering her body, with 400 watts becoming kinetic energy of swimming (the useful output) and 1,200 watts becoming thermal energy that her body must dissipate through sweating and blood flow to the skin. This 25% efficiency is actually similar to a coal power station — but Campbell's "waste" heat is essential for maintaining body temperature in a cool pool.
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.
1. In a Sankey diagram, what does the width of each arrow represent?
2. A Sankey diagram for a device has an input arrow 10 cm wide representing 1,000 J. The useful output arrow is 4 cm wide. What is the efficiency?
3. Using a scale of 1 cm = 50 J, what should be the width of the waste energy arrow for a device with 400 J input and 25% efficiency?
4. Two Sankey diagrams are drawn for different devices, both with 1,000 J input. Device A has a useful output arrow 2 cm wide. Device B has a useful output arrow 8 cm wide. Which statement is correct?
5. A student constructs a Sankey diagram for a natural gas power station (50% efficiency) with a scale of 1 cm = 200 J and an input of 1,000 J. They draw the input arrow 6 cm wide, the useful output 2.5 cm wide, and the waste arrow 3.5 cm wide. What is wrong with their diagram?
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.
7. The following two Sankey diagrams are drawn for two different light bulbs, both with 200 J of electrical energy input:
Bulb X: useful output = 10 J light, waste = 190 J thermal.
Bulb Y: useful output = 40 J light, waste = 160 J thermal.
Describe what each diagram would look like, calculate the efficiency of each bulb, and explain which bulb a school in Perth should choose to reduce energy costs. Use Sankey reasoning in your answer. 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.
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.
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].
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].
1. B — Arrow width is proportional to energy amount. This is the defining feature of a Sankey diagram.
2. C — Efficiency = (useful width ÷ input width) × 100 = (4 ÷ 10) × 100 = 40%. The scale cancels out because both widths use the same scale.
3. A — Useful = 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. D — Device 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. B — Input = 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.
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].
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.
Want to review any section before moving on?
Tick when you can read, construct, and compare Sankey diagrams to analyse energy efficiency.