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# What does a Sankey diagram show?

Year 9 Physics · Conservation of energy and efficiency

<!-- Speaker note: Students construct and interpret Sankey diagrams, read efficiency and the largest waste from them, and apply efficiency and conservation to compare real energy systems (AC9S9U05, nodes 3 and 4). About 26 minutes (Engage and Explore 9 min · Explain 10 min · Evaluate 3 min · Typical adds 3 min, Wider about 2 min). -->

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## Today

**We are learning to** a Sankey diagram shows energy flowing through a system as bands whose widths are proportional to the amounts. The input splits into the useful output (straight on) and the wasted outputs (bending away). You can read the efficiency off it and see at a glance where energy is wasted, which is how engineers compare real systems.

- I can build a Sankey diagram from energy data.
- I can read the efficiency and the biggest waste from a Sankey diagram.
- I can say what a Sankey diagram doesn't show.

<!-- Speaker note: Before class: A concept tutorial for introducing or revising the idea. Set the width with `?width=minimum`, `typical` (default) or `wider`. It closes Year 9 energy, after How much is useful? Neither is a hinge node. The common slips are reading band widths as unrelated numbers and judging efficiency by the size of the useful band rather than its share of the input. The prediction targets the second. Board notes: the board draws one split (input to outputs), not multi-stage chains. Power station figures are rounded and typical: coal about 35%, hydro about 90%, solar panels about 20%. Teacher: In your own words: the two sketches with a comparison. -->

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## Why it matters

> About two thirds of the energy in the coal burned at a power station never becomes electricity. You can see exactly where it goes in one picture.

<!-- Speaker note: You can calculate efficiency. This lesson draws it, and uses the drawings to compare real systems. -->

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<span style="background:#dbeafe; color:#1a1a1a; border:1.5px solid #3b82f6; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">💬 Discussion</span>

## Engage: predict

**In a Sankey diagram, the input band is 1000 J wide. The useful band is about a third as wide. Roughly what is the efficiency?**

- About 3%
- About 1000%
- About 33%
- You can't tell from widths

<!-- Speaker note: What happens: About 33%. Band widths are proportional to energy, so a band a third as wide as the input carries about a third of the energy: an efficiency of about a third. Take two or three predictions before anyone runs it. -->

<!-- Speaker note: Teacher: ask students who chose 'can't tell' what the widths are drawn to show. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Explore it

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fscience%2Fphysics-9%2Fsankey%2Fstep-2&code=widget%3A+energy%0Amode%3A+sankey%0Adevice%3A+Coal+power+station%0Ainput%3A+1000%2C+chemical%0Aoutput%3A+Electricity%2C+350%2C+useful%0Aoutput%3A+Cooling+water%2C+550%0Aoutput%3A+Chimney%2C+100%0Abuild%3A+on%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/science/physics-9/sankey/?full=step-2#step-2)

<!-- Speaker note:  -->

<!-- Speaker note: Teacher: ask which station's useful band is wider compared with its input. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## What happened?

* About 33%. Band widths are proportional to energy, so a band a third as wide as the input carries about a third of the energy: an efficiency of about a third.

<!-- Speaker note: Reveal after running. Ask who predicted it, and what made them think so. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## What widths mean

**What do the widths of the bands in a Sankey diagram show?**

- How important each output is
- The amount of energy in each flow, to scale
- How fast the energy moves

* Answer: The amount of energy in each flow, to scale

<!-- Speaker note: Band widths are proportional to energy, and the output bands always add up to the input band (conservation of energy). -->

<!-- Speaker note: Teacher: the biggest-waste question and the solar efficiency are the success criteria; 'what it hides' is the critique. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Biggest waste

**In the coal station's diagram, which output is the biggest waste?**

- Heat in the cooling water (550 J)
- Heat up the chimney (100 J)
- Electricity (350 J)

* Answer: Heat in the cooling water (550 J)

<!-- Speaker note: The widest wasted band shows where improvements would save the most: here, the heat carried away by cooling water. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Solar panel

**A solar panel's Sankey diagram shows 1000 J of light in and 200 J of electricity out. What is its efficiency (%)?**

* Answer: 20

<!-- Speaker note: 200 ÷ 1000 × 100% = 20%. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## What it hides

**What does a Sankey diagram NOT show?**

- How much the system costs, or the pollution it makes
- The efficiency
- Where energy is wasted

* Answer: How much the system costs, or the pollution it makes

<!-- Speaker note: It shows energy only. Comparing real systems also needs cost, emissions and whether the energy source runs out. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Make it better

**The coal station's biggest waste is the 550 J of heat carried off by the cooling water. Which change would make the most use of it?**

- Narrow the chimney so less heat escapes up it
- Burn more coal so more electricity comes out
- Pipe the warm cooling water to heat nearby homes or greenhouses

* Answer: Pipe the warm cooling water to heat nearby homes or greenhouses

<!-- Speaker note: Target the widest wasted band first. Combined heat and power stations pipe their warm water to nearby buildings, so much of that energy becomes useful. -->

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<span style="background:#fef3c7; color:#1a1a1a; border:1.5px solid #f59e0b; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✍️ Activity</span>

## Elaborate: a kettle

{{embed: https://studio.learningwaypoints.com/tutorials/_playground-board/index.html?id=deck%2Fscience%2Fphysics-9%2Fsankey%2Fstep-4&code=widget%3A+energy%0Amode%3A+sankey%0Adevice%3A+Electric+kettle%0Ainput%3A+2000%2C+electrical%0Aoutput%3A+Hot+water%2C+1800%2C+useful%0Aoutput%3A+Kettle+and+air%2C+180%0Aoutput%3A+Sound%2C+20%0Abuild%3A+on%0A&fresh=1}}

[Open this step in the tutorial](https://studio.learningwaypoints.com/tutorials/science/physics-9/sankey/?full=step-4#step-4)

<!-- Speaker note: What this step is for: A device whose useful output is heat checks that 'useful' depends on the job, not on the type of energy. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Useful depends on the job

**In a kettle, heat is the useful output. In a light bulb, heat is waste. Why?**

- Kettles make a different kind of heat
- 'Useful' means what the device is for: a kettle's job is heating water
- Light bulbs don't really make heat

* Answer: 'Useful' means what the device is for: a kettle's job is heating water

<!-- Speaker note: The same type of energy can be useful in one device and wasted in another. -->

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Elaborate: choosing an energy source

**A hydro station is about 90% efficient and a coal station about 35%. Why doesn't every country just build hydro stations?**

- Hydro stations make no electricity in winter
- Hydro needs the right rivers and valleys, and dams flood land; efficiency is only one factor
- Coal is more efficient really

* Answer: Hydro needs the right rivers and valleys, and dams flood land; efficiency is only one factor

<!-- Speaker note: Real choices weigh efficiency with cost, location, pollution and whether the source is renewable. What this step is for: Efficiency is one factor among several in real energy decisions; Sankey diagrams inform but don't decide. -->

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## Evaluate: look back

Write one sentence: "At first I thought… Now I think… because…"

**Revision summary**

- A **Sankey diagram** shows energy flows as bands whose widths are proportional to the amounts.
- The input band splits into the useful output (straight on) and wasted outputs (bending away); outputs always add up to the input.
- Read the efficiency as useful ÷ input, and find the biggest waste by the widest wasted band.
- Sankey diagrams show energy only, not cost or pollution.

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<span style="background:#dcfce7; color:#1a1a1a; border:1.5px solid #22c55e; padding:6px 18px; border-radius:8px; font-size:1em; font-weight:500;">✅ Check</span>

## Exit ticket

**A wind turbine takes in 500 J of kinetic energy and gives out 200 J of electricity. What is its efficiency, and how would its Sankey diagram show the rest?**

* 200 ÷ 500 × 100% = 40%. The other 300 J would bend away as wasted bands (heat and sound), together as wide as 300 J.

<!-- Speaker note: Students answer on paper or a mini whiteboard before the reveal. Anyone who cannot answer needs the main idea again next lesson. Where this leads: Next: Year 10 energy (climate and the energy balance) uses the same accounting. In class: draw Sankey diagrams on grid paper (1 square = 10 J) for three appliances from their labels or data sheets. -->