4. Energy Flow Diagrams

Learning outcomes

I can construct energy flow diagrams that show how energy is transferred between stores within a system.
I can identify the energy stores and transfer pathways involved in a variety of physical situations.
I can distinguish between useful energy transfers and energy dissipated to the surroundings.
I can interpret and construct Sankey diagrams to represent energy transfers and transformations.
I can use energy flow diagrams and Sankey diagrams to demonstrate the conservation of energy in real-world systems.

Introduction

Energy is constantly transferred between stores.

A battery powers a torch, a falling object speeds up, a kettle heats water, and a car slows when its brakes are applied. In each case, energy moves from one store to another through one or more transfer pathways.

Energy flow diagrams help us represent these changes clearly. They show:

Where the energy starts.
How the energy is transferred.
Where the energy ends up.
Which transfers are useful.
Which transfers are dissipated to the surroundings.

A special type of energy flow diagram called a Sankey diagram also shows the relative amounts of energy involved.

Energy Stores and Transfer Pathways

Before constructing an energy flow diagram, it is important to distinguish between energy stores and transfer pathways.

Energy Stores

Energy stores describe where energy is held.

Common stores include:

Kinetic
Gravitational potential
Chemical
Elastic
Nuclear
Electrostatic
Internal

Transfer Pathways

Transfer pathways describe how energy moves between stores.

The four main pathways are:

Mechanical work
Electrical work
Heating
Waves

What is an Energy Flow Diagram?

An energy flow diagram is a simple representation of energy being transferred between stores.

A typical diagram includes:

\text{Initial store} \rightarrow \text{Transfer pathway} \rightarrow \text{Final store}

$Initial store \to Transfer pathway \to Final store$

Example: Falling Ball

\text{Gravitational potential store} \rightarrow \text{Mechanical transfer} \rightarrow \text{Kinetic store}

$Gravitational potential store \to Mechanical transfer \to Kinetic store$

As the ball falls:

Its gravitational potential energy decreases.
Its kinetic energy increases.

If air resistance is present, some energy is also transferred to the internal stores of the air and the ball.

Constructing an Energy Flow Diagram

Use the following steps.

Step 1: Identify the System

Decide which objects are included.

Example:

A torch and its battery.

Step 2: Identify the Initial Energy Store

Ask:

Where is the energy stored at the beginning?

For a torch:

Chemical store in the battery.

Step 3: Identify the Transfer Pathway

Ask:

How does the energy move?

For a torch:

Electrical transfer through the circuit.

Step 4: Identify the Final Stores

Ask:

Where does the energy end up?

For a torch:

Internal store of the lamp.
Internal store of the surroundings.
Energy transferred by light waves.

Step 5: Include Useful and Dissipated Transfers

Label which transfer is intended and which is less useful.

Example 1: Battery-Powered Torch

\text{Chemical store in battery} \rightarrow \text{Electrical transfer} \rightarrow \text{Light waves} + \text{Internal stores of lamp and surroundings}

$Chemical store in battery \to Electrical transfer \to Light waves + Internal stores of lamp and surroundings$

Useful transfer:

Light emitted by the torch.

Dissipated transfer:

Heating of the bulb, battery, and surroundings.

Example 2: Braking Bicycle

\text{Kinetic store of bicycle and rider} \rightarrow \text{Mechanical transfer by friction} \rightarrow \text{Internal stores of brakes, tyres, road, and air}

$Kinetic store of bicycle and rider \to Mechanical transfer by friction \to Internal stores of brakes, tyres, road, and air$

The bicycle's kinetic store decreases.

The energy is not destroyed. It is transferred mainly into internal energy stores.

Example 3: Electric Kettle

\text{Electrical transfer} \rightarrow \text{Internal store of heating element} \rightarrow \text{Heating} \rightarrow \text{Internal store of water}

$Electrical transfer \to Internal store of heating element \to Heating \to Internal store of water$

Useful transfer:

Heating the water.

Dissipated transfer:

Heating the kettle body and surrounding air.
Sound.

Useful and Dissipated Energy

A useful energy transfer is the transfer intended to achieve the device's purpose.

A dissipated energy transfer spreads energy into the surroundings, usually increasing internal energy stores.

Examples:

Device	Useful Transfer	Dissipated Transfer
Lamp	Light waves	Heating
Car	Increase in kinetic store	Heating and sound
Kettle	Increase in water's internal store	Heating surroundings
Speaker	Sound waves	Heating
Motor	Increase in kinetic store	Heating and sound

Dissipated energy is not lost. It is still present but is usually less useful because it has spread into the surroundings.

What is a Sankey Diagram?

A Sankey diagram is a special type of energy flow diagram in which the width of each arrow represents the amount of energy transferred.

The input arrow represents the total energy supplied.

The output arrows show how that energy is divided into:

Useful energy
Dissipated energy

The total width of the output arrows must equal the width of the input arrow.

This demonstrates conservation of energy.

Reading a Sankey Diagram

Suppose a lamp receives 100 J of electrical energy.

It transfers:

20 J as useful light.
80 J into internal energy stores.

A Sankey diagram would show:

One 100 J input arrow.
A smaller 20 J arrow continuing forward.
A larger 80 J arrow branching downward.

Because:

100\text{ J}=20\text{ J}+80\text{ J}

$100 J = 20 J + 80 J$

energy is conserved.

Constructing a Sankey Diagram

Follow these steps.

Step 1: Identify the Total Input Energy

Example:

200\text{ J}

200 J

Step 2: Identify Each Output

Example:

Useful kinetic energy = 140 J
Dissipated energy = 60 J

Step 3: Check Conservation

140+60=200\text{ J}

$140 + 60 = 200 J$

Step 4: Choose a Scale

For example:

1\text{ mm}=10\text{ J}

$1 mm = 10 J$

Then:

Input arrow width = 20 mm
Useful arrow width = 14 mm
Dissipated arrow width = 6 mm

Step 5: Draw and Label the Arrows

Ensure the widths are proportional.

Worked Example 1: Electric Motor

An electric motor receives 500 J of electrical energy.

It transfers:

350 J into kinetic energy.
100 J into internal energy stores.
50 J by sound waves.

Check:

350+100+50=500\text{ J}

$350 + 100 + 50 = 500 J$

Useful energy:

350\text{ J}

350 J

Dissipated energy:

100+50=150\text{ J}

$100 + 50 = 150 J$

The Sankey diagram must show a 500 J input divided into 350 J useful and 150 J dissipated.

Worked Example 2: Car Engine

A car engine receives 1,000 J of chemical energy.

Outputs:

250 J transferred into the car's kinetic store.
600 J transferred into internal energy stores.
150 J transferred by sound.

Check:

250+600+150=1,000\text{ J}

$250 + 600 + 150 = 1, 000 J$

Only one-quarter of the input becomes useful kinetic energy.

The remaining energy is dissipated.

Conservation of Energy

The principle of conservation of energy states:

Energy cannot be created or destroyed. It can only be transferred between stores.

Energy flow diagrams demonstrate this by accounting for all energy transfers.

Sankey diagrams show conservation visually because:

\text{Total input energy}=\text{Total output energy}

$Total input energy = Total output energy$

The combined widths of all output arrows must equal the width of the input arrow.

Interpreting Energy Flow Diagrams

When reading a diagram, ask:

What is the initial energy store?
Which transfer pathway is involved?
Which final stores gain energy?
Which transfer is useful?
Which transfers are dissipated?
Is all input energy accounted for?
Does the diagram obey conservation of energy?

Real-World Systems

Roller Coaster

At the top:

Large gravitational potential store.
Small kinetic store.

Moving downward:

\text{Gravitational potential} \rightarrow \text{Mechanical transfer} \rightarrow \text{Kinetic}

$Gravitational potential \to Mechanical transfer \to Kinetic$

Friction also transfers energy into internal stores.

Solar Panel and Battery

\text{Nuclear store of Sun} \rightarrow \text{Light waves} \rightarrow \text{Electrical transfer} \rightarrow \text{Chemical store in battery}

$Nuclear store of Sun \to Light waves \to Electrical transfer \to Chemical store in battery$

Some energy is dissipated through heating.

Hydroelectric Power Station

\text{Gravitational potential store of water} \rightarrow \text{Mechanical transfer} \rightarrow \text{Kinetic store of turbine} \rightarrow \text{Electrical transfer}

$Gravitational potential store of water \to Mechanical transfer \to Kinetic store of turbine \to Electrical transfer$

Some energy is dissipated through heating and sound.

Loudspeaker

\text{Electrical transfer} \rightarrow \text{Kinetic store of speaker cone} \rightarrow \text{Sound waves}

$Electrical transfer \to Kinetic store of speaker cone \to Sound waves$

Some energy also increases the internal energy stores of the speaker and air.

Energy Flow Diagrams vs Sankey Diagrams

Energy Flow Diagram	Sankey Diagram
Shows stores and pathways	Shows stores/pathways and energy quantities
Arrows show direction	Arrow widths show amounts
Useful for conceptual explanations	Useful for comparing efficiency and losses
Does not need a numerical scale	Requires proportional arrow widths

Both types can demonstrate conservation of energy.

Common Mistakes

Avoid these errors:

Treating heat, light, or electricity as energy stores.
Forgetting to include the initial energy store.
Leaving out dissipated energy.
Saying energy has been “used up” or “lost.”
Drawing Sankey arrows with widths that do not match the energy values.
Forgetting that all output energies must add to the input energy.
Labelling all output energy as useful.
Confusing a transfer pathway with a final energy store.

Key Vocabulary

Energy Flow Diagram – A diagram showing transfers between energy stores.
Sankey Diagram – A diagram in which arrow widths represent energy quantities.
Useful Energy Transfer – Energy transferred in the intended way.
Dissipated Energy – Energy spread into the surroundings, usually into internal stores.
Energy Store – A way in which energy is held.
Transfer Pathway – A process through which energy moves between stores.
Conservation of Energy – The principle that energy cannot be created or destroyed.
Input Energy – The total energy supplied to a system.
Output Energy – Energy transferred from the system into one or more stores or pathways.

Summary

Energy flow diagrams show how energy moves between stores through transfer pathways.
The initial store, transfer pathway, and final stores should all be identified.
Useful transfers achieve the intended purpose, while dissipated energy spreads into the surroundings.
Sankey diagrams use proportional arrow widths to represent energy quantities.
In every Sankey diagram, total input energy must equal total output energy.
Both energy flow diagrams and Sankey diagrams provide clear evidence of the conservation of energy.

Suggested Images

1. Energy Flow Diagram and Sankey Diagram Comparison ⭐

A side-by-side example of the same device, such as a lamp:

Standard flow diagram showing chemical store → electrical transfer → light and internal stores.
Sankey diagram showing 100 J input, 20 J useful light, and 80 J dissipated heating.

This clearly distinguishes the purpose of each type of diagram.

2. Parts of a Sankey Diagram

A labelled Sankey diagram identifying:

Input arrow
Useful output
Dissipated output
Direction of energy transfer
Arrow width proportional to energy
Conservation check

3. Constructing a Sankey Diagram

A step-by-step visual:

List input and outputs.
Check that totals match.
Choose a scale.
Calculate arrow widths.
Draw and label the diagram.

Use a simple 200 J example.

4. Useful vs Dissipated Energy

A four-panel infographic using:

Lamp
Kettle
Motor
Car

For each device, identify the useful and dissipated transfers.

5. Energy Conservation in Real Systems

A collage showing:

Roller coaster
Hydroelectric station
Solar panel and battery
Braking bicycle

Include simple flow arrows and numerical examples showing that total input equals total output.