Energy Transfer Diagrams

Energy can be transferred through four pathways:

• mechanically, when a force moves an object through a distance;
• electrically, when moving charges transfer energy;
• by heating, because of a temperature difference;
• by radiation, such as light, infrared or sound waves.

Keeping stores and pathways distinct makes a diagram more precise. For example, as a toy car rolls to a stop, its kinetic energy store decreases. Friction transfers energy mechanically to the internal energy stores of the car, floor and surroundings, making them warmer.

Drawing a transfer diagram

Begin by deciding what process and system the diagram describes. Then:

1. identify the store that initially contains the energy;
2. identify every store that gains energy;
3. draw arrows in the direction of transfer;
4. label each store and, where useful, each transfer pathway;
5. include energy values in joules if they are given.

For a child sliding down a slide, the child's gravitational potential energy store decreases. Energy is transferred mechanically: some increases the child's kinetic energy store, while some increases the internal energy stores of the child, slide and surroundings because of friction.

A complete diagram must include unwanted transfers. A lamp, for instance, transfers energy usefully by light radiation, but it also transfers energy by heating to the surroundings.

Reading a Sankey diagram

A Sankey diagram is a quantitative energy transfer diagram. A single input arrow enters the process and divides into two or more output arrows. The straight continuation commonly represents the useful transfer, while branches represent other transfers.

The crucial feature is the width of each arrow. Width is proportional to the amount of energy transferred, so a 60 J arrow should be twice as wide as a 30 J arrow. Arrow length does not represent energy.

Electrical energy supplied: 100 J. Useful light radiation: 25 J. Heating the surroundings: 75 J. Wasted energy = 100 − 25 = 75 J. Efficiency = 25 ÷ 100 × 100% = 25%. Arrow shaft widths are proportional to energy.

To interpret the illustrated diagram, read the input first and then follow each branch. The 100 J input divides into 25 J transferred usefully by light radiation and 75 J transferred by heating. The output widths therefore represent the ratio $25:75$, or $1:3$.

The numerical check is

$E_{\text{input}}=E_{\text{useful}}+E_{\text{other outputs}}.$

Here, $100\text{ J}=25\text{ J}+75\text{ J}$. If the outputs did not total 100 J, the diagram would be incomplete or its values would be inconsistent.

Drawing a Sankey diagram to scale

Choose a convenient width scale, such as 1 mm for every 5 J. Apply that same scale to the input and every output. Draw the input arrow, split it into correctly sized branches, and label each arrow with the type and amount of energy transferred.

The output widths together must equal the input width. This makes the diagram both a picture of the transfers and a visual comparison of their relative sizes.