Efficiency & Sankey Diagrams

Explained

Efficiency and Sankey diagrams

No device transfers all the energy put into it usefully. Some always ends up somewhere unhelpful, usually heating the surroundings. Efficiency is the measure of how much escapes that fate: useful energy output divided by total energy input, multiplied by 100 to give a percentage.

Using the equation

Efficiency equals useful energy transferred divided by total energy supplied. Both quantities must be in the same units, and the answer has no units of its own because it is a ratio.

An efficiency above 100 per cent is always an error. Energy cannot be created, so the useful output cannot exceed the input. If a calculation gives more than 100 per cent, the two figures have been divided the wrong way round.

The same equation works with power in watts instead of energy in joules, since power is energy per second and the seconds cancel.

Reading a Sankey diagram

A Sankey diagram shows the same information as a picture. The width of each arrow is proportional to the amount of energy it represents. The total input enters from the left, the useful output continues to the right, and the wasted energy branches off, usually downwards.

Because the arrows are drawn to scale, the widths must add up. The useful arrow plus every waste arrow equals the input arrow. That is conservation of energy drawn to scale, and it gives you a way to find a missing value: subtract what you can see from the total.

A wide waste arrow means an inefficient device. A lamp that gives a thin light arrow and a thick heat arrow is telling you its efficiency is low before you calculate anything.

Where the wasted energy goes

Wasted energy is not destroyed. It is transferred to the surroundings, most often by heating, and it becomes spread out and difficult to use. Saying that energy is lost is acceptable shorthand in many mark schemes, but saying where it went is stronger and never wrong.

Reducing waste

Most improvements attack one of two routes. Lubrication reduces friction between moving surfaces, so less energy is transferred as heat. Insulation reduces the rate of transfer to the surroundings.

Loft and cavity wall insulation both work by trapping air. Air is a poor conductor, and trapping it stops convection currents forming, so it cannot carry energy away either. If asked why a material insulates well, say both parts: it conducts poorly, and the trapped air cannot circulate.