LightMySky

Efficiency, Sankey diagrams, and work done

Calculate energy efficiency as the ratio of useful output energy to total input energy, construct and interpret Sankey diagrams, and calculate work done using work = force × distance

No account needed. Progress saves in this browser.

What a learner can do afterwards

  • Calculates efficiency as a percentage from given input and useful output energy values
  • Draws a Sankey diagram to represent energy transfers in a device, with arrow widths proportional to energy amounts
  • Uses W = Fd to calculate work done when a force moves through a distance
  • Identifies which energy transformations in a Sankey diagram are useful and which are wasted

The lesson

Not all the energy that goes into a machine ends up doing something useful. Some of it escapes as heat, sound, or light you did not want. Efficiency tells you how much of the input energy became useful output. You work it out as a percentage: efficiency = (useful output energy ÷ total input energy) × 100.

Try it together

An electric heater takes in 500 J of energy. Of that, 450 J turns into useful heat, and 50 J is wasted as sound. Efficiency = 450 ÷ 500 × 100 = 90%. The heater wastes 10% of its energy.

Input500Usefulheat450Wastedsound50
Most of the 500 J became useful heat. Only a small bar was wasted as sound.

A Sankey diagram shows this same idea with arrows instead of bars. One arrow goes in, standing for the total input energy. It splits into two or more arrows going out: one for useful energy, one for wasted energy. The width of each arrow stands for how much energy it carries, so a wide arrow means a lot of energy and a narrow arrow means only a little. Since energy cannot be created or destroyed, the widths of the arrows going out always add up to the width of the arrow going in.

Try it together

Work done measures how much a force achieves by moving something. Work done = force × distance, or W = F × d. If you push a shopping trolley with a force of 20 N and it moves 5 m, the work done is 20 × 5 = 100 J.

Efficiency compares useful output to total input as a percentage, a Sankey diagram shows that split with arrow width, and work done is force times distance.

Watch it

Where it sits

Where this leads

Jobs that lean on this skill. Follow one to see everything it is built on.

Then practise

8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.

Efficiency, Sankey diagrams, and work done · Science, ages 12 to 13 · LightMySky