--- title: "Efficiency, Sankey diagrams, and work done" description: "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" canonical: https://lightmysky.com/learn/science/efficiency-sankey-diagrams-and-work-done-mt_JyfLtl_nhw source: https://lightmysky.com/learn/science/efficiency-sankey-diagrams-and-work-done-mt_JyfLtl_nhw.md retrieved: 2026-10-19 --- > **Agent view.** This is the Markdown twin of the page, for tools and assistants. > When to use this site, and the call that answers each job: https://lightmysky.com/agent-instructions.md > API description (OpenAPI 3.1): https://lightmysky.com/openapi.json · Authentication: https://lightmysky.com/auth.md > Pricing: https://lightmysky.com/pricing.md · Catalog: https://lightmysky.com/llms.txt · Full catalog: https://lightmysky.com/llms-full.txt > Every machine-readable file on this domain: https://lightmysky.com/.well-known/ai-catalog.json > Ask for Markdown with `Accept: text/markdown`, a `.md` address, or `?mode=agent`. # 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 Subject: Science · Area: Energy · Ages 12 to 13 Page: https://lightmysky.com/learn/science/efficiency-sankey-diagrams-and-work-done-mt_JyfLtl_nhw ## Ready when they can - 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 - Calculates work against gravity using weight = mg and work = mgh near Earth's surface. - Calculates useful output energy or work from a percentage efficiency and total input. ## Lesson: Efficiency, Sankey diagrams, and work done Efficiency compares useful output energy with total input: efficiency (%) = useful ÷ input × 100. For the same useful job, a more efficient machine needs less input energy. Some output may be unwanted heat, sound, or light. A lamp's light is useful; its heat is usually wasted. When all output is counted as useful or wasted, useful = input minus wasted. To find useful output from efficiency, multiply input by efficiency ÷ 100. **Example.** In a model heater, 500 J enters. It transfers 450 J as useful heat to water and 50 J as unwanted sound. Efficiency = 450 ÷ 500 × 100 = 90%. The remaining 10% is wasted in this model. *(drawing: Most of the 500 J became useful heat. Only a small bar was wasted as sound.)* A Sankey diagram uses arrow widths proportional to energy amounts. One input arrow splits into useful and wasted outputs. Twice the width means twice the energy. Outgoing widths add to the incoming width because energy is conserved. A large useful share means high efficiency. In a car engine, energy not transferred usefully can heat the engine and surroundings, or leave as sound. **Example.** Work transfers energy through a force. For a constant force along the motion, W = F × d: work in joules, force in newtons, distance in metres. A 20 N push along a trolley's 5 m motion does 100 J of work. To lift against gravity, use weight F = mg, so work = mgh. Here m is mass in kilograms, g is gravitational acceleration, and h is the height gained in metres. **Recap.** Efficiency compares useful output with input. Sankey widths show energy amounts. For a constant force along the motion, work = force × distance. ## Practice 14 questions on this page, each with its working shown. ## Needs first - [Energy can't be created or destroyed](https://lightmysky.com/learn/science/energy-cant-be-created-or-destroyed-mt_68pIoiiG4g) - [Resultant Forces](https://lightmysky.com/learn/science/resultant-forces-mt_AiWlJfvC3O) - [Calculating percentages](https://lightmysky.com/learn/mathematics/calculating-percentages-mt_PNSyfH56eQ) ## Opens up - [Heating experiments and Q = mcΔT](https://lightmysky.com/learn/science/heating-experiments-and-q-mc-t-mt_DI1cyAyGyN) - [Calculating work done and power](https://lightmysky.com/learn/science/calculating-work-done-and-power-mt_udulQxseg1)