The Leaky Bucket Problem
♻️ The Leaky Bucket Problem
Here is a humbling truth: every machine ever built wastes energy. Every single one. An old incandescent light bulb converts only about 5% of electrical energy into useful light — the other 95% becomes heat, which is why they burn your fingers. Modern LED bulbs reach around 40–50% efficiency. Even the human body is only about 25% efficient at converting food energy into movement. Engineers have spent centuries trying to reduce waste and get closer to 100% efficiency — but it remains physically impossible. The second law of thermodynamics guarantees that some energy will always be "wasted" as heat. Your job in physics is to calculate how much useful energy actually makes it through.
Figure 1: A Sankey diagram — arrow width is proportional to energy. 100 J in → 40 J useful (cyan) + 60 J wasted as heat (amber). Efficiency = 40%.
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🧠 Memory Aids
The leaky bucket analogy: Imagine carrying water from a tap to your garden in a bucket with holes. You fill it with 100 litres (input), but only 40 litres reach the plants (useful output) — that is 40% efficiency. The leaked water (wasted energy) cannot be recovered. Every device is a leaky bucket; your job is to calculate how full the garden gets.
Formula — "Useful over Useless total":
- Efficiency = Useful Output ÷ Total Input (remember: U.O.T.I.)
Sankey diagram tip: The useful arrow always points straight through (to the right). Wasted arrows bend downward. The thicker the downward arrows, the lower the efficiency — it is visual.
Now try it yourself
Quiz · Question 1 of 19
Which equation correctly defines efficiency?
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This topic in real past papers
Every real exam question we've found on efficiency, with a full worked answer.