Energy diagrams, thermal conductivity and insulation

Energy is often wasted by heating the surroundings. Diagrams show where the energy goes, and insulation slows down unwanted transfers.

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Energy transfer diagrams

A Sankey diagram shows energy transfers with arrows. The width of each arrow is proportional to the amount of energy.
The input arrow splits into useful energy (straight on) and wasted energy (bending away, usually to thermal stores of the surroundings).
The total out always equals the total in (conservation of energy).

Thermal conductivity and wall thickness

Thermal conductivity tells you how quickly energy is transferred through a material by heating.
Materials with high conductivity (metals) transfer energy quickly. Materials with low conductivity (air, wool, foam) are insulators.
A building loses energy more slowly if its walls are thicker and made of material with lower thermal conductivity.

Reducing unwanted transfers at home

Loft insulation (mineral wool traps air) reduces transfer through the roof.
Cavity wall insulation (foam in the gap between walls) reduces transfer through walls.
Double glazing (a gap between two panes) reduces transfer through windows.
Draught excluders reduce warm air escaping.
In machines, lubrication reduces friction, so less energy is wasted heating the moving parts.
Worked example

A lamp is supplied with 100 J. 25 J is transferred as light. Describe the Sankey diagram.

  1. Input arrow: 100 J.
  2. Useful arrow: 25 J, one quarter of the width.
  3. Wasted arrow: 100 − 25 = 75 J to thermal stores of the surroundings, three quarters of the width.

Answer: 100 J in; 25 J out as light (useful); 75 J wasted heating the surroundings.

Key idea

In a Sankey diagram arrow width shows the amount of energy, and useful plus wasted equals input. Low thermal conductivity and thicker walls slow energy transfer. Loft insulation, cavity wall insulation, double glazing and lubrication all reduce unwanted transfers.

Quick check

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Extra practice

2 more questions

Try each one, then tap to check.

  1. A heater is supplied with 800 J and transfers 560 J usefully. How much energy is wasted?

    Show the answer

    Answer: 240 J

    Wasted = 800 − 560 = 240 J

  2. A Sankey diagram shows 600 J in and 450 J of useful output. What is the efficiency as a percentage?

    Show the answer

    Answer: 75 %

    450 ÷ 600 × 100 = 75%

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Sources and references

Checked by the GCSE-ready editorial team, 17 October 2026. Last updated 2 October 2026. Spotted a mistake? Tell us and we will fix it.

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