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Keeping homes warm

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Efficiency and payback time

Efficiency

The efficiency of a device is the proportion of the energy supplied that is transferred in useful ways. You should be able to calculate the efficiency of a device as a decimal or as a percentage.

The efficiency of a device can be calculated:

• efficiency = useful energy out ÷ total energy in (for a decimal efficiency)
• efficiency = (useful energy out ÷ total energy in) × 100 (for a percentage efficiency)

Sankey diagram for a filament lamp

The efficiency of the filament lamp is 10 ÷ 100 = 0.10 (or 10 per cent)

This means that only 10 per cent of the electrical energy supplied is transferred as light energy (90 per cent is transferred as heat or 'wasted' energy).

Note that the efficiency of a device will always be less than 1.

Payback time

Home owners may install double glazing or extra insulation to reduce heat energy losses and so save money. However, these energy-saving solutions cost money to buy and install. The payback time of an energy-saving solution is a measure of how cost-effective it is. Here is the equation to calculate payback time:

payback time (years) = cost of installation (£) ÷ savings per year in fuel costs (£)

The payback time will be shortest if the cost of installation is low compared to the savings made each year.

Question

The double-glazing for a house costs £3,000 but saves £150 per year in fuel costs. What is its payback time?