Efficiency

The efficiency of a device is a measure of how much of the input energy appears as useful output energy.

The more energy a device wastes, the less efficient it is.

curriculum-key-fact
Efficiency = \frac{\text{useful output energy}}{\text{total input energy}}

This is when:

  • useful output energy refers to the useful energy in J (Joules) that is transferred by the device;
  • input energy refers to the total energy in J supplied to a device.

Efficiency doesn't have a unit

Calculating efficiency

Filament lamp

This is the Sankey diagram for a typical filament lamp:

100 joules of electrical energy is converted to 10 joules of light energy and 90 joules of heat energySankey diagram for a filament lamp

Efficiency = \frac{\text{useful output energy}}{\text{total input energy}}

Useful output energy = 10 J

Total input energy = 100 J

efficiency = \frac{\text{10}}{\text{100}}

efficiency = 0.1

This means that 0.1 (or 10 %) of the electrical energy supplied is transferred as light energy.

The light bulb is not very efficient since most of the energy supplied is not transferred usefully.

Most of the energy will have been dissipated as heat energy.

This is because light bulbs become very hot when they are switched on.

Another way of thinking about this is that for every £100 spent on lighting, £10 is spent on the light and £90 is wasted heating the surroundings.

The efficiency of a device can never be greater than 1 otherwise energy would be created, and the Principle of Conservation of Energy violated.

Occasionally power is shown in W instead of energy in J. The equation for efficiency is similar – just substitute power for energy: efficiency = \frac {useful~output~power}{total~input~power}