4.4 - Efficiency

Efficiency is the proportion transferred usefully

• A device is useful because it transfers energy to a useful store. But not all the input energy ends up there.
• Some energy is always wasted, usually transferred to the thermal energy stores of the device and its surroundings.
• Efficiency measures how much of the input energy is transferred usefully rather than wasted. The less energy wasted, the more efficient the device.

Energy is conserved

None of the input energy disappears - it's split between useful and wasted output:

Total energy input = useful energy output + wasted energy

The total energy output always equals the total energy input. A more efficient device transfers a larger share to the useful store and wastes less.

No device is 100% efficient

• Because some energy is always wasted, no real device can transfer all of its input energy usefully.
• This means efficiency can never reach or go above 1 (or 100%).
• The wasted energy is usually transferred to the thermal energy stores of the surroundings, where it's no longer useful.

Electric heaters are a special case

• Heaters are usually almost 100% efficient, because the energy they transfer electrically is meant to end up in a thermal energy store.
• The energy other devices waste as heat is the useful output of a heater.

Efficiency has no units

• Efficiency is a ratio of two energies (or two powers), so it has no units.
• It's written either as a decimal between 0 and 1, or as a percentage between 0% and 100%.

Wasted energy spreads out and can't be reused

• Wasted energy is transferred to less useful stores, normally by heating, or by light or sound.
• As it moves into the surroundings, it spreads out and becomes less concentrated. We say it dissipates.
• Example: a pan of water heated on a hob gains energy in its thermal store, but some energy is also dissipated to the surrounding air by heating.
• The energy hasn't been destroyed, but once it has spread out it can no longer be easily collected back in and put to use.

Worked example - Efficiency of a microwave oven

A microwave oven transfers 180,000 J of energy electrically from the mains. Of this, 110,000 J is transferred usefully to the thermal energy store of the food. Calculate the efficiency of the microwave oven.

Formula for efficiency (energy)

Where:

• Useful energy output is the energy that does the intended job, in joules (J)
• Total energy output is the total energy transferred by the device, in joules (J)

This gives efficiency as a decimal. To express it as a percentage, multiply by 100. Because energy is conserved, total energy output equals total energy input, so either can be used as the denominator.