7.9 - 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.

Formula for efficiency (energy)

Where:

• Useful energy output is the energy that does the intended job, in joules (J)
• Total energy input is the total energy supplied to 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 input equals total energy output, so either can be used as the denominator.

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 (power)

Where:

• Useful power output is the rate at which energy is transferred to the useful store, in watts (W)
• Total power input is the rate at which energy is supplied to the device, in watts (W)

As with the energy form, this gives a decimal, which can be multiplied by 100 to give a percentage.

Worked example - Useful power output of a drill

An electric drill is 65% efficient and has a total input power of 800 W. Calculate its useful output power.

Power ratings and the energy transferred

• Electrical appliances have a power rating - the power at which they work for a given voltage.
• This tells you how much energy the appliance transfers each second in use:
  • A 2,000 W kettle transfers 2,000 J from the mains every second.
  • A 60 W lamp transfers 60 J each second.
• The total energy an appliance transfers depends on both its power rating and how long it runs.

Power rating isn't the whole story

• No appliance is 100% efficient - only part of the input power ends up in the useful store.
• Two kettles with the same power rating draw the same power from the mains, but the more efficient one sends a larger share to the water's thermal store, so it boils the water sooner and uses less energy overall.

Energy band labels

• Many appliances carry an energy band label, graded from A (most efficient) down to G (least efficient).
• A more efficient appliance wastes less of the energy it transfers, which usually means lower running costs.

Improving the efficiency of a device

• Efficiency can be increased by reducing the energy that is wasted.
• Unwanted transfers are usually reduced by tackling friction and heating losses, for example by:
  • Lubricating moving parts
  • Making moving objects more streamlined
  • Insulating objects to slow energy loss by heating