2.1 - 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%.

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.

Energy bands and power ratings show running costs

Energy bands

• Many appliances carry an energy band label running from band A (most efficient) down to band G (least efficient).
• Band A appliances are very energy efficient, so running costs are low.
• Band G appliances are inefficient, so running costs are higher.

Power ratings and efficiency

• An appliance's power rating tells you the power it works at for a given voltage. Its efficiency tells you how much of that power is transferred usefully.
• If two appliances have the same power rating but different efficiencies, the more efficient one does the job faster, so it's switched on for less time and uses less energy overall.

Light bulbs compared

A more efficient bulb needs less power to give the same brightness, so it costs less to run. All three bulbs below give the same light output.

The LED costs the most to buy, but it uses the least power, costs the least each month, and lasts far longer, so it's cheapest overall.

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