2.5 - 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.
Step 1 - Identify the useful and total energy
- Useful energy output = 110,000 J
- Total energy input = 180,000 J
Step 2 - Substitute into the efficiency equation
Step 3 - Round, and convert to a percentage
Efficiency = 0.61 (to 2 s.f.)
As a percentage: 0.61 × 100 = 61%.
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.
Step 1 - Write the efficiency as a decimal
Efficiency = 65% = 0.65
Step 2 - Rearrange the power efficiency equation
Useful power output = efficiency × total power input
Step 3 - Substitute the values
Useful power output = 0.65 × 800 = 520 W
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