Power and efficiencyEdexcel A-Level Physics: Revision notes

Power is the rate at which energy is transferred, or the rate at which work is done:

P = E / t and P = W / t

The unit is the watt (W), which is one joule per second (J s⁻¹). A machine with a power of 500 W transfers 500 J of energy every second. Larger units are the kilowatt (kW, 10³ W) and megawatt (MW, 10⁶ W).

To find the energy transferred, rearrange to E = Pt. Convert time to seconds first.

Power calculations often use the energy equations from mechanics. When a load is raised at constant speed, the useful energy gained is mgΔh, so the useful power is the energy gained per second:

P = mgΔh / t

Worked example. A motor lifts 250 kg through 12 m in 30 s. Useful energy = 250 × 9.81 × 12 = 2.94 × 10⁴ J, so the useful power output = 2.94 × 10⁴ / 30 = 981 W.

For a cyclist riding up a slope, find the height gained each second, then multiply by mg.

No device transfers all of its input energy usefully. Some is wasted, usually as thermal energy. Efficiency compares the useful output with the total input:

efficiency = useful energy output / total energy input

efficiency = useful power output / total power input

Efficiency has no unit. It is a number between 0 and 1, or a percentage when multiplied by 100%. It can never exceed 100%, because that would mean creating energy.

Worked example. The hoist motor above takes 1.4 kW. Efficiency = 981 / 1400 = 0.70, or 70%.

By conservation of energy, total input energy = useful output energy + wasted energy. The wasted energy is therefore the input minus the useful output. For the hoist, in 30 s the input energy is 1400 × 30 = 4.2 × 10⁴ J, so the wasted energy is 4.2 × 10⁴ − 2.94 × 10⁴ = 1.3 × 10⁴ J.

If several devices work in a chain, such as a pump then a turbine, the overall efficiency is the product of the individual efficiencies. Two stages of 85% and 90% give 0.85 × 0.90 = 0.77.