8.12–8.14Power
Power is defined as the rate at which energy is transferred, or the rate at which work is done.
power = energy transferred / time P = E / t power = work done / time P = W / t
power, P, in watts, W; energy transferred, E, in joules, J; time, t, in seconds, s; work done, W, in joules, J.
You should be able to recall and apply both equations. They are the same equation written twice, because energy transferred and work done are the same thing measured in the same unit.
An energy transfer of 1 joule per second is equal to a power of 1 watt.
You should be able to give examples that illustrate the definition of power — for instance, comparing two electric motors that both lift the same weight through the same height, but one does it faster than the other.
That example is the definition made concrete. Both motors transfer the same energy, because the weight and the height are the same. The faster motor does it in less time, so its power is greater. Power is not about how much energy, but how quickly.
Worked example
A motor lifts a load, transferring 9000 J of energy in 30 s. A second motor lifts the same load through the same height in 20 s. Calculate both powers.
- Both motors transfer the same energy, 9000 J, because the load and the height are the same.
- First motor: P = E ÷ t = 9000 ÷ 30 = 300 W.
- Second motor: P = 9000 ÷ 20 = 450 W.
- Compare: the second is more powerful because it transfers the same energy in less time.
Answer: 300 W and 450 W. The energy transferred is identical; only the rate differs.
Common mistake
Time must be in seconds. A power given in watts with a time in minutes is out by a factor of 60 — convert first.
- Power
- the rate at which energy is transferred, or the rate at which work is done, measured in watts
8.10–8.11, 8.15Where the energy goes, and how efficient the device is
No machine transfers all the energy supplied to it usefully. Some always ends up stored somewhere it cannot easily be got at again — usually the thermal store of the surroundings — and that is what dissipated means. The energy has not disappeared; it has spread out.
Mechanical processes are wasteful because of friction. Two surfaces sliding over each other do work against friction, the temperature of both rises, and that thermal energy is then transferred to the surroundings by heating. The same happens in a wire carrying a current, and in air resistance on a moving vehicle.
Efficiency measures how much of the supply comes out usefully:
efficiency = useful energy transferred by the device ÷ total energy supplied to the device
The same relationship works with power in place of energy, and a question will give you whichever pair it wants used. The answer is a number between 0 and 1, or a percentage if you multiply by 100, and it can never exceed 1 — an efficiency over 100% means an arithmetic slip, not a remarkable machine.
Worked example
A motor is supplied with 750 J of energy and does 300 J of useful work lifting a load. Calculate its efficiency, and state what happens to the rest of the energy.
- efficiency = useful ÷ total = 300 ÷ 750.
- 300 ÷ 750 = 0.40.
- As a percentage: 0.40 × 100 = 40%.
- The other 450 J is dissipated, mostly by friction warming the motor and then the surroundings.
Answer: 0.40, or 40%. The remaining 450 J is transferred to the thermal store of the motor and the surroundings.
Common mistake
Energy is never "lost" and never "used up". Say where it went — dissipated to the thermal store of the surroundings — because that is the phrasing the mark scheme is looking for.
Before you practise
- Power is the rate at which energy is transferred, or the rate at which work is done.
- power = energy transferred ÷ time, and power = work done ÷ time.
- One watt is one joule per second.
- A more powerful device transfers the same energy in less time — that is the comparison a question wants.
- efficiency = useful energy transferred ÷ total energy supplied, and the same with powers.
- Dissipated energy has spread to a less useful store, usually thermal; it has not been lost or used up.
- Reduce unwanted transfers by lubrication, streamlining and thermal insulation.