Power: the rate of energy transfer

By the end of this lesson

By the end you can define power as work done per unit time (the rate of energy transfer), use $P = \dfrac{W}{t}$ , and give the unit as the watt (W), where $1\ \text{W} = 1\ \text{J s}^{-1}$ .

Same job, different speed

Two cranes lift identical loads from the ground to the same height. Each transfers the same energy — the same work is done.

But one takes $10\ \text{s}$ and the other takes $40\ \text{s}$ . The faster crane is more powerful, even though it did the same amount of work.

Power is not how much energy is transferred; it is how fast the transfer happens.

Definition

Power

Power is the work done per unit time, or equivalently the rate of transfer of energy:

$P = \dfrac{W}{t}$

$W$ is the work done (or energy transferred), in joules, and $t$ is the time taken, in seconds.

Unit: the watt (W), where $1\ \text{W} = 1\ \text{J s}^{-1}$ .

Watt, kilowatt and megawatt

A watt is small: a torch bulb is a few W, a kettle about $2\ \text{kW}$ , a car engine tens of kW, a power station hundreds of MW.

Unit	Symbol	In watts
watt	W	$1\ \text{W}$
kilowatt	kW	$10^3\ \text{W}$
megawatt	MW	$10^6\ \text{W}$

Energy and power often get mixed up in one sentence: a $2\ \text{kW}$ kettle is a statement about power, while the number of joules it transfers is a statement about energy.

Worked example: Worked example: a motor at work

A motor does $9.0\ \text{kJ}$ of work in $1.5$ minutes. Calculate its power output.

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Quick check

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