Power
Energy and Thermal Physics

# Power

Glossary Definition for 16-19

## Description

Power is defined as the rate at which energy is transferred to or from a system. The transfer may involve heating, working or both.

Power is usually represented by the symbol P.

When the energy of a system changes by ΔE in time Δt,

P = ΔEΔt

## Discussion

Power ratings
The power rating of a domestic electrical device indicates the electrical power input when a device is connected across the potential difference for which it has been designed. If a device is connected across a higher (or lower) potential difference, the current in the device will be greater (or less) than that for which the device is designed, and the input power will be greater (or less) than the stated power rating. For example, a kettle manufactured for use in the UK might be rated at 1 kW. Provided it is connected to the UK mains, so that p.d. across the kettle is 230 V, then the kettle operates with a power of 1 kW (the current in the kettle is about 4.3 A). But if it is connected to the USA mains supply, which provides 120 V, then the current is only about 2.3 A and the kettle operates with a power of about 270 W. It will therefore take the kettle around four times as long to heat the same quantity of water in the US as in the UK.

Power and efficiency
The performance of a machine might be described in terms of the power input required to operate it, or in terms of its useful power output. A machine’s efficiency is defined as

efficiency = useful power outputtotal power input

and is often quoted as a percentage. The efficiency of a machine can never be greater than 100% and is often considerably lower.

The power ratings of domestic appliances generally refer to the electrical power input, rather than the useful power output.

For example, an electric drill typically has a power rating of 500 W, meaning that energy is transferred to the drill at a rate of 500 J s-1. The efficiency of an electric drill might be about 50%, in which case the useful power output is about 250 W.

watt, W

kg m2 s-3

## Other commonly used unit(s)

horsepower, hp ( 1 hp~746 W); J s-1

## Mathematical expressions

• If the energy of a system changed by ΔE in time Δt, then

P = ΔEΔt = W + QΔt

where energy Q or W, or both, may be transferred by heating or working, respectively.
• P = VI = I 2R = V 2R

applies to an electric circuit where P is the power dissipated in a component with resistance R, V is the potential difference (voltage) across the component and I is the current.

## Related entries

• Energy of a system
• Heat
• Internal energy
• Temperature
• Work

## In context

Power ratings are commonly used to describe the performance of industrial machinery and domestic appliances. Often, though not always, power ratings refer to electrical power input. For example, a torch bulb in normal use might have a current of 0.5 A when connected to a 3 V battery, so the electrical power input to the bulb is 1.5 W. An electric kettle typically has a power of about 1 kW.

Coal-fired and gas-fired power stations generally produce output powers of many MW. One of the largest in the UK is Drax in Yorkshire, which has an output power of about 3,900 MW, supplying, on average, around 7,400,000 homes. Nuclear power stations have similar output powers, for example the Heysham 2 nuclear power plant in Lancashire produces about 1,200 MW. Power stations using renewable sources, such as hydropower, solar or biomass, generally have lower outputs; for example the small hydro power station at Kielder Water in Northumberland produces about 12 MW.

###### Power
appears in the relation P=VI P=I^2R P=V^2/R ΔQ=PΔt