Watt

The watt ( ; symbol: W) is a derived unit of power in the International System of Units (SI), named after the Scottish engineer James Watt (1736–1819). The unit measures the rate of energy conversion. It is defined as one joule per second.

Definition

In terms of classical mechanics, one watt is the rate at which work is done when an object's velocity is held constant at one meter per second against constant opposing force of one newton.

:$\backslash mathrm\{W\; =\; \backslash frac\{J\}\{s\}\; =\; \backslash frac\{N\backslash cdot\; m\}\{s\}\; =\; \backslash frac\{kg\backslash cdot\; m^2\}\{s^3\}\}$

In terms of electromagnetism, one watt is the rate at which work is done when one ampere (A) of current flows through an electrical potential difference of one volt (V).

:$\backslash mathrm\{W\; =\; V\; \backslash cdot\; A\}$

:Two additional unit conversions for watt can be found using the above equation and Ohm's Law. :$\backslash mathrm\{W\; =\; \backslash frac\{V^2\}\{\backslash Omega\}\; =\; A^2\backslash cdot\backslash Omega\}$ :Where ohm ($\backslash Omega$) is the SI derived unit of electrical resistance.

Examples

A person having a mass of 100 kilograms who climbs a 3 meter high ladder in 5 seconds is doing work at a rate of about 600 watts. Mass times acceleration due to gravity times height divided by the time it takes to lift the object to the given height gives the rate of doing work or power. A laborer over the course of an 8-hour day can sustain an average output of about 75 watts; higher power levels can be achieved for short intervals and by athletes.

A medium-sized passenger automobile engine is rated at 50–100 kW (kilowatts) – while cruising it will typically yield half that amount. Larger or high performance vehicles have more powerful engines.

A typical household incandescent light bulb has a power rating of 25 to 100 watts; fluorescent lamps typically consume 5 to 30 watts to produce a similar amount of light.

A typical coal powered power station produces around 600-700 MW (megawatts).

Origin and adoption as an SI unit

The watt is named after James Watt for his contributions to the development of the steam engine. The unit was recognized by the Second Congress of the British Association for the Advancement of Science in 1882. The 11th General Conference on Weights and Measures in 1960 adopted it for the measurement of power into the International System of Units (SI).

Multiples

:For additional examples of magnitude for multiples and submultiples of the Watt, see Orders of magnitude (power) {|class=infobox |- | |}

Femtowatt

The femtowatt is equal to one quadrillionth (10⁻¹⁵) of a watt. Technologically important powers that are measured in femtowatts are typically found in reference(s) to radio and radar receivers. For example, FM tuner performance figures for sensitivity/quieting and signal-to-noise require that the RF energy applied to the antenna input be specified in order to be meaningful. These input levels are often stated in dBf (decibels referenced to 1 femtowatt which is equal to .2739 microvolt across a 75 ohm load or .5477 microvolt across a 300 ohm load) so that the specification takes into account the RF input impedance of the tuner.

Picowatt

The picowatt is equal to one trillionth (10⁻¹²) of a watt. Technologically important powers that are measured in picowatts are typically used in reference to radio and radar receivers, and also in the science of radio astronomy.

Nanowatt

The nanowatt is equal to one billionth (10⁻⁹) of a watt. A surface area of one square meter on Earth receives one nanowatt of power from a single star of apparent magnitude +3.5. Important powers that are measured in nanowatts are also typically used in reference to radio and radar receivers.

Microwatt

The microwatt is equal to one millionth (10⁻⁶) of a watt. Important powers that are measured in microwatts are typically stated in medical instrumentation systems such as the EEG and the EKG, in a wide variety of scientific and engineering instruments and also in reference to radio and radar receivers. Compact solar cells for devices such as calculators and watches are typically measured in microwatts.

Milliwatt

The milliwatt is equal to one thousandth (10⁻³) of a watt. A typical laser pointer outputs about five milliwatts of light power, whereas a typical hearing aid for people consumes less than one milliwatt.

Kilowatt

The kilowatt is equal to one thousand (10³) watts. This unit is typically used to express the output power of engines and the power consumption of electric motors, tools, machines, and heaters. It is also a common unit used to express the electromagnetic power output of broadcast radio and television transmitters.

One kilowatt of power is approximately equal to 1.34 horsepower. A small electric heater with one heating element can use 1.0 kilowatt. The average annual electrical energy consumption of a household in the United States is about 8,900 kilowatt-hours (cf the average UK household's approx 4,700 kilowatt-hours for example), equivalent to a steady power consumption of about 1 kW for an entire year. Also, kilowatts of light power can be measured in the output pulses of some lasers.

Megawatt

The megawatt is equal to one million (10⁶) watts. Many events or machines produce or sustain the conversion of energy on this scale. For example: lightning strikes, large electric motors, large warships, such as aircraft carriers, cruisers, and submarines, engineering hardware, large Server farms or data centers and some scientific research equipment, such as supercolliders, and in the output pulses of very large lasers. A large residential or commercial building may consume several megawatts in electric power and heat.

The productive capacity of electrical generators operated by a utility company is often measured in MW. On railways, modern high-powered electric locomotives typically have a peak power output of 5 or 6 MW although some produce much more—the Eurostar, for example, consumes more than 12 MW—while heavy diesel-electric locomotives typically consume 3 to 5 MW. U.S. nuclear power plants have net summer capacities between about 500 and 1300 MW.

The earliest citing of the megawatt in the Oxford English Dictionary (OED) is a reference in the 1900 Webster's International Dictionary of English Language. The OED also states that megawatt appeared in a 28 November 1947 article in the journal Science (506:2).

Gigawatt

The gigawatt is equal to one billion (10⁹) watts or 1 gigawatt = 1000 megawatts. This unit is sometimes used for large power plants or power grids. For example, by the end of 2010 power shortages in China's Shanxi province will increase to 5–6 GW. and the installed capacity of wind power in Germany was 25.8 GW. The largest unit (out of four) of the Belgian Nuclear Plant Doel has a peak output of 1.04 GW.

Though obscure, the "j" sound is still an accepted pronunciation.

Terawatt

The terawatt is equal to one trillion (10¹²) watts. The total power used by humans worldwide (about 16 TW in 2006) is commonly measured in this unit. The most powerful lasers from the mid-1960s to the mid-1990s produced power in terawatts, but only for nanosecond time frames. The average stroke of lightning peaks at 1 terawatt, but these strokes only last for 30 microseconds.

Petawatt

The petawatt is equal to one quadrillion (10¹⁵) watts and can be produced by the current generation of lasers for time-scales of the order of femtoseconds (10⁻¹⁵ s). Based on the average of 1.366 kW/m² of total solar irradiance the total energy flow of sunlight striking Earth's atmosphere is estimated at 174 PW (cf. Solar Constant).

Electrical and thermal watts

In the electric power industry, megawatt electrical (abbreviation: MW_e or MWe) is a term that refers to electric power, while megawatt thermal or thermal megawatt (abbreviations: MW_t, MW_th, MWt, or MWth) refers to thermal power produced. Other SI prefixes are sometimes used, for example gigawatt electrical (GW_e).

For example, the Embalse nuclear power plant in Argentina uses a fission reactor to generate 2109 MW_t of heat, which creates steam to drive a turbine, which generates 648 MW_e of electricity. The difference is due to the inefficiency of steam-turbine generators and the limitations of the theoretical Carnot Cycle.

Confusion of watts, watt-hours, and watts per hour

The terms power and energy are frequently confused. Power is the rate at which energy is generated and consumed.

For example, when a light bulb with a power rating of is turned on for one hour, the energy used is 100 watt-hours (W•h), 0.1 kilowatt-hour, or 360 kJ. This same amount of energy would light a 40-watt bulb for 2.5 hours, or a 50-watt bulb for 2 hours. A power station would be rated in multiples of watts, but its annual energy sales would be in multiples of watt-hours. A kilowatt-hour is the amount of energy equivalent to a steady power of 1 kilowatt running for 1 hour, or 3.6 MJ.

Terms such as watts per hour are often misused. Watts per hour properly refers to the change of power per hour. Watts per hour (W/h) might be useful to characterize the ramp-up behavior of power plants. For example, a power plant that reaches a power output of 1 MW from 0 MW in 15 minutes has a ramp-up rate of 4 MW/h. Hydroelectric power plants have a very high ramp-up rate, which makes them particularly useful in peak load and emergency situations.

Major energy production or consumption is often expressed as terawatt-hours for a given period that is often a calendar year or financial year. One terawatt-hour is equal to a sustained power of approximately 114 megawatts for a period of one year.

See also

Conversion of units

Declared net capacity (power plants)

Kilowatt-peak

Orders of magnitude (power)

Power factor

Root mean square (RMS)

Volt-ampere

Watt balance

Wattmeter

Notes

References

External links

Nelson, Robert A., "The International System of Units Its History and Use in Science and Industry". Via Satellite, February 2000.

Category:SI derived units Category:Units of power