Watt

Last updated
Watt
Unit system SI derived unit
Unit of Power
SymbolW
Named after James Watt
Conversions
1 W in ...... is equal to ...
    SI base units     kg m 2 s −3
    CGS units    1×107 erg s −1

The watt (symbol: W) is a unit of power. In the International System of Units (SI) it is defined as a derived unit of 1 joule per second, [1] and is used to quantify the rate of energy transfer. In dimensional analysis, power is described by . [2]

In physics, power is the rate of doing work or of transferring heat, i.e. the amount of energy transferred or converted per unit time. Having no direction, it is a scalar quantity. In the International System of Units, the unit of power is the joule per second (J/s), known as the watt (W) in honour of James Watt, the eighteenth-century developer of the condenser steam engine. Another common and traditional measure is horsepower ; 1 horsepower equals about 745.7 watts. Being the rate of work, the equation for power can be written as:

International System of Units a system of units of measurement for base and derived physical quantities

The International System of Units is the modern form of the metric system and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the second, metre, kilogram, ampere, kelvin, mole, candela, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.

SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.

Contents

Examples

When an object's velocity is held constant at one meter per second against a constant opposing force of one newton, the rate at which work is done is 1 watt.

Velocity rate of change of the position of an object as a function of time, and the direction of that change

The velocity of an object is the rate of change of its position with respect to a frame of reference, and is a function of time. Velocity is equivalent to a specification of an object's speed and direction of motion. Velocity is a fundamental concept in kinematics, the branch of classical mechanics that describes the motion of bodies.

Newton (unit) SI unit of force

The newton is the International System of Units (SI) derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion.

Work (physics) process or amount (and direction) of energy transfer to an object via the application of forces on it through a displacement

Work is the product of force and displacement. In physics, a force is said to do work if, when acting, there is a movement of the point of application in the direction of the force.

In terms of electromagnetism, one watt is the rate at which electrical work is performed when a current of one ampere (A) flows across an electrical potential difference of one volt (V), meaning the watt is equivalent to the volt-ampere (the latter unit, however, is used for a different quantity from the real power of an electrical circuit).

Electromagnetism Branch of science concerned with the phenomena of electricity and magnetism

Electromagnetism is a branch of physics involving the study of the electromagnetic force, a type of physical interaction that occurs between electrically charged particles. The electromagnetic force is carried by electromagnetic fields composed of electric fields and magnetic fields, and it is responsible for electromagnetic radiation such as light. It is one of the four fundamental interactions in nature, together with the strong interaction, the weak interaction, and gravitation. At high energy the weak force and electromagnetic force are unified as a single electroweak force.

Ampere SI base unit of electric current

The ampere, often shortened to "amp", is the base unit of electric current in the International System of Units (SI). It is named after André-Marie Ampère (1775–1836), French mathematician and physicist, considered the father of electrodynamics.

Volt SI derived unit of voltage

The volt is the derived unit for electric potential, electric potential difference (voltage), and electromotive force. It is named after the Italian physicist Alessandro Volta (1745–1827).

Two additional unit conversions for watt can be found using the above equation and Ohm's Law.

Conversion of units is the conversion between different units of measurement for the same quantity, typically through multiplicative conversion factors.

Where ohm () is the SI derived unit of electrical resistance.

Ohm SI derived unit of electrical resistance

The ohm is the SI derived unit of electrical resistance, named after German physicist Georg Simon Ohm. Although several empirically derived standard units for expressing electrical resistance were developed in connection with early telegraphy practice, the British Association for the Advancement of Science proposed a unit derived from existing units of mass, length and time and of a convenient size for practical work as early as 1861. The definition of the ohm was revised several times. Today, the definition of the ohm is expressed from the quantum Hall effect.

Origin and adoption as an SI unit

The watt is named after the Scottish inventor James Watt. [4] This unit was proposed initially by C. William Siemens in August 1882 in his President's Address to the Fifty-Second Congress of the British Association for the Advancement of Science. [5] Noting that units in the practical system of units were named after leading physicists, Siemens proposed that Watt might be an appropriate name for a unit of power. [6] Siemens defined the unit consistently within the then-existing system of practical units as "the power conveyed by a current of an Ampère through the difference of potential of a Volt." [7]

In October 1908, at the International Conference on Electric Units and Standards in London, [8] so-called "international" definitions were established for practical electrical units. [9] Siemens' definition was adopted as the "international" watt. (Also used: 1 ampere2 x 1 ohm.) [4] The watt was defined as equal to 107 units of power in the "practical system" of units. [9] The "international units" were dominant from 1909 until 1948. After the 9th General Conference on Weights and Measures in 1948, the "international" watt was redefined from practical units to absolute units (i.e., using only length, mass, and time). Concretely, this meant that 1 watt was now defined as the quantity of energy transferred in a unit of time, namely 1 J/s. In this new definition, 1 "absolute" watt = 1.00019 "international" watts. Texts written before 1948 are likely to be using the "international" watt, which implies caution when comparing numerical values from this period with the post-1948 watt. [4] In 1960 the 11th General Conference on Weights and Measures adopted the "absolute" watt into the International System of Units (SI) as the unit of power. [10]

Multiples

For additional examples of magnitude for multiples and submultiples of the watt, see Orders of magnitude (power)
SI multiples of watt (W)
SubmultiplesMultiples
ValueSI symbolNameValueSI symbolName
10−1 WdWdeciwatt101 WdaWdecawatt
10−2 WcWcentiwatt102 WhWhectowatt
10−3 WmWmilliwatt103 WkWkilowatt
10−6 WµWmicrowatt106 WMWmegawatt
10−9 WnWnanowatt109 WGWgigawatt
10−12 WpWpicowatt1012 WTWterawatt
10−15 WfWfemtowatt1015 WPWpetawatt
10−18 WaWattowatt1018 WEWexawatt
10−21 WzWzeptowatt1021 WZWzettawatt
10−24 WyWyoctowatt1024 WYWyottawatt
Common multiples are in bold face

Attowatt

The attowatt (aW) is equal to 10−18 watt. The sound intensity in water corresponding to the international standard reference sound pressure of 1 μPa is approximately 0.65 aW/m2. [11]

Femtowatt

The femtowatt (fW) is equal to one quadrillionth (10−15) of a watt. Technologically important powers that are measured in femtowatts are typically found in references to radio and radar receivers. For example, meaningful FM tuner performance figures for sensitivity, quieting and signal-to-noise require that the RF energy applied to the antenna input be specified. These input levels are often stated in dBf (decibels referenced to 1 femtowatt). This is 0.2739 microvolt across a 75-ohm load or 0.5477 microvolt across a 300-ohm load; the specification takes into account the RF input impedance of the tuner.

Picowatt

The picowatt (pW), not to be confused with the much larger petawatt (PW), 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, acoustics and in the science of radio astronomy. One picowatt is the international standard reference value of sound power when this quantity is expressed as a level in decibels. [12]

Nanowatt

The nanowatt (nW) is equal to one billionth (10−9) of a watt. Important powers that are measured in nanowatts are also typically used in reference to radio and radar receivers.

Microwatt

The microwatt (µW) 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 ECG, 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. [13]

Milliwatt

The milliwatt (mW) 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 uses less than one milliwatt. [14] Audio signals and other electronic signal levels are often measured in dBm, referenced to one milliwatt.

Kilowatt

The kilowatt (kW) is equal to one thousand (103) watts. This unit is typically used to express the output power of engines and the power 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 is approximately equal to 1.34 horsepower. A small electric heater with one heating element can use 1.0 kilowatt. The average electric power consumption of a household in the United States is about one kilowatt. [lower-roman 2]

A surface area of one square meter on Earth receives typically about one kilowatt of sunlight from the sun (the solar irradiance) (on a clear day at mid day, close to the equator). [16]

Megawatt

The megawatt (MW) is equal to one million (106) watts. Many events or machines produce or sustain the conversion of energy on this scale, including large electric motors; large warships such as aircraft carriers, cruisers, and submarines; large server farms or data centers; and some scientific research equipment, such as supercolliders, and the output pulses of very large lasers. A large residential or commercial building may use several megawatts in electric power and heat. On railways, modern high-powered electric locomotives typically have a peak power output of 5 or 6 MW, while some produce much more. The Eurostar, for example, uses more than 12 MW, while heavy diesel-electric locomotives typically produce/use 3 to 5 MW. U.S. nuclear power plants have net summer capacities between about 500 and 1300 MW. [17]

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 (GW) is equal to one billion (109) watts or 1 gigawatt = 1000 megawatts. This unit is often used for large power plants or power grids. For example, by the end of 2010 power shortages in China's Shanxi province were expected to increase to 5–6 GW [18] and the installed capacity of wind power in Germany was 25.8 GW. [19] The largest unit (out of four) of the Belgian Doel Nuclear Power Station has a peak output of 1.04 GW. [20] HVDC converters have been built with power ratings of up to 2 GW. [21]

Terawatt

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

Petawatt

The petawatt (PW) is equal to one quadrillion (1015) watts and can be produced by the current generation of lasers for time scales on the order of picoseconds (1012 s). One such laser is the Lawrence Livermore's Nova laser, which achieved a power output of 1.25 PW (1.25×1015 W) by a process called chirped pulse amplification. The duration of the pulse was roughly 0.5  ps (5×10−13 s), giving a total energy of 600 J. [22] Another example is the Laser for Fast Ignition Experiments (LFEX) at the Institute of Laser Engineering (ILE), Osaka University, which achieved a power output of 2 PW for a duration of approximately 1  ps. [23] [24]

Based on the average total solar irradiance [25] of 1.366 kW/m2, the total power of sunlight striking Earth's atmosphere is estimated at 174 PW.

Conventions in the electric power industry

In the electric power industry, megawatt electrical (MWe [26] or MWe [27] ) refers by convention to the electric power produced by a generator, while megawatt thermal or thermal megawatt [28] (MWt, MWt, or MWth, MWth) refers to thermal power produced by the plant. For example, the Embalse nuclear power plant in Argentina uses a fission reactor to generate 2109 MWt (i.e. heat), which creates steam to drive a turbine, which generates 648 MWe (i.e. electricity). Other SI prefixes are sometimes used, for example gigawatt electrical (GWe). The International Bureau of Weights and Measures, which maintains the SI-standard, states that further information about a quantity should not be attached to the unit symbol but instead to the quantity symbol (i.e., Pthermal = 270 W rather than P = 270 Wth) and so these units are non-SI. [29] In compliance with SI the energy company DONG Energy uses the unit megawatt for produced electrical power and the equivalent unit megajoules for delivered heating power in a combined heat and power station such as Avedøre Power Station. [30]

When describing alternating current (AC) electricity, another distinction is made between the watt and the volt-ampere. While these units are equivalent for simple resistive circuits, they differ when loads exhibit electrical reactance.

Radio transmission

Radio stations usually report the power of their transmitters in units of watts, referring to the effective radiated power. This refers to the power that a half-wave dipole antenna would need to radiate to match the intensity of the transmitter's main lobe.

Distinction between watts and watt-hours

The terms power and energy are frequently confused. Power is the rate at which energy is generated or consumed and hence is measured in units (e.g. watts) that represent energy per unit time.

For example, when a light bulb with a power rating of 100W 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.

Power stations are rated using units of power, typically megawatts or gigawatts (for example, the Three Gorges Dam is rated at approximately 22 gigawatts). This reflects the maximum power output it can achieve at any point in time. A power station's annual energy output, however, would be recorded using units of energy (not power), typically gigawatt hours. Major energy production or consumption is often expressed as terawatt hours for a given period; often a calendar year or financial year. One terawatt hour of energy is equal to a sustained power delivery of one terawatt for one hour, or approximately 114 megawatts for a period of one year:

Power output = energy / time
1 terawatt hour per year = 1×1012 Wh / (365 days × 24 hours per day) ≈ 114 million watts,

equivalent to approximately 114 megawatts of constant power output.

The watt second is a unit of energy, equal to the joule. One kilowatt hour is 3,600,000 watt seconds.

While a watt per hour exists in principle (as a unit of rate of change of power with time [lower-roman 3] ), it is not correct to refer to a watt (or watt hour) as a "watt per hour". [31]

See also

Notes

  1. The energy in climbing the stairs is given by mgh. Setting m = 100 kg, g = 9.8 m/s2 and h = 3 m gives 2940 J. Dividing this by the time taken (5 s) gives a power of 588 W.
  2. Average household electric power consumption is 1.19 kW in the US, 0.53 kW in the UK. In India it is 0.13 kW (urban) and 0.03 kW (rural) – computed from GJ figures quoted by Nakagami, Murakoshi and Iwafune. [15]
  3. Watts per hour would properly refer to a rate of change of power being used (or generated). Watts per hour might be useful to characterize the ramp-up behavior of power plants, or slow-reacting plant where their power could only change slowly. For example, a power plant that changes its power output from 1 MW to 2 MW in 15 minutes would have a ramp-up rate of 4 MW/h.

Related Research Articles

The joule is a derived unit of energy in the International System of Units. It is equal to the energy transferred to an object when a force of one newton acts on that object in the direction of the force's motion through a distance of one metre. It is also the energy dissipated as heat when an electric current of one ampere passes through a resistance of one ohm for one second. It is named after the English physicist James Prescott Joule (1818–1889).

The coulomb is the International System of Units (SI) unit of electric charge. It is the charge transported by a constant current of one ampere in one second:

Kilowatt hour Unit of energy

The kilowatt hour is a unit of energy equal to 3.6 megajoules. If energy is transmitted or used at a constant rate (power) over a period of time, the total energy in kilowatt hours is equal to the power in kilowatts multiplied by the time in hours. The kilowatt hour is commonly used as a billing unit for energy delivered to consumers by electric utilities.

Power station facility generating electric power

A power station, also referred to as a power plant or powerhouse and sometimes generating station or generating plant, is an industrial facility for the generation of electric power. Most power stations contain one or more generators, a rotating machine that converts mechanical power into three-phase electric power. The relative motion between a magnetic field and a conductor creates an electric current. The energy source harnessed to turn the generator varies widely. Most power stations in the world burn fossil fuels such as coal, oil, and natural gas to generate electricity. Cleaner sources include nuclear power, biogas and an increasing use of renewables such as solar, wind, wave and hydroelectric.

The efficiency of an entity in electronics and electrical engineering is defined as useful power output divided by the total electrical power consumed, typically denoted by the Greek small letter eta.

In electrical engineering and mechanical engineering, the power rating of equipment is the highest power input allowed to flow through particular equipment. According to the particular discipline, the term "power" may refer to the electrical or mechanical power. A power rating can also involve average and maximum power, which may vary depending on the kind of equipment and its application.

Electricity meter

An electricity meter, electric meter, electrical meter, or energy meter is a device that measures the amount of electric energy consumed by a residence, a business, or an electrically powered device.

Volt-ampere unit used for the apparent power in an electrical circuit

A volt-ampere (VA) is the unit used for the apparent power in an electrical circuit. The apparent power equals the product of root-mean-square (RMS) voltage and RMS current. In direct current (DC) circuits, this product is equal to the real power (active power) in watts. Volt-amperes are useful only in the context of alternating current (AC) circuits (sinusoidal voltages and currents of the same frequency). The volt-ampere is dimensionally equivalent to the watt (in SI units, 1 VA = 1 N m A-1 s -1 A = 1 N m s -1 = 1 J s -1 = 1 W).

Electric power the rate per unit of time at which electrical energy is transferred by an electric circuit

Electric power is the rate, per unit time, at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second.

Energy conversion efficiency ratio between the useful output and the input of a machine

Energy conversion efficiency (η) is the ratio between the useful output of an energy conversion machine and the input, in energy terms. The input, as well as the useful output may be chemical, electric power, mechanical work, light (radiation), or heat.

Quad (unit) unit of energy

A quad is a unit of energy equal to 1015 (a short-scale quadrillion) BTU, or 1.055 × 1018 joules (1.055 exajoules or EJ) in SI units.

Winnipeg Hydro

Winnipeg Hydro is a former provider of electrical power for the city of Winnipeg, Manitoba, Canada. Winnipeg Hydro was established in 1906 as "City Hydro". It was purchased by Manitoba Hydro in 2002.

The nominal power is the nameplate capacity of photovoltaic (PV) devices, such as solar cells, panels and systems, and is determined by measuring the electric current and voltage in a circuit, while varying the resistance under precisely defined conditions. These Standard Test Conditions (STC) are specified in standards such as IEC 61215, IEC 61646 and UL 1703; specifically the light intensity is 1000 W/m2, with a spectrum similar to sunlight hitting the earth's surface at latitude 35°N in the summer (airmass 1.5), the temperature of the cells being 25 °C. The power is measured while varying the resistive load on the module between an open and closed circuit. The highest power thus measured is the 'nominal' power of the module in watts. This nominal power divided by the light power that falls on a given area of a photovoltaic device defines its efficiency, the ratio of the device's electrical output to the incident energy.

Gross generation or gross electric output is the total amount of electricity generated by a power plant over a specific period of time. It is measured at the generating terminal and is measured in kilowatt-hours (kW·h), megawatt-hours (MW·h), gigawatt-hours (GW·h) or for the largest power plants terawatt-hours (TW·h). It includes the electricity used in the plant auxiliaries and in the transformers.

Beryozovskaya GRES

Beryozovskaya GRES is a coal-fired power plant near the town of Sharypovo in Krasnoyarsk Krai, Russia. The power plant is owned by Unipro. The installed capacity of the plant is 1,600 megawatts (2,100,000 hp).

Growth of photovoltaics Worldwide growth of photovoltaics. History, current status and forecast.

Worldwide growth of photovoltaics has been close to exponential between 1992 and 2018. During this period of time, photovoltaics (PV), also known as solar PV, evolved from a niche market of small scale applications to a mainstream electricity source. When solar PV systems were first recognized as a promising renewable energy technology, subsidy programs, such as feed-in tariffs, were implemented by a number of governments in order to provide economic incentives for investments. For several years, growth was mainly driven by Japan and pioneering European countries. As a consequence, cost of solar declined significantly due to experience curve effects like improvements in technology and economies of scale. Several national programs were instrumental in increasing PV deployment, such as the Energiewende in Germany, the Million Solar Roofs project in the United States, and China's 2011 five-year-plan for energy production. Since then, deployment of photovoltaics has gained momentum on a worldwide scale, increasingly competing with conventional energy sources. In the early 21st Century a market for utility-scale plants emerged to complement rooftop and other distributed applications. By 2015, some 30 countries had reached grid parity.

The siemens is the derived unit of electric conductance, electric susceptance, and electric admittance in the International System of Units (SI). Conductance, susceptance, and admittance are the reciprocals of resistance, reactance, and impedance respectively; hence one siemens is redundantly equal to the reciprocal of one ohm, and is also referred to as the mho. The 14th General Conference on Weights and Measures approved the addition of the siemens as a derived unit in 1971.

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