Watt

Last updated
watt
Unit system SI
Unit of power
SymbolW
Named after James Watt
Conversions
1 W in ...... is equal to ...
    SI base units    1 kg m 2 s −3
    CGS units    107  ergs −1
    English Engineering Units    0.7375621 ft⋅lbf/s = 0.001341022 hp

The watt (symbol: W) is the unit of power or radiant flux in the International System of Units (SI), equal to 1 joule per second or 1 kg⋅m2⋅s−3. [1] [2] [3] It is used to quantify the rate of energy transfer. The watt is named after James Watt (1736–1819), an 18th-century Scottish inventor, mechanical engineer, and chemist who improved the Newcomen engine with his own steam engine in 1776. Watt's invention was fundamental for the Industrial Revolution.

Contents

Overview

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

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).

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

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

Examples

Origin and adoption as an SI unit

The watt is named after the Scottish inventor James Watt. [5] The unit name 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. [6] 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. [7] 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". [8]

In October 1908, at the International Conference on Electric Units and Standards in London, [9] so-called "international" definitions were established for practical electrical units. [10] Siemens' definition was adopted as the "international" watt. (Also used: 1 A2 × 1 Ω.) [5] The watt was defined as equal to 107 units of power in the "practical system" of units. [10] 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. [5] 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. [11]

Multiples

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
10−27 WrWrontowatt1027 WRWronnawatt
10−30 WqWquectowatt1030 WQWquettawatt
Common multiples are in bold face
Attowatt
The sound intensity in water corresponding to the international standard reference sound pressure of 1  μPa is approximately 0.65 aW/m2. [12]
Femtowatt
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 microvolts 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
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. [13]
Nanowatt
Important powers that are measured in nanowatts are also typically used in reference to radio and radar receivers.
Microwatt
Important powers that are measured in microwatts are typically stated in medical instrumentation systems such as the electroencephalograph (EEG) and the electrocardiograph (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. [14]
Milliwatt
A typical laser pointer outputs about five milliwatts of light power, whereas a typical hearing aid uses less than one milliwatt. [15] Audio signals and other electronic signal levels are often measured in dBm, referenced to one milliwatt.
Kilowatt
The kilowatt 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 kilowatt. The average electric power consumption of a household in the United States is about 1 kilowatt. [lower-roman 2]
A surface area of 1 square metre on Earth receives typically about one kilowatt of sunlight from the Sun (the solar irradiance) (on a clear day at midday, close to the equator). [17]
Megawatt
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 e300, for example, uses more than 12 MW, while heavy diesel-electric locomotives typically produce and use 3 and 5 MW. U.S. nuclear power plants have net summer capacities between about 500 and 1300 MW. [18] :84–101
The earliest citing of the megawatt in the Oxford English Dictionary (OED) is a reference in the 1900 Webster's International Dictionary of the English Language. The OED also states that megawatt appeared in a 28 November 1947 article in the journal Science (506:2).
A United States Department of Energy video explaining gigawatts
Gigawatt
A gigawatt is typical average power for an industrial city of one million habitants and also the output of a large power station. The GW unit is thus used for large power plants and power grids. For example, by the end of 2010, power shortages in China's Shanxi province were expected to increase to 5–6 GW [19] and the installation capacity of wind power in Germany was 25.8 GW. [20] The largest unit (out of four) of the Belgian Doel Nuclear Power Station has a peak output of 1.04 GW. [21] HVDC converters have been built with power ratings of up to 2 GW. [22]
Terawatt
The primary energy used by humans worldwide was about 160,000 terawatt-hours in 2019, corresponding to an average continuous power consumption of 18 TW that year. [23] The most powerful lasers from the mid-1960s to the mid-1990s produced power in terawatts, but only for nanosecond intervals. The average lightning strike peaks at 1 TW, but these strikes only last for 30 microseconds.
Petawatt
A petawatt can be produced by the current generation of lasers for time scales on the order of picoseconds. One such laser is the Lawrence Livermore's Nova laser, which achieved a power output of 1.25 PW by a process called chirped pulse amplification. The duration of the pulse was roughly 0.5  ps, giving a total energy of 600 J. [24] 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. [25] [26]
Based on the average total solar irradiance of 1.361 kW/m2, [27] the total power of sunlight striking Earth's atmosphere is estimated at 174 PW. The planet's average rate of global warming, measured as Earth's energy imbalance, reached about 0.5 PW (0.3% of incident solar power) by 2019. [28]
Yottawatt
The power output of the Sun is 382.8 YW. [29]

Conventions in the electric power industry

In the electric power industry, megawatt electrical (MWe [30] or MWe [31] ) refers by convention to the electric power produced by a generator, while megawatt thermal or thermal megawatt [32] (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. [33] In compliance with SI, the energy company Ørsted A/S uses the unit megawatt for produced electrical power and the equivalent unit megajoule per second for delivered heating power in a combined heat and power station such as Avedøre Power Station. [34]

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 closely related but distinct physical quantities. 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 in China, 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 W·h / (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 is 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". [35]

See also

Explanatory 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. [16]
  3. Watts per hour refers to the rate of change of power being used (or generated). For example, a power plant that changes its power output from 100 MW to 200 MW in 15 minutes would have a ramp-up rate of 400 MW/h. Gigawatts per hour are used to characterize the ramp-up required of the power plants on an electric grid to compensate for loss of output from other sources, such as when solar power generation drops to zero as the sun sets. See duck curve.

Related Research Articles

The joule is the unit of energy in the International System of Units (SI). It is equal to the amount of work done when a force of 1 newton displaces a mass through a distance of 1 metre in the direction of the force applied. 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).

<span class="mw-page-title-main">Kilowatt-hour</span> Unit of energy, often used for electrical billing

A kilowatt-hour is a unit of energy: one kilowatt of power for one hour. In terms of SI derived units with special names, it equals 3.6 megajoules (MJ). Kilowatt-hours are a common billing unit for electrical energy delivered to consumers by electric utilities.

<span class="mw-page-title-main">Power station</span> Facility generating electric power

A power station, also referred to as a power plant and sometimes generating station or generating plant, is an industrial facility for the generation of electric power. Power stations are generally connected to an electrical grid.

<span class="mw-page-title-main">Manitoba Hydro</span> Electric power and natural gas utility company in Manitoba, Canada

The Manitoba Hydro-Electric Board, operating as Manitoba Hydro, is the electric power and natural gas utility in the province of Manitoba, Canada. Founded in 1961, it is a provincial Crown Corporation, governed by the Manitoba Hydro-Electric Board and the Manitoba Hydro Act. Today the company operates 15 interconnected generating stations. It has more than 527,000 electric power customers and more than 263,000 natural gas customers. Since most of the electrical energy is provided by hydroelectric power, the utility has low electricity rates. Stations in Northern Manitoba are connected by a HVDC system, the Nelson River Bipole, to customers in the south. The internal staff are members of the Canadian Union of Public Employees Local 998 while the outside workers are members of the International Brotherhood of Electrical Workers Local 2034.

In the United States, the efficiency of air conditioners is often rated by the seasonal energy efficiency ratio (SEER) which is defined by the Air Conditioning, Heating, and Refrigeration Institute, a trade association, in its 2008 standard AHRI 210/240, Performance Rating of Unitary Air-Conditioning and Air-Source Heat Pump Equipment. A similar standard is the European seasonal energy efficiency ratio (ESEER).

<span class="mw-page-title-main">Electric power</span> Rate at which electrical energy is transferred by an electric circuit

Electric power is the rate at which electrical energy is transferred by an electric circuit. The SI unit of power is the watt, one joule per second. Standard prefixes apply to watts as with other SI units: thousands, millions and billions of watts are called kilowatts, megawatts and gigawatts respectively.

<span class="mw-page-title-main">Solar power by country</span>

Many countries and territories have installed significant solar power capacity into their electrical grids to supplement or provide an alternative to conventional energy sources. Solar power plants use one of two technologies:

<span class="mw-page-title-main">Energy conversion efficiency</span> 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. The resulting value, η (eta), ranges between 0 and 1.

<span class="mw-page-title-main">Solar power in Australia</span> Overview of solar power in Australia

Solar power in Australia is a fast growing industry. As of June 2022, Australia's over 3.19 million solar PV installations had a combined capacity of 27,167 MW photovoltaic (PV) solar power, of which at least 3,271 MW was installed in the preceding 12 months. In 2019, 59 solar PV projects with a combined capacity of 2,881 MW was either under construction, constructed or due to start construction having reached financial closure. Solar accounted for 9.9% of Australia's total electrical energy production in 2020.

<span class="mw-page-title-main">Andasol Solar Power Station</span> Concentrated solar thermal power station in Spain

The Andasol solar power station is a 150-megawatt (MW) concentrated solar power station and Europe's first commercial plant to use parabolic troughs. It is located near Guadix in Andalusia, Spain, and its name is a portmanteau of Andalusia and Sol. The Andasol plant uses tanks of molten salt as thermal energy storage to continue generating electricity, irrespective of whether the sun is shining or not.

<span class="mw-page-title-main">Grid-tie inverter</span>

A grid-tie inverter converts direct current (DC) into an alternating current (AC) suitable for injecting into an electrical power grid, normally 120 V RMS at 60 Hz or 240 V RMS at 50 Hz. Grid-tie inverters are used between local electrical power generators: solar panel, wind turbine, hydro-electric, and the grid.

The nominal power is the nameplate capacity of photovoltaic (PV) devices, such as solar cells, modules and systems, and is determined by measuring the electric current and voltage in a circuit, while varying the resistance under precisely defined conditions. The nominal power is important for designing an installation in order to correctly dimension its cabling and converters.

<span class="mw-page-title-main">Beryozovskaya GRES</span>

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).

<span class="mw-page-title-main">Growth of photovoltaics</span>

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.

<span class="mw-page-title-main">Wind power in Japan</span>

In Japan's electricity sector, wind power generates a small proportion of the country's electricity. It has been estimated that Japan has the potential for 144 gigawatts (GW) for onshore wind and 608 GW of offshore wind capacity. As of 2020, the country had a total installed capacity of 4.2 GW.

<span class="mw-page-title-main">Electricity sector in Switzerland</span> Overview of the electricity sector in Switzerland

The electricity sector in Switzerland relies mainly on hydroelectricity, since the Alps cover almost two-thirds of the country's land mass, providing many large mountain lakes and artificial reservoirs suited for hydro power. In addition, the water masses drained from the Swiss Alps are intensively used by run-of-the-river hydroelectricity (ROR). With 9,052 kWh per person in 2008, the country's electricity consumption is relatively high and was 22% above the European Union's average.

<span class="mw-page-title-main">Solar power in New Zealand</span> Overview of solar power in New Zealand

Solar power in New Zealand is on the rise, but there are no subsidies or intervention from the New Zealand Government. As at the end of December 2021, New Zealand has 186.7 MW of grid-connected photovoltaic (PV) solar power installed, of which 72.4 MW (8.8%) was installed in the preceding 24 months. In the year to December 2021, 203,000 megawatt-hours of electricity was generated by solar power, or 0.47% of all electricity generated in the country.

<span class="mw-page-title-main">Energy in California</span> Overview of the use of energy in California, U.S.

Energy in California is a major area of the economy of California. California is the state with the largest population and the largest economy in the United States. It is second in energy consumption after Texas. As of 2018, per capita consumption was the fourth-lowest in the United States partially because of the mild climate and energy efficiency programs.

Hydroelectricity is the second most important renewable energy source after solar energy in Japan with an installed capacity of 50.0 gigawatt (GW) as of 2019. According to the International Hydropower Association Japan was the world's sixth largest producer of hydroelectricity in 2020. Most of Japanese hydroelectric power plants are pumped-storage plants. Conventional hydropower plants account for about 20 GW out of the total installed capacity as of 2007.

Zagtouli Solar Power Station, is an operational 33 MW (44,000 hp) solar power plant in Burkina Faso. At the time of its commissioning, in November 2017, it was one of the largest grid-connected solar power stations in West Africa.

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