A person having a mass of 100 kg 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.[i]
A labourer over the course of an eight-hour day can sustain an average output of about 75 watts; higher power levels can be achieved for short intervals and by athletes.
Origin and adoption as an SI unitedit
The watt is named after the Scottish inventor James Watt. 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. 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. 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".
In October 1908, at the International Conference on Electric Units and Standards in London, so-called "international" definitions were established for practical electrical units. Siemens' definition was adopted as the "international" watt. (Also used: 1 A2 × 1 Ω.) The watt was defined as equal to 107 units of power in the "practical system" of units. 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. 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.
SI multiples of watt (W)
Common multiples are in bold face
The sound intensity in water corresponding to the international standard reference sound pressure of 1 μPa is approximately 0.65 aW/m2.
Powers 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.
Powers 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 in decibels.
Powers measured in nanowatts are also typically used in reference to radio and radar receivers.
A typical laser pointer outputs about five milliwatts of light power, whereas a typical hearing aid uses less than one milliwatt.Audio signals and other electronic signal levels are often measured in dBm, referenced to one milliwatt.
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.[ii] A surface area of 1 square meter 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).
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 and the installation capacity of wind power in Germany was 25.8 GW. The largest unit (out of four) of the Belgian Doel Nuclear Power Station has a peak output of 1.04 GW.HVDC converters have been built with power ratings of up to 2 GW.
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. 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.
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. 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. Based on the average total solar irradiance of 1.361 kW/m2, 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.
The power output of the Sun is 382.8 YW, about 2 billion times the power estimated to reach Earth's atmosphere.
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,[iii] it is not correct to refer to a watt (or watt-hour) as a "watt per hour".
^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.
^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.
^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.
^Newell, David B; Tiesinga, Eite (2019). The international system of units (SI) (PDF) (Report). Gaithersburg, MD: National Institute of Standards and Technology. doi:10.6028/nist.sp.330-2019. §2.3.4, Table 4.
^Yildiz, I.; Liu, Y. (2018). "Energy units, conversions, and dimensional analysis". In Dincer, I. (ed.). Comprehensive energy systems. Vol 1: Energy fundamentals. Elsevier. pp. 12–13. ISBN 9780128149256.
^"Bye-Bye Batteries: Radio Waves as a Low-Power Source", The New York Times, Jul 18, 2010, archived from the original on 2017-03-21.
^Stetzler, Trudy; Magotra, Neeraj; Gelabert, Pedro; Kasthuri, Preethi; Bangalore, Sridevi. "Low-Power Real-Time Programmable DSP Development Platform for Digital Hearing Aids". Datasheet Archive. Archived from the original on 3 March 2011. Retrieved 8 February 2010.
^Nakagami, Hidetoshi; Murakoshi, Chiharu; Iwafune, Yumiko (2008). International Comparison of Household Energy Consumption and Its Indicator(PDF). ACEEE Summer Study on Energy Efficiency in Buildings. Pacific Grove, California: American Council for an Energy-Efficient Economy. Figure 3. Energy Consumption per Household by Fuel Type. 8:214–8:224. Archived (PDF) from the original on 9 January 2015. Retrieved 14 February 2013.
^Elena Papadopoulou, Photovoltaic Industrial Systems: An Environmental Approach, Springer 2011 ISBN 3642163017, p.153
^"Appendix A | U.S. Commercial Nuclear Power Reactors" (PDF). 2007–2008 Information Digest (Report). Vol. 19. United States Nuclear Regulatory Commission. 1 August 2007. pp. 84–101. Archived from the original (PDF) on 16 February 2008. Retrieved 27 December 2021.
^Bai, Jim; Chen, Aizhu (11 November 2010). Lewis, Chris (ed.). "China's Shanxi to face 5–6 GW power shortage by yr-end – paper". Peking: Reuters.
^"Not on my beach, please". The Economist. 19 August 2010. Archived from the original on 24 August 2010.
^"Chiffres clés" [Key numbers]. Electrabel. Who are we: Nuclear (in French). 2011. Archived from the original on 2011-07-10.
^Davidson, CC; Preedy, RM; Cao, J; Zhou, C; Fu, J (October 2010), "Ultra-High-Power Thyristor Valves for HVDC in Developing Countries", 9th International Conference on AC/DC Power Transmission, London: IET.
^Hannah Ritchie; Max Roser (2020). "Global Direct Primary Energy Consumption". Our World in Data. Published online at OurWorldInData.org. Retrieved 2020-02-09.
^"Crossing the Petawatt threshold". Livermore, CA: Lawrence Livermore National Laboratory. Archived from the original on 15 September 2012. Retrieved 19 June 2012.
^World's most powerful laser: 2 000 trillion watts. What's it?, IFL Science, 12 August 2015, archived from the original on 2015-08-22.
^Eureka alert (publicity release), Aug 2015, archived from the original on 2015-08-08.
^"Construction of a Composite Total Solar Irradiance (TSI) Time Series from 1978 to present". CH: PMODWRC. Archived from the original on 2011-08-30. Retrieved 2005-10-05.
^Loeb, Norman G.; Johnson, Gregory C.; Thorsen, Tyler J.; Lyman, John M.; et al. (15 June 2021). "Satellite and Ocean Data Reveal Marked Increase in Earth's Heating Rate". Geophysical Research Letters. 48 (13). Bibcode:2021GeoRL..4893047L. doi:10.1029/2021GL093047.
^Williams, Dr. David R. "Sun Fact Sheet". nasa.gov. NASA. Retrieved 26 February 2022.