Kilowatt-hour
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The kilowatt hour, which is also written kilowatt-hour,[1] (symbol kW·h, kW h or kWh) is a unit of energy.[2] It is most commonly used on household electricity meters, and is 1,000 watt hours.
It is not used in the International System of Units (SI), despite being based on the watt, as the hour is not an SI unit. The SI unit of energy is the joule (J), equal to one watt second. The kilowatt hour is, however, a commonly used unit, especially for measuring electric energy.
One watt hour is equivalent to 3,600 joules (1 J/s × 3600 s), the joule being the SI unit of energy. Thus a kilowatt hour is 3,600,000 joules or 3.6 megajoules, and a kilowatt refers to the specific rate at which the amount of joules is used in a second (also known as power). As such, a kilowatt equals the production or usage of 1,000 joules of energy per second (that is, a definitive rate), and a kilowatt hour is the specific amount of energy produced, transmitted, distributed, or consumed in a 3,600-second time period, which is 3,600,000 joules as mentioned above.
Definition
One watt hour is the amount of (usually electrical or natural gas) energy expended by a one-watt load (e.g., light bulb) drawing power for one hour.
Laymen and utilities tend to use watt hours to measure energy for reasons of convenience and intuition, rather than scientists, who use joules (J). For example, a light bulb draws power (units of watts) over a certain amount of time, resulting in a net amount of used energy; a watt has units of energy-per-time, and an hour is a convenient unit for measuring time, so when multiplied together they produce a unit of energy called the watt hour. The watt hour is derived from the multiplication of the SI unit of power (watt) and a non-SI unit of time (hour). In simple terms, it means the amount of power (watts) used for any given number of hours. A lightbulb that needs 50 J of energy per second to light up (50 watts) will consume 500 watt hours of energy if left on for 10 hours.
The kilowatt hour is commonly used for electrical and natural gas energy. Many electric utility companies use the kilowatt hour for billing. This is a convenient unit because the energy usage of a typical home in one month is several hundred kilowatt hours. In addition, the typical consumer can readily conceptualize the notion of "using a kilowatt for one hour”; common appliances that consume approximately 1 kW include hairdryers, microwave ovens, and vacuum cleaners. Megawatt hours are used for metering of larger amounts of electrical energy.
Pricing for kilowatt hours
Power companies sell energy in units of kilowatt hours. In general, energy (E) is equivalent to power (P) multiplied by time (t). To determine E in kilowatt hours, P must be expressed in kilowatts and t must be expressed in hours. Suppose a 1.5 kW electric heater runs for 3 h. Then P = 1.5 kW and t = 3 h, so the energy E in kilowatt hours is: E = Pt = 1.5 kW × 3 h = 4.5 kW·h. If P and t are not specified in kilowatts and hours respectively, then they must be converted to those units before determining E in kilowatt hours. Consider the use of one 100 W light bulb (0.1 kW) used for 10 hours per day. This will consume 1 kilowatt hour per day (0.1 kW × 10 h). If a power company charges $0.10/kW·h, then this light bulb will cost $0.10 a day and $0.70 a week to operate (0.1 kW × 10 h × $0.10/kW·h × 7 d/week.) (See Units of measurement#Expressing a physical value in terms of another unit for more information).
Other expressions of the watt hour
Another derived unit that is sometimes used for household purposes is the kW·h/yr., usually considered in annual energy consumption calculations, but with the dimensions of power, with 1 kW·h/yr. = 0.114 W. Note that this unit uses three units of time in one unit, namely second, hour and year, of which only the first is an SI unit.
The Board of Trade unit or B.O.T.U. is an obsolete UK synonym for kilowatt hour. The term derives from the name of the Board of Trade that regulated the electricity industry. The B.O.T.U. should not be confused with the British thermal unit or BTU, which is a much smaller quantity of thermal energy.
Burnup of nuclear fuel is normally quoted in megawatt days per ton (MWd/MTU), where ton refers to a metric ton of uranium metal or its equivalent, and megawatt refers to the entire thermal output, not the fraction which is recovered as electricity.
Multiples
| Submultiples | Multiples | ||||
|---|---|---|---|---|---|
| Value | SI symbol | Name | Value | SI symbol | Name |
| 10−1 W·h | dW·h | deciwatt hour | 101 W·h | daW·h | decawatt hour |
| 10−2 W·h | cW·h | centiwatt hour | 102 W·h | hW·h | hectowatt hour |
| 10−3 W·h | mW·h | milliwatt hour | 103 W·h | kW·h | kilowatt hour |
| 10−6 W·h | μW·h | microwatt hour | 106 W·h | MW·h | megawatt hour |
| 10−9 W·h | nW·h | nanowatt hour | 109 W·h | GW·h | gigawatt hour |
| 10−12 W·h | pW·h | picowatt hour | 1012 W·h | TW·h | terawatt hour |
| 10−15 W·h | fW·h | femtowatt hour | 1015 W·h | PW·h | petawatt hour |
| 10−18 W·h | aW·h | attowatt hour | 1018 W·h | EW·h | exawatt hour |
| 10−21 W·h | zW·h | zeptowatt hour | 1021 W·h | ZW·h | zettawatt hour |
| 10−24 W·h | yW·h | yoctowatt hour | 1024 W·h | YW·h | yottawatt hour |
| 10−27 W·h | rW·h | rontowatt hour | 1027 W·h | RW·h | ronnawatt hour |
| 10−30 W·h | qW·h | quectowatt hour | 1030 W·h | QW·h | quettawatt hour |
| Common multiples are in bold face | |||||
Symbol and abbreviation for kilowatt hour
The brochure for SI[3] and a voluntary standard[4] issued jointly by an international (IEEE) and national (ASTM) organization state that when compound unit symbols are formed by multiplication, the individual symbols should be separated by a half-high dot or a space (for example, "kW·h" or "kW h"). However, at least one major usage guide[5] and the IEEE/ASTM standard allow kWh (but do not mention other multiples of the watt hour). One guide published by NIST specifically recommends avoiding "kWh" "to avoid possible confusion".[6] Nonetheless, it is commonly used in commercial, educational, scientific and media publications.[7]
Conversions
| from / to | joule | watt hour | electronvolt | calorie |
|---|---|---|---|---|
| 1 J = 1 kg m2 s-2 = | 1 | 0.278 × 10−3 | 6.241 × 1018 | 0.239 |
| 1 W·h = | 3600 | 1 | 2.247 × 1022 | 859.8 |
| 1 eV = | 1.602 × 10−19 | 4.45 × 10−23 | 1 | 3.827 × 10−20 |
| 1 cal = | 4.1868 | 1.163 × 10−3 | 2.613 × 1019 | 1 |
See also
References
- ^ Taylor, Barry N. (1995). Guide for the Use of the International System of Units (SI) (Special publication 811). Gaithersburg, MD: National Institute of Standards and Technology. 31.
- ^ "Half-high dots or spaces are used to express a derived unit formed from two or more other units by multiplication." Barry N. Taylor. (2001 ed.) The International System of Units. (Special publication 330). Gaithersburg, MD: National Institute of Standards and Technology. 20.
- ^ The International System of Units (SI). (2006, 8th ed.) Paris: International Bureau of Weights and Measures. 130.
- ^ Standard for the Use of the International System of Units (SI): The Modern Metric System. (1997). (IEEE/ASTM SI 10-1997). New York and West Conshohoken, PA: Institute of Electrical and Electronics Engineers and ASTM. 15.
- ^ Chicago Manual of Style. (14th ed., 1993) University of Chicago Press. 482.
- ^ Taylor, Barry N. (1995). 13
- ^ See for example: Wind Energy Reference Manual Part 2: Energy and Power Definitions Danish Wind Energy Association. Retrieved 9 January 2008; "Kilowatt-Hour (kWh)" BusinessDictionary.com. Retrieved 9 January 2008; "US Nuclear Power Industry" www.world-nuclear.org. Retrieved 9 January 2008; "Energy. A Beginners Guide: Making Sense of Units" Renew On Line (UK). The Open University. Retrieved 9 January 2008.
External links
- Power and Energy in the Home - The Trustworthy Cyber Infrastructure for the Power Grid (TCIP) group at the University of Illinois at Urbana-Champaign has developed an applet which illustrates the consumption and cost of energy in the home, and allows the user to see the effects of manipulating the flow of electricity to various household appliances.