Conversion of units is the conversion of the unit of measurement in which a quantity is expressed, typically through a multiplicative conversion factor that changes the unit without changing the quantity. This is also often loosely taken to include replacement of a quantity with a corresponding quantity that describes the same physical property.
39-722: The Amaranth Wind Farm , also known as the Melancthon EcoPower Centre , is a 199.5 megawatt (MW) wind farm in Amaranth and Melancthon Township , near Shelburne, Ontario . The centre is owned and operated by TransAlta and at the time of opening, was Canada's largest wind energy installation. Construction of the Melancthon EcoPower Centre began with the 67.5 MW Phase I in 2005 and achieved commercial operation in March 2006. Construction of
78-432: A ⋅ m 3 m o l K × K 1 {\displaystyle \mathrm {Pa{\cdot }m^{3}} ={\frac {\cancel {\mathrm {mol} }}{1}}\times {\frac {\mathrm {Pa{\cdot }m^{3}} }{{\cancel {\mathrm {mol} }}\ {\cancel {\mathrm {K} }}}}\times {\frac {\cancel {\mathrm {K} }}{1}}} As can be seen, when the dimensional units appearing in
117-558: A light bulb with a power rating of 100 W 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
156-607: A metric system such as the SI than in others, due to the system's coherence and its metric prefixes that act as power-of-10 multipliers. The definition and choice of units in which to express a quantity may depend on the specific situation and the intended purpose. This may be governed by regulation, contract , technical specifications or other published standards . Engineering judgment may include such factors as: For some purposes, conversions from one system of units to another are needed to be exact, without increasing or decreasing
195-458: A 5 °C change is the same as a 9 °F change. Thus, to convert from units of Fahrenheit to units of Celsius, one subtracts 32 °F (the offset from the point of reference), divides by 9 °F and multiplies by 5 °C (scales by the ratio of units), and adds 0 °C (the offset from the point of reference). Reversing this yields the formula for obtaining a quantity in units of Celsius from units of Fahrenheit; one could have started with
234-411: A period of one year: 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, it is not correct to refer to a watt (or watt-hour) as a watt per hour. Unit conversion Unit conversion is often easier within
273-541: A turbine, which generates 648 MW e (i.e. electricity). Other SI prefixes are sometimes used, for example gigawatt electrical (GW e ). 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 (e.g., P th = 270 W rather than P = 270 W th ) and so these unit symbols are non-SI. In compliance with SI,
312-495: 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
351-457: Is chosen based on the relationship between one of the original units and one of the desired units (or some intermediary unit), before being rearranged to create a factor that cancels out the original unit. For example, as "mile" is the numerator in the original fraction and 1 m i = 1609.344 m {\displaystyle \mathrm {1~mi} =\mathrm {1609.344~m} } , "mile" will need to be
390-478: Is especially useful for programming and/or making a worksheet , where input quantities are taking multiple different values; For example, with the factor calculated above, it is very easy to see that the healing length of Yb with chemical potential 20.3 nK is There are many conversion tools. They are found in the function libraries of applications such as spreadsheets databases, in calculators, and in macro packages and plugins for many other applications such as
429-689: Is important to point out that such 'mathematical manipulation' is neither without prior precedent, nor without considerable scientific significance. Indeed, the Planck constant , a fundamental physical constant, was 'discovered' as a purely mathematical abstraction or representation that built on the Rayleigh–Jeans law for preventing the ultraviolet catastrophe . It was assigned and ascended to its quantum physical significance either in tandem or post mathematical dimensional adjustment – not earlier. The factor–label method can convert only unit quantities for which
SECTION 10
#1732802592206468-453: Is just mathematically the same thing, multiply Z by unity, the product is still Z : For example, you have an expression for a physical value Z involving the unit feet per second ( [ Z ] i {\displaystyle [Z]_{i}} ) and you want it in terms of the unit miles per hour ( [ Z ] j {\displaystyle [Z]_{j}} ): Or as an example using
507-733: Is named after the Scottish inventor James Watt . The unit name was proposed 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
546-423: Is neither a constant difference nor a constant ratio. There is, however, an affine transform ( x ↦ a x + b {\displaystyle x\mapsto ax+b} , rather than a linear transform x ↦ a x {\displaystyle x\mapsto ax} ) between them. For example, the freezing point of water is 0 °C and 32 °F, and
585-684: Is our factor. Now, make use of the fact that ξ ∝ 1 m μ {\displaystyle \xi \propto {\frac {1}{\sqrt {m\mu }}}} . With m = 23 Da , μ = 128 k B ⋅ nK {\displaystyle m=23\,{\text{Da}},\mu =128\,k_{\text{B}}\cdot {\text{nK}}} , ξ = 15.574 23 ⋅ 128 μm = 0.287 μm {\displaystyle \xi ={\frac {15.574}{\sqrt {23\cdot 128}}}\,{\text{μm}}=0.287\,{\text{μm}}} . This method
624-523: 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). 1 W = 1 V ⋅ A . {\displaystyle \mathrm {1~W=1~V{\cdot }A} .} Two additional unit conversions for watt can be found using
663-554: Is usually given in daltons , instead of kilograms , and chemical potential μ is often given in the Boltzmann constant times nanokelvin . The condensate's healing length is given by: ξ = ℏ 2 m μ . {\displaystyle \xi ={\frac {\hbar }{\sqrt {2m\mu }}}\,.} For a Na condensate with chemical potential of (the Boltzmann constant times) 128 nK,
702-825: The Newcomen engine with his own steam engine in 1776. Watt's invention was fundamental for the Industrial Revolution . 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 one watt. 1 W = 1 J / s = 1 N ⋅ m / s = 1 k g ⋅ m 2 ⋅ s − 3 . {\displaystyle \mathrm {1~W=1~J{/}s=1~N{\cdot }m{/}s=1~kg{\cdot }m^{2}{\cdot }s^{-3}} .} In terms of electromagnetism , one watt
741-549: The 132 MW Phase II of the project began in 2007 and achieved full commercial operation in November 2008. Megawatt 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⋅m ⋅s . It is used to quantify the rate of energy transfer . The watt is named in honor of James Watt (1736–1819), an 18th-century Scottish inventor , mechanical engineer , and chemist who improved
780-423: The above equation and Ohm's law . 1 W = 1 V 2 / Ω = 1 A 2 ⋅ Ω , {\displaystyle \mathrm {1~W=1~V^{2}/\Omega =1~A^{2}{\cdot }\Omega } ,} where ohm ( Ω {\displaystyle \Omega } ) is the SI derived unit of electrical resistance . The watt
819-532: The calculation of healing length (in micrometres) can be done in two steps: Assume that m = 1 Da , μ = k B ⋅ 1 nK {\displaystyle m=1\,{\text{Da}},\mu =k_{\text{B}}\cdot 1\,{\text{nK}}} , this gives ξ = ℏ 2 m μ = 15.574 μ m , {\displaystyle \xi ={\frac {\hbar }{\sqrt {2m\mu }}}=15.574\,\mathrm {\mu m} \,,} which
SECTION 20
#1732802592206858-414: The denominator in the conversion factor. Dividing both sides of the equation by 1 mile yields 1 m i 1 m i = 1609.344 m 1 m i {\displaystyle {\frac {\mathrm {1~mi} }{\mathrm {1~mi} }}={\frac {\mathrm {1609.344~m} }{\mathrm {1~mi} }}} , which when simplified results in
897-550: The desired unit [ Z ] j {\displaystyle [Z]_{j}} , e.g. if [ Z ] i = c i j × [ Z ] j {\displaystyle [Z]_{i}=c_{ij}\times [Z]_{j}} , then: Now n i {\displaystyle n_{i}} and c i j {\displaystyle c_{ij}} are both numerical values, so just calculate their product. Or, which
936-433: The dimensionless 1 = 1609.344 m 1 m i {\displaystyle 1={\frac {\mathrm {1609.344~m} }{\mathrm {1~mi} }}} . Because of the identity property of multiplication, multiplying any quantity (physical or not) by the dimensionless 1 does not change that quantity. Once this and the conversion factor for seconds per hour have been multiplied by
975-515: 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 . 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 stations usually report
1014-448: The equation. Having the same units on both sides of an equation does not ensure that the equation is correct, but having different units on the two sides (when expressed in terms of base units) of an equation implies that the equation is wrong. For example, check the universal gas law equation of PV = nRT , when: P a ⋅ m 3 = m o l 1 × P
1053-524: The equivalence between 100 °C and 212 °F, which yields the same formula. Hence, to convert the numerical quantity value of a temperature T [F] in degrees Fahrenheit to a numerical quantity value T [C] in degrees Celsius, this formula may be used: To convert T [C] in degrees Celsius to T [F] in degrees Fahrenheit, this formula may be used: Starting with: replace the original unit [ Z ] i {\displaystyle [Z]_{i}} with its meaning in terms of
1092-460: 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
1131-430: The metric system, you have a value of fuel economy in the unit litres per 100 kilometres and you want it in terms of the unit microlitres per metre : In the cases where non- SI units are used, the numerical calculation of a formula can be done by first working out the factor, and then plug in the numerical values of the given/known quantities. For example, in the study of Bose–Einstein condensate , atomic mass m
1170-858: The numerator and denominator of any of the fractions can be cancelled out until only the desired set of dimensional units is obtained. For example, 10 miles per hour can be converted to metres per second by using a sequence of conversion factors as shown below: 10 m i 1 h × 1609.344 m 1 m i × 1 h 3600 s = 4.4704 m s . {\displaystyle {\frac {\mathrm {10~{\cancel {mi}}} }{\mathrm {1~{\cancel {h}}} }}\times {\frac {\mathrm {1609.344~m} }{\mathrm {1~{\cancel {mi}}} }}\times {\frac {\mathrm {1~{\cancel {h}}} }{\mathrm {3600~s} }}=\mathrm {4.4704~{\frac {m}{s}}} .} Each conversion factor
1209-452: The numerator and denominator of the equation's right hand side are cancelled out, both sides of the equation have the same dimensional units. Dimensional analysis can be used as a tool to construct equations that relate non-associated physico-chemical properties. The equations may reveal undiscovered or overlooked properties of matter, in the form of left-over dimensions – dimensional adjusters – that can then be assigned physical significance. It
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1248-448: The numerators and the denominators of the fractions in the above equation, the NO x concentration of 10 ppm v converts to mass flow rate of 24.63 grams per hour. The factor–label method can also be used on any mathematical equation to check whether or not the dimensional units on the left hand side of the equation are the same as the dimensional units on the right hand side of
1287-449: The original fraction to cancel out the units mile and hour , 10 miles per hour converts to 4.4704 metres per second. As a more complex example, the concentration of nitrogen oxides ( NO x ) in the flue gas from an industrial furnace can be converted to a mass flow rate expressed in grams per hour (g/h) of NO x by using the following information as shown below: After cancelling any dimensional units that appear both in
1326-488: 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 . 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
1365-510: The precision of the expressed quantity. An adaptive conversion may not produce an exactly equivalent expression. Nominal values are sometimes allowed and used. The factor–label method , also known as the unit–factor method or the unity bracket method , is a widely used technique for unit conversions that uses the rules of algebra . The factor–label method is the sequential application of conversion factors expressed as fractions and arranged so that any dimensional unit appearing in both
1404-569: The unit of power. In the electric power industry , megawatt electrical ( MWe or MW e ) refers by convention to the electric power produced by a generator, while megawatt thermal or thermal megawatt (MWt, MW t , or MWth, MW th ) refers to thermal power produced by the plant. For example, the Embalse nuclear power plant in Argentina uses a fission reactor to generate 2,109 MW t (i.e. heat), which creates steam to drive
1443-570: The unit within the 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 A × 1 Ω.) The watt
1482-644: The units are in a linear relationship intersecting at 0 ( ratio scale in Stevens's typology). Most conversions fit this paradigm. An example for which it cannot be used is the conversion between the Celsius scale and the Kelvin scale (or the Fahrenheit scale ). Between degrees Celsius and kelvins, there is a constant difference rather than a constant ratio, while between degrees Celsius and degrees Fahrenheit there
1521-420: Was defined as equal to 10 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 defined as the quantity of energy transferred in
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