Some of these derived units are used often enough that special names and symbols are used for them. They are listed in the table above with their definitions in terms of base units of the SI. This list is not all that are available. The volt is often described as the unit of electromotive force as well as the unit of potential difference.
The SI unit of area is the square of the SI unit of length, and so it is the square metre (m2). Conversion factors between other metric units and the square metre are: 1 cm2 = 10-4 m2 (exactly); 1 are = 100 m2 (exactly); 1 hectare = 10000 m2 (exactly). Conversion factors between English units and the square metre are: 1 square foot = 0.09290304 m2 (exactly); 1 square yard = 0.83612736 m2 (exactly).
VolumeThe SI unit of volume is the cube of the SI unit of length, and so it is the cubic metre (m3). The cubic centimetre (cm3) and cubic decimetre (dm3) are convenient units of volume which are widely used in chemistry; 1000 cm3 = 1 dm3 and 1000 dm3 = 1 m3. The litre is an older, but common, name for the cubic decimetre. Both the symbol l and the symbol L have been used for the litre, but the capital L symbol is preferred and will be used. The millilitre (mL) is identical to the cubic centimetre (cm3).
ForceThe SI unit of force is the kilogram-metre per second squared which is called the newton (1 N = 1 kg-m/s2). The newton is obtained as a result of Newton's first law of motion, force equals mass times acceleration; one newton is that force which when applied to a mass of one kilogram imparts to it an acceleration of one metre/second2. Conversion factors between the other units of force and the newton are: 1 dyne = 1.0 x 10-5 N (exactly); 1 kilogram-force = 9.80665 N (exactly).
Both the pound-force and the kilogram-force are units which depend upon the force of terrestrial gravitation; the value of the kilogram-force is defined in terms of the standard terrestrial force of gravity. The relation between the actual force of gravity and mass is given by Newton's law of gravitation, F = gmm'/l2, where m and m' are the masses of the two attracting objects, l is the linear distance separating them, and g is the Newtonian constant of gravitation. The value of g is found to be 6.67259(85) x 10-11 m3 kg-1 s-2.
PressureThe SI unit of pressure is the kilogram per metre-second squared, which is called the pascal (1 Pa = 1 kg/m s2). Since pressure is force per unit area, one pascal (Pa) is one newton per square metre. An alternative way of thinking of the pascal is as one joule/m3 which is helpful in compression work. Conversion between other units of pressure and the pascal are:
1 mmHg (0oC) = 133.322... Pa. The millimeter of mercury, mm of Hg, is almost the same as the exactly defined torr; 1 torr = (101325/760) Pa (exactly)
1 bar = 100000 Pa (exactly)
1 standard atmosphere (atm) = 101325 Pa (exactly) = 760 Torr = 760 mmHg
EnergyThe SI unit of energy is the kilogram-metre2 per second squared which is called the joule (1 J = 1 kg-m2/s2). In the SI, work and energy have the same units since energy is the ability to do work. Work may be considered in either of two equivalent ways: as the product of a force and the distance over which that force is exerted, so that one joule equals one newton-metre, or as the product of a potential difference and the charge separated by that potential difference, so that one joule equals one volt-coulomb. Conversion factors between other units of energy and the joule are:
1 erg = 1.0 x 10-7 J (exactly)
1 foot-pound = 1.355818... J
1 calorie (cal) = 4.184 J (exactly)
1 litre-atmosphere = 101.325 J (exactly)
1 British Thermal Unit (BTU) = 1055.06 J (exactly)
1 kilowatt-hour (kWh) = 3.6 MJ (exactly)
The electron-volt is used as an energy unit in nuclear physics; 1 electron-volt (eV) = 1.6021773... x 10-19 J. One eV/particle corresponds to an energy of 96485.309... J/mol. The calorie and BTU given here are the modern thermochemical values. Other archaic calories and BTUs did exist and were of slightly different magnitude.
PowerThe SI unit of power is the kilogram-meter2 per second cubed, which is called the watt (1 W = 1 kg-m2/s3). Since power is the energy used per unit of time, it is derived as the energy/time quotient. A power of one watt is used when an energy of one joule is expended in one second, so one watt equals one joule/second or one volt-ampere. The only significant unit of power used prior to the SI in English-speaking countries was the mechanical horsepower, defined as equal to 550 foot-pounds per second and 1 mechanical horsepower (hp) = 745.700 W. Other horsepower units used were not exact equivalents. Some of these were: 1 horsepower (boiler) = 9.80950 kW; 1 horsepower (electric) = 746.0 W; 1 horsepower (water) = 746.043 W; 1 horsepower (metric) = 735.499 W. There are also several different (and flexibly defined) horsepowers used in automotive measurements.
Electrical ChargeThe SI unit of electrical charge is the ampere-second, which is called the coulomb. The coulomb is the amount of charge passed when a current of one ampere flows for one second. There are no other modern units of electrical charge, although the Faraday (amount of electrical charge possessed by one mole of electrons) is sometimes considered to be such a unit. The Faraday is actually the ratio of electrical charge/amount of substance and has the modern value and units of 96485.309... C/mol of elementary charges.
Electrical PotentialThe SI unit of electrical potential or electrical potential difference, sometimes also known as the unit of electromotive force, is the volt. The volt is the kilogram-metre2 per second-cubed ampere(1 V = 1 kg m2/s3A) which is the ratio of energy to electrical charge (1 V = 1 J/C). The volt may be viewed as the electrical force which is equivalent to a physical force of one newton moving a charge of one coulomb over a distance of one metre.
1 V = 1 N m/C = 1 N/(C/m))
There are no other modern units of potential difference. The SI volt is identical to the "absolute volt" used in some non-SI systems of measurement.
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