Appendix
International system of units (SI)
Updated: 2008-07-16
Please send comments to: J.Elfick@uq.edu.au
Table of contents
7.0 International system of units (SI), the 7 base units
7.1 SI derived units
7.2 Other derived units based on SI
7.3 Units used with SI units
7.4 SI prefixes
7.5 Surface / volume ratio
7.6 Temperature, the Fahrenheit scale and the Celsius scale
7.7 Kelvin scale
7.8 Triple point
7.9 Amount of substance, the mole
7.10 Current, ampere
7.11 Time, second
7.12 Length, metre
7.13 Mass, kilogram
7.14 Luminous intensity, candela (candlepower)
7.0 International system of units (SI), the seven base units
SI UNITS = SYSTEME INTERNATIONAL D'UNITES (French)
The units of measurement that form the basis of any system of measurement are the defined mechanical units of mass, length and time.
Quantity Dimension Name of SI unit Symbol
(1) Length
 L metre m
(2) Mass M kilogram kg
(3) Time T second s
(4) Electric current I ampere A
(5) Temperature (absolute zero = -273.15 o) - kelvin (not "degree Kelvin") K
(6) Amount of substance - mole mol
(7) Luminous intensity J candela cd
7.1 SI derived units
These units are physical quantities formed from the base units. Some of these units are as follows:
Quantity Dimension Name of unit Symbol Equivalent
1. Velocity (speed) L T-1 - m s-1 -
2. Acceleration L T-2 - m s-2 -
3. Momentum M L T-1 - kg m s-1 -
4. Force M L T-2 newton N kg m s-2 = J m-1
5. Pressure (stress) M L-1T-2 pascal Pa N m-2
6. Energy (work) M L2T-2 joule J N m
6. Power M L2 T-3 watt W J s-1
8. Electric charge - coulomb C A s
9. Electric potential difference - volt V W A-1
10. Electric capacitance - farad F C V-1
11. Electric resistance - ohm omega V A-1
12. Frequency T-1 hertz Hz s-1
13. Radioactivity T-1 becquerel Bq s-1
14. Viscosity M L-1T-1 - N s m-2 kg m-1 s-1
15. Density M L-3 - kg m-3 -
16. Plane angle - radian rad = 180o / pi
7.2 Other derived units based on SI
Physical quantity Name of unit Symbol
Surface tension newton per metre N m-1
Electric field strength volt per metre V m-1
Magnetic field strength ampere per metre A m-1
Specific heat capacity joule per kilogram kelvin J kg-1 K-1
Concentration mole per cubic metre mol m-3
7.3 Units used with SI units
Physical quantity Name of unit Symbol Definition of unit
Area hectare ha 104 m2
Mass tonne t 103 kg = Mg
Pressure bar bar 105 N m-2
Volume litre L 10-3 m3 = dm3
A "litre", L, is now the name of a cubic decimetre, dm3, but when a litre was defined as equal to the volume of 1 kilogram of pure water at 4oC, then 1 litre was equal to 1.000028 dm3.
7.4 SI prefixes
Decimal fractions and multiples
Symbol - Prefix -Factor X
P peta, X 1000,000,000,000,000,
e.g. 1 petajoule (1 PJ)		 1015
T tera, X 1000,000,000,000 1012
G giga, X 1000,000,000 109
M mega, X 1000,000 106
k kilo, X 1000 103
h hecto, X 100 102
da deca, X 10 10
d deci, X 0.1 10-1
c cent, X 0.01 10-2
m milli, X 0.001 10-3
mu micro, X 0.000001 10-6
n nano, X 0.000000001 10-9
p pico, X 0.000000000001 10-12
7.5 Surface / volume ratio
A larger cube has more surface area and more volume than a smaller cube but less surface area for each unit of volume. Smaller objects have a greater surface / volume ratio than larger objects with the same shape. This ratio also applies to the surface to volume ratio of small and large cells in animals and plants.
Length L
 1
 2
 3
 4
 5
Area L2
 1
 4
 8
 16
 25
Volume L3
 1
 8
 27
 64
 125
Total surface area 6L2 6
 24
 54
 96
 150
Surface to volume ratio
 6
 3
 2
 1.5
 1.2
7.6 Temperature, the Fahrenheit scale and the Celsius scale
See diagram 7.6: Celsius temperature scale
The temperature of a body is its hotness or coldness with reference to a standard of comparison. Temperature varies with the amount of heat energy in the body.
The Fahrenheit temperature scale (Gabriel Fahrenheit 1686 - 1736) has graduations on the thermometer based on a lower fixed point of 32oF, the freezing point of water, and an upper fixed point of 212oF, the boiling point of water. So the fundamental interval is 180 Fahrenheit degrees. The Fahrenheit scale is still used in USA.
The Celsius temperature scale (Anders Celsius 1701 -1744) has graduations on the thermometer based on a lower fixed point of 0oC, the freezing point of water, and an upper fixed point of 100oC, the boiling point of water. So the fundamental interval is 100 Celsius degrees. The Celsius scale was formerly called the centigrade scale, "100 steps" scale, Some people still incorrectly quote temperatures in "degrees centigrade". C = "Celsius" NOT "Centigrade". To convert the Fahrenheit scale to the Celsius scale (F-32) / 9 = C/5. The Celsius and Fahrenheit scales have the same value at -40oC or -40oF. Human body temperature = 37oC (Celsius).
Equivalent temperatures in different scales
-KelvinCelsiusFahrenheit
Absolute zero0oK-273oC-459oF
Freezing point of water273oK0oC32oF
Boiling point of water373oK100oC212oF
7.7 Kelvin scale
The Kelvin scale (Lord Kelvin 1824 - 1907) is based on the idea of absolute zero. Molecular motion, heat, approaches zero as the temperature approaches -273.15oC. One kelvin degree, 1 K = 1 Celsius degree, 1oC. Absolute zero = -273.15oC = 0 K. To convert the Celsius scale to the Kelvin scale, add 273.15. For example, 0oC = 273.15 K, 100oC = 373.15 K, and 10oC = 283.15 K. So this scale begins at absolute zero and increases in kelvins. The Kelvin scale is the preferred scale for scientific experiments.
The temperature, kelvin, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water.
Proposed alternative definition of temperature, kelvin: The kelvin is such that the Boltzmann constant is exactly 1.3806505 X 10-23 joules per kelvin.
7.8 Triple point
See diagram 7.8: Triple point of water
The triple point is the temperature at which the three phases of a substance can exist together. The triple point temperature of water is the equilibrium point = 0.01°C (273.16 K) and 611.2 Pa (N m-2) in a sealed vacuum flask. It is an important fixed point for kelvin and thermodynamic scales of temperature. The ice point temperature, 273.15 K, is the temperature when equilibrium exists between ice and water at standard pressure. It is the lower fixed point of the Celsius scale.
7.9 Amount of substance, the mole
The mole, symbol mol, is the SI unit for amount of substance. A mole represents how much substance that contains as many atoms or molecules (elementary units) as there are atoms in 0.012 kg of the carbon isotope carbon-12. A mole of a substance is the amount of that substance whose weight is equal to the molecular or formula weight. The molecular weight of H2 = 2, so 1 mole of H2 weighs 2 g. The molecular weight of CO2 = 44, so 1 mole of CO2 weighs 44 g. A mole of any substance has the same number of molecules, Avogadro's constant (formerly Avogadro's number), 6.022 X 1023. Strictly speaking, to get a mole of a substance, weigh out its relative atomic mass or relative molecular mass in grams.
A proposed new definition of amount of substance, mole: A mole is such that the Avogadro constant is exactly 6.0221415 X 1023 per mole.
Avogadro's hypothesis (Avogadro's principle)
Equal volumes of all gases contain the same numbers of molecules, under identical conditions of temperature and pressure. So one mole of any substance contains the same number of particles. One mole of any gas, under identical conditions of temperature and pressure, has the same fixed volume, the molar volume (molecular volume) of a gas, 22.414 litres at s.t.p. (standard temperature and pressure), T = 273.15 K, P = 1 atmosphere (atm).
Molality is the concentration of a solution expressed as number of moles of the dissolved substance per kilogram of solvent.
Molarity is the concentration of the solution expressed as the number of moles of the dissolved substance per dm3 (litre) of solution. A molar solution has a concentration of one mole per dm3 (litre).
Normality was a concentration unit formerly used for acid, bases, oxidizing agents and reducing agents, based on the concentration of H+ and OH- in a solution. A normal solution has a concentration of one gram equivalent per dm3 (litre). One litre of a normal solution contains the weight in grams of the solute that is equivalent to 1 g of replaceable hydrogen. So 25 mL of N HCl would react exactly with 25 mL of N NaOH or 250 mL of N / 10 NaOH. For monobasic acids, the equivalent is numerically the same as the molecular weight. For dibasic acids, the equivalent is numerically equal to half the molecular weight. So a 2M (2 moles per litre) solution of H2SO4 = 4N solution of H2SO4.
A standard solution is a solution with accurately known concentration.
7.10 Current, ampere
An ampere is the current which, if maintained in two parallel straight conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in a vacuum, would produce between these conductors a force equal to 2 X 10-7 newtons per metre of length.
Proposed alternative definition: The ampere is such that the elementary charge is exactly 1.60217653 X 10-19 coulombs. (1 coulomb = 1 ampere second)
7.11 Time, second
A second is the time equal to the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium-133 atom.
7.12 Length, metre
A metre is the length of a path travelled by light in a vacuum during a time interval of 1/299,792,458 of a second.
7.13 Mass, kilogram
A kilogram is the mass of the international prototype kilogram kept in Sevres, France.
Proposed alternative definition: A kilogram is such that the Planck constant is exactly 6.6260693 X 10-34 joule seconds.
7.14 Luminous intensity, candela, cp
A candela is the intensity in a given direction, of a light source that emits monochromatic radiation of frequency 540 X 1012 hertz with a radiant intensity in that direction of 1/683 watts per steradian.
The previous unit was the candlepower, about 0.98 of a candela, that was defined in various ways, including the light from a standard whale oil candle. However, people liked to continue to use the term candlepower, so nowadays 1 candlepower = 1 candela. The zirconium wire in a camera flash cube ignites to release a 2,000 modern candlepower burst of light for about 30 millionths of a second.