# SI units and dimension

## SI units and dimension formula

The IUPAC recommended seven physical quantities has thair own SI units and dimension. Other physical quantities like force, energy, work, heat, etc can be derived from the basic SI unit. But SI unit of luminous intensity or candela not needed in chemistry. It used in optical photochemistry but it included only for the shake of completeness.

In physical chemistry, we commonly deal with quantities such as pressure, volume, mass, temperature, current, etc. These quantities are physical quantities and are two types

1. The quantity which has a magnitude but not a definite direction known as a scalar quantity.
2. But quantity which has both magnitudes and direction known as a vector quantity.

Every physical quantity has two components, namely, the numerical value and unit.

Physical quantity = numerical value × unit

Thus the quantity 5 Joule means, numerical value = 5, and unit = 5 Joule.

### International System of Units

The International System of Units or SI units used for the determination of most of the physical quantities. But CGS units broadly used in the wavenumber.

Thus in order to consistency in scientific recording, IUPAC recommended the use of these SI units and dimension.

So the seven base physical quantities used to describe by these units are

1. Length (meter)
2. Mass (kilogram)
3. Time (second)
4. Electric current (ampere)
5. Thermodynamic temperature (kelvin)
6. Amount of substance (mole)
7. The luminous intensity of light (candela)

#### Definition of base SI units

Meter
A meter is a length of the path traveled by light in vacuum during a time interval of 1/299792458 second.

Kilogram
The weight of the platinum-iridium cylinder kept at the International Bureau of Weights and Measures in a suburb of Paris, France called one kilogram.

Second
Second is the duration of 9192631770 periods of the radiation corresponding to the transition between two hyperfine levels of the cesium-133 atom in the ground state.

Ampere
Ampere is the constant current flowing if maintained in two parallel conductors of infinite length, negligible cross-section and placed one meter apart in a vacuum. Thus the forces produced between these conductors = 2 × 10-7 newton per meter length.

Kelvin
The fraction of 1/273.16 of the thermodynamic temperature of the triple point of water.

Mole
The amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12.

Candela
The candela is the luminous intensity, in a given direction of a source that emits monochromatic radiation of frequency 540 × 1012 hertz. But the radiant intensity in that direction of 1/683 watt per steradian.

#### Multiples of SI units

 Multiple Prefix Symbol 10 deca da 102 hecto h 103 kilo k 106 mega M 109 giga G 1012 tera T 1015 peta P 1018 exa E

#### Submultiples of SI units

 Submultiple Prefix Symbol 10-1 deci d 10-2 centi c 10-3 milli m 10-6 micro µ 10-9 nano n 10-12 pico p 10-15 femto f 10-18 atto a

### SI units and dimension of force

Newton second law of motion,

force = mass × acceleration

$\therefore&space;force=mass\times&space;\frac{velocity}{time}=mass\times&space;\frac{length}{\left&space;(time&space;\right&space;)^{2}}$

Because velocity = length/time

$unit\,&space;of\,&space;force=\left&space;(&space;unit\,&space;of\,&space;mass&space;\right&space;)\times&space;\frac{\left&space;(unit\,&space;of\,&space;length&space;\right&space;)}{\left&space;(unit\,&space;of\,&space;time&space;\right&space;)^{2}}$

Thus CGS unit of force = gm × (cm/sec2)
= gm cm sec-2 or simply dyne.

SI unit of force = Kg × (m/sec2)
= Kg m sec-2 or simply newton.

From the above discussion dimension of force
= [M L T -2]

#### Newton to dyne conversion

$1\,&space;newton=\frac{1\,&space;kg\times&space;1\,&space;m}{\left&space;(&space;1\,&space;sec&space;\right&space;)^{2}}$

1 kg = 103 gm and 1 m = 102 cm

$\therefore&space;1\,&space;newton=\frac{10^{3}\,&space;gm\times&space;10^{2}\,&space;cm}{\left&space;(&space;1\,&space;sec&space;\right&space;)^{2}}$

=105 gm cm sec-2

Thus 1 Newton = 105 dyne

### SI units and dimensions of energy

From the definition of work Work = force × displacement or, W = F × S

∴ Unit of work = unit of force × unit of displacement

∴ CGS unit of work = gm cm sec-2 × cm
= gm cm2 sec-2 or simply erg

SI unit of work = kg m sec-2 × m
= kg m2 sec-2 or simply joule

From the above discussion dimension of work

= dimension of force × dimension of length

∴ The dimension of work = [M L T-2] × [L]
= [M L2 T-2]

The ability to doing work is termed as energy. Thus, the unit and dimension of energy and work are the same.

∴ CGS and SI units of energy are erg and joule respectively.

Energy can take on many forms and can change from one form to another. Heat is one form of energy. Thus the unit of heat and energy are the same.

#### Erg to joule conversion

$1\,&space;joule=\frac{1\,&space;kg\times&space;\left&space;(1\,&space;m&space;\right&space;)^{2}}{\left&space;(&space;1\,&space;sec&space;\right&space;)^{2}}$

1 kg = 103 gm and 1 m = 102 cm

$\therefore&space;1\,&space;joule=\frac{10^{3}\,&space;gm\times&space;\left&space;(10^{2}\,&space;cm&space;\right&space;)^{2}}{\left&space;(&space;1\,&space;sec&space;\right&space;)^{2}}$

=107 gm cm2 sec-2

Thus 1 joule = 105 erg