SI units and dimension analysis

SI units and dimension measurement

In physical chemistry, we commonly deal with scaler and vector quantities such as pressure, volume, mass, temperature, current, etc with its CGS and SI units and dimension.

The quantity which has a magnitude but not a definite direction known as a scalar quantity.

The quantity which has both magnitudes and a definite direction known as a vector quantity.

The physical quantity has two components, namely, numerical value and its unit.

The quantity 5 newton means the unit is newton and the numerical value 5.

In this web page, we study some basic and commonly used scaler and vector quantity with its unit and dimension.

Basic units

In this website, the International system of SI units and CGS units broadly used but the wave number is given in reciprocal of a centimeter.

Thus in order to consistency in scientific recording, IUPAC recommended the use of coherent units. Known as the International System Units or commonly abbreviated as SI.

Thus seven base physical quantities used to describe these units

  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 meter, kilogram, and second

Definition of meter

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

Definition of 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. Platinium-iridium alloy used due to durability and resistance to corrosion.

Definition of second

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.

Submultiple prefixes for SI units


Multiple prefixes for SI units


Definition of ampere, kelvin, mole, candela

Definition of Ampere

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

Definition of Kelvin

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

Definition of 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.

Definition of Candela

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

SI unit of force

Newton second law of motion,

force = mass × acceleration

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

Because velocity = length/time

unit\, of\, force=\left ( unit\, of\, mass \right )\times \frac{\left (unit\, of\, length \right )}{\left (unit\, of\, time \right )^{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]

Convert 1 newton into dyne

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

1 kg = 103 gm and 1 m = 102 cm

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

=105 gm cm sec-2

Thus 1 Newton = 105 dyne

Electron cloud model

SI unit of work, energy, and heat

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.

Convert 1 joule into erg

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

1 kg = 103 gm and 1 m = 102 cm

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

=107 gm cm2 sec-2

Thus 1 joule = 105 erg

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