Unit and dimension formula

Units dimensions (SI and CGS system) formula or measurement in physics and chemistry or science recommended by the International Union of Pure and Applied Chemistry (IUPAC). In the International unit (SI) system in science, we used the seven base physical units for dimensional formula analysis, measurement, conversion. For example, we use the base SI unit and dimension formula for measurement and conversion of force (newton or dyne), energy (joule or erg), work, specific heat, etc. But the SI unit of luminous intensity or candela is not needed in physics or chemistry learning but it is included only for the shake of completeness.

In physical chemistry, we commonly deal with the CGS and SI units and dimensions data and formula of pressure, volume, the atomic mass or weight of the molecule, temperature, electric current, density, concentration, dipole moment, electrode potential in oxidation reduction reaction, etc. Unit and dimension formula in International System of Units (SI) in science Every physical property has two components, namely, the numerical value and base units. Physical property = numerical value × unit. Thus the quantity 5 Joule means numerical value = 5, and unit = 5 Joule.

International System of Units

The International unit (SI) systems of units and dimensions are used for the measurement and study of most types of physical quantities. CGS units list used for the measurement of wavelengths or wavenumber in spectroscopy. In order to consistency in scientific recording, the international unit system recommended the use of these CGS units. Length, mass, time, electric power, thermodynamics temperature, amount of substance, and luminous intensity are seven base physical quantities describe by unit meter, kilogram, ampere, kelvin, mole, and candela are the unit of these quantities. From these basic fundamental units, dimensions data derived the unit and dimension of activation energy, concentration, density, enthalpy, entropy, force, Gibbs free energy function, quantum yield, the specific heat of gas, and solid substances, etc.

Definition of units of measurement

  • A meter is the length of the path traveled by light in a vacuum during a time interval of 1/299792458 second.
  • 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 is the duration of 9192631770 periods of the electromagnetic spectrum radiation corresponding to the transition between two hyperfine energy levels of the f-block element cesium-133 atom in the ground state.
  • 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 conductance forces produced between these conductors = 2 × 10-7 newton per meter length.
  • The fraction of 1/273.16 of the thermodynamic temperature of the triple point of the water molecule.
  • The amount of substance of a system that contains as many elementary particles entities as there are atoms in 0.012 kilograms of carbon-12.
  • The candela is the unit of luminous intensity, in a given direction of a source that emits a monochromatic radiation spectrum of frequency 540 × 1012 hertz. But the radiant intensity in that direction of 1/683 watt per steradian.

Unit Conversion Table

In the below measurement table or chart used to define the multiple and submultiple prefixes for unit conversion by the roman symbol. Unit Conversion Table for measurement of units and dimension in physical science

Unit of Force

From the Newton second law of motion, force (F) = mass (M) × acceleration (F). Therefore, force = (mass × length)/(time)2, where velocity = length/time. From this unit dimensions measurement equation, the CGS unit of force = gm × (cm/sec2) = gm cm sec-2 or simply dyne and SI unit of force = Kg × (m/sec2) = Kg m sec-2 or simply newton.

Dimension of force

The base unit dimension measurement data for length, mass, and time used to derive the dimension of force = [M L T -2].

Force Unit Conversion

From the definition of the unit of force, 1 Newton = (1 kg × 1 m)/(1 sec)2, where 1 kg = 103 gm, and 1 m = 102 cm Therefore, 1 Newton = (103 gm × 102 m)/(1 sec)2 =105 gm cm sec-2 = 105 dyne.

Unit of work energy and heat

The definition or measurement of work, the unit of work = unit of force × unit of displacement. Therefore, the CGS unit of work = gm cm sec-2 × cm = gm cm2 sec-2 or simply erg and SI unit of work = kg m sec-2 × m = kg m2 sec-2 or simply joule.

Dimension of work energy and heat

Dimensional analysis of work is also given from the definition of work. Therefore the dimension of work = dimension of force × dimension of length = [M L T-2] × [L] = [M L2 T-2]. The ability to doing work is termed as energy like kinetic energy, potential, mechanical, internal, electromagnetic, surface energy, etc. Therefore, measurements of fundamental SI units and dimensions formula for energy and work are the same. Hence the CGS and SI units of work or energy = erg and Joule respectively.

Heat is also another form of energy to produce work. But is somewhat different from the other form of energy like chemical or electrical energy. Because all the other forms of energy are completely converted into work but heat is not wholly converted into work. Therefore, the unit and dimensional equation for heat and energy are identical.

Energy unit conversion

From the definition of units or dimensions of energy, 1 Joule = 1 kg × (1 m)2/(1 sec)2. Therefore, 1 Joule = 103 gm × (102 cm)2/(1 sec)2 =107 gm cm2 sec-2 = 105 erg (unit of energy in CGS system).


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