Units and dimensions formulas

Units and dimensions formulas and measurements in SI or CGS system in science recommended by the International Union of Pure and Applied Chemistry (IUPAC). In the standard unit system or SI system, we used the seven base units and dimensions formulas of physical quantities for analysis, measurement, and conversion. For example, we use the base unit and dimension of mass, length, time for measurement and conversion of force, density, energy, work, heat capacity, pressure, surface tension, etc. These physical quantities can be derived from base units or dimensions data. 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.

International system of units

Unit and dimension formulas in International System of Units (SI) in science

International unit systems or simply SI systems of units and dimensions are used for the measurement and study of most types of physical quantities. For the measurement of wavelengths or wavenumber in the electromagnetic spectrum, we used commonly the CGS system. Length, mass, time, electric power, thermodynamics temperature, amount of substance, and luminous intensity are seven base physical quantities according to the International Union of Pure and Applied Chemistry (IUPAC).

Fundamental quantities and their units and symbols

SI unit of seven fundamental quantities
Fundamental quantities SI unit Symbol for SI unit
length meter m
mass kilogram kg
time second s
electric current ampere A
thermodynamic temperature kelvin K
amount of substance mole mol
luminous intensity candela cd

From these basic fundamental units and dimensions data, we derived the unit and dimension of activation energy, concentration, density, enthalpy, entropy, force, free energy function, the specific heat of gas, and solid substances, etc.

Definition of units of measurement

How long is a meter?

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

Definition of kilogram

The kilogram is the SI unit of mass. It is the weight of the platinum-iridium polished cylinder which is kept at the International Bureau of Weights and Measures in a suburb of Paris, France. Platinum-iridium alloy is chosen due to its durability and resistance to corrosion.

Definition of second

The second is the duration of 9192631770 periods of the radiation corresponding to the transition between two hyperfine levels of the f-block element cesium-133 atom in the ground state.

What is ampere?

Ampere is that constant current folwing if we maintained two straight parallel conductors of infinite length which are placed one meter apart in a vacuum with negligible cross-section. The force produced between these two conductors is equal to 2 × 10-7 newton per meter.

What is kelvin temperature?

Kelvin is the SI unit of temperature. It is the fraction of 1/273.16 of the thermodynamic temperature of the triple point of the water.

What is mole in science?

Mole or simply mol is the SI unit of the amount of substances. It is the amount of substance of a system that contains as many elementary entities as there are atoms in 0.012 kilograms of carbon-12.

Candela meaning

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

Unit conversion table

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

Derived units examples

Unit of force

The SI unit of force is Newton and it can be derived from Newton’s second law of motion. From Newton’s second law of motion, force (F) = mass (M) × acceleration (F). Again, acceleration = velocity/time = length/time2, where velocity = length/time. From the above equation or formula, the CGS unit of force = g cm s-2 or simply dyne and SI unit of force = Kg m s-2 or simply newton.

Dimension of force

From the dimension of length, mass, and time, the derive the dimension of force = [M L T -2].

Relation between newton and dyne

From the definition of newton, 1 Newton = (1 kg × 1 m)/(1 s)2. Again, 1 kg = 103 g, and 1 m = 102 cm Therefore, 1 Newton = (103 g × 102 m)/(1 s)2 =105 g cm s-2 = 105 dyne.

What is the unit of work and energy?

From the definition of work, the unit of work = unit of force × unit of displacement. Therefore, the CGS unit of work = g cm2 s-2 or simply erg. The SI unit of work = kg m2 s-2 or simply joule.

Dimension of work

From the definition, the dimension of work = dimension of force × dimension of length = [M L T-2] × [L] = [M L2 T-2].

Joule to erg conversion

From the definition joule, 1 Joule = 1 kg × (1 m)2/(1 s)2. Therefore, 1 Joule = 103 g × (102 cm)2/(1 s)2 =107 g cm2 s-2 = 105 erg.

Unit of energy

The ability to doing work is termed energy. Therefore, the SI unit of energy is the joule, and the CGS unit of energy is erg. The unit of the different forms of energy like kinetic energy, potential, mechanical, internal, electromagnetic, and surface energy is the same.

Unit of heat energy

Heat is another form of energy for the production of work. It is different energy because all the other forms of energy are completely converted into work but heat is not wholly converted into work. The unit and dimension of heat and energy are identical. The SI unit of heat joule.

What is the unit of power?

The rate at which energy is transferred or converted is called power. Therefore, the SI unit of power = energy/time. From the above formula, the SI unit of power is joule/s or watt in honor of Scottish inventor James Watt.

SI units table

Quantity SI unit Symbol Base unit
frequency hertz Hz s-1
force newton N kg m s-2
pressure pascal Pa kg m-1 s-2
energy, work, heat joule J kg m2 s-2
power watt W kg m2 s-3
electric charge coulomb C A s
electric resistance ohm Ω kg m2 s-3 A-2
electric conductance siemens S kg-1 m-2 s3 A2
electric capacitance farad F kg-1 m-2 s4 A2

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