# Unit dimension for students

### Scaler and vector quantity

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

A physical quantity has two components, namely, numerical value and it's unit and is written as,
The quantity 5 Newton means the physical quantity Newton and its numerical value 5.
 SI unit of scalar and vector quantities
The dimension of length = L, mass = M, and time = T.

#### How to the definition of a meter?

The meter is the length of the path traveled by light in vacuum during a time interval of 1/299 792 458 of a second.

#### What is the SI unit of area?

Area = length × length
Unit of area = unit of length × unit of length.

∴ CGS unit of area = cm × cm
= cm².

SI unit of area = m × m
= m².

The dimension of area = L × L = [L]².

#### CGS and SI unit of volume

Volume = length × length × length.
∴ Unit of volume = (unit of length)³

CGS unit of volume = cm³.

SI unit of volume = m³.

The dimension of volume = [L³].

#### CGS and SI unit of density

From the definition of density (d) = mass/volume.

∴ Unit of density = unit of mass/unit of volume.

CGS unit of density = gm/cm³
= gm cm⁻³.

SI unit of density = Kg/m³
= Kg m⁻³.
Dimension of density = [M]/[L³]
= [M L⁻³].

#### CGS and SI unit of force

Newton second law of motion,
force = mass × acceleration.
or, force = mass × velocity/time
or, force = mass × (length/time)/time.

Velocity = length/time.

∴ Force = mass × (length/time²).

CGS unit of force = gm × cm/sec²
= gm cm sec⁻².
Simply, dyne.

SI unit of force = Kg m/sec²
= Kg m sec⁻².
Simply, Newton.

From the above discussion dimension of force, = dimension of mass × dimension of length/dimension of time².

∴ Dimension of force = [M L T⁻²].
Problem
How to convert 1 newton into a dyne?

Solution
1 newton = Kg m/sec²
= (1 Kg × 1 m )/(1 sec)².

1 Kg = 10³ gm and 1 m = 10² cm.

∴ 1 Newton = (10³ gm × 10² cm)/(1 sec)²
= 10⁵ gm cm/sec².

1 Newton = 10⁵ dyne.

#### CGS and SI unit of work

Definition of work,
Work = force × displacement.
∴ W = F × S.

∴ CGS unit of work = (gm cm/sec²) × cm
= gm cm²/sec²
= gm cm² sec⁻².
Simply, erg.

SI unit of work = (kg m/sec²) × m
= kg m²/sec²
= kg m² sec⁻²
Simply, the joule.

From the above discussion dimension of work, = (dimension of mass × dimension of length)²)/(dimension of time²)

∴ Dimension of work = [ML²T⁻²]
Problem
How to convert 1 joule into erg?

Solution
1 Joule = 1 kg m²/sec²
= (1 Kg × 1 m² )/1 sec²

1 kg = 10³ gm and 1 m = 10² cm.

∴ 1 Joule = {10³ gm × (10²)² cm}/1 sec²
= 10⁷ gm cm²/sec²
= 10⁷ erg

#### CGS and SI unit of work

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 work are erg and joule respectively.

#### CGS and SI unit of pressure

Definition of pressure = force/area.

∴ Unit of pressure = unit of force/unit of area.

CGS unit of pressure = erg/cm²
= erg cm⁻².

SI unit of pressure = Joule/m²
= Joule m⁻².

∴ The dimension of pressure = [M L⁻²].

Study CGS and SI Unit and dimension scaler and vector quantities for students, SI unit of density, force, work, pressure, energy