Convert 1 joule to ergs in dimensional analysis.

Convert 1 joule to ergs in dimensional analysis.

To know how 1 joule can be converted into ergs in dimensional analysis, it is essential to understand the concept of joule and ergs.

According to the International System of Units, one joule is measured as equal to the work done on a particular object upon which the force of one Newton has been applied so that the object can move by one meter in the same direction in which the force has been applied. It is James Prescott Joule, an English mathematician, and physicist after whom the SI unit of energy is named.

• Joule is referred to as the heat energy that gets dissipated due to the one ampere of electric current that flows through one meter of a suitable conductor the resistance of which is equal to one ohm
• The SI unit of energy is Joule and on the other hand, the CGS unit of energy is erg

It is known that,

1 Joule of Energy = 1 Newton x 1 meter

1 erg = 1 dyne x 1 cm

1 joule = 10⁵ dynes x 10² cm

1 joule = 10⁷ erg 

The dimensional formula for Joule is,

1 joule = [M¹L²T-²]

Consider N₁(joule) = N₂(erg)

Hence, 1 Joule = 10⁷erg

Therefore, it can be concluded that 1 joule is equal to 10⁷ erg in dimensional analysis.