Question

Find The Conversion factor in between joule & erg​

Answer 1

Answer:

Joule is the SI unit of energy while erg is the cgs unit of energy.

1 Joule of Energy = 1 Newton x 1 metre

1 erg= 1 dyne x 1 cm

1 joule= 1 newton x 1 metre=105 dynes x 102 cm=107 erg

1 J = 107 erg

Therefore, 1 Joule is equal to 107 erg.

Answer 2

The conversion factor between joule and erg can be found using dimensional analysis​.

• The dimensional formula of work is ML²T⁻².
• Its unit in S.I. system is 'joule' and in C.G.S. system is 'erg'.
• Let M₁, L₁, T₁ represent kilogram (kg), metre (m), second (s) and M₂, L₂, T₂ represent gram (g), centimetre (cm), second (s) respectively.
• Then, the units of work in S.I. and C.G.S. systems will be (M₁L₁²T₁⁻²) and (M₂L₂²T₂⁻²) respectively.
• If the numerical values of work are n₁ and n₂ respectively, then

       $n_{1} (M_{1} L_{1}^{2} T_{1}^{-2}) = n_{2} (M_{2} L_{2}^{2} T_{2}^{-2})$

       $n_{2} = n_{1} (\frac{M_{1} }{M_{2}}) (\frac{L_{1} }{L_{2}})^{2} (\frac{T_{1} }{T_{2}})^{-2}$      

• Here, n₁ = 1.

       $n_{2} = 1 (\frac{kg}{g} ) (\frac{m}{cm})^{2} ( \frac{s}{s} )^{-2}$

            $= 1 (\frac{1000 g}{g} ) (\frac{100 cm}{cm})^{2} ( \frac{s}{s} )^{-2}$

            $= 1 * 10^{3} * 10^{4} * 1$

            $= 10^{7}$

• 1 joule = 10⁷ ergs.