Question

What is the relationship between joule and erg?

Answer 1

Step 1: Definition

1. An erg is the amount of work done by exerting a force of one dyne across a one-centimeter distance. It will be one gram centimeter-squared per second-squared throughout CGS base units.
2. A joule seems to be the amount of work done by exerting a force of one newton across a one-meter distance.

Step 2: Finding the relationship between joule and erg

$$\begin{gathered} 1\mathrm{joule}=1\mathrm{newton}\times 1\mathrm{m} \\ =1{\mathrm{s}}^{2}1\mathrm{kg}\times 1\mathrm{m}\times 1\mathrm{m} \\ =1{\mathrm{s}}^{2}1000\mathrm{g}\times 100\mathrm{cm}\times 100\mathrm{cm} \\ ={10}^7\mathrm{erg} \end{gathered}$$

Therefore, the relationship between joule and erg $1\mathrm{J}={10}^7\mathrm{erg}$.