Physics - Unit & Dimension Question with Solution | TestHub

$1\mathrm{J}=10^7$ erg

To convert Stefan's constant from CGS to SI units:

Given: ${\sigma }_{CGS}=5.67\times 10^{-5}erg{s}^{-1}c{m}^{-2}{K}^{-4}$

We know:

$1J=10^{7}erg$

$1m=100cm⟹1cm=10^{-2}m$

Substitute these conversions into the CGS value:

${\sigma }_{SI}=5.67\times 10^{-5}\times \frac{1J}{10^{7}erg}\times (\frac{1cm}{10^{-2}m}{)}^{-2}J{s}^{-1}{m}^{-2}{K}^{-4}$

${\sigma }_{SI}=5.67\times 10^{-5}\times 10^{-7}\times (10^{-2}{)}^{-2}J{s}^{-1}{m}^{-2}{K}^{-4}$

${\sigma }_{SI}=5.67\times 10^{-5}\times 10^{-7}\times 10^{4}J{s}^{-1}{m}^{-2}{K}^{-4}$

${\sigma }_{SI}=5.67\times 10^{(-5-7+4)}J{s}^{-1}{m}^{-2}{K}^{-4}$

${\sigma }_{SI}=5.67\times 10^{-8}J{s}^{-1}{m}^{-2}{K}^{-4}$

Comparing with $5.67\times 10^{-X}J{s}^{-1}{m}^{-2}{K}^{-4}$, we find $X=8$.