The value of Stefan's constant in CGS system is $\mathrm{\sigma }=5.67\times {10}^{-5} \mathrm{erg} {\mathrm{s}}^{-1} {\mathrm{cm}}^{-2} {\mathrm{K}}^{-4}$ . Its value in SI units is $\_\_\_\_\_\_\_\_\_\_\_\_$.

${\mathrm{n}}_1{\mathrm{u}}_1={\mathrm{n}}_2{\mathrm{u}}_2$

$\Rightarrow \left({\mathrm{n}}_1\right)\left({\mathrm{Js}}^{-1}{\mathrm{m}}^{-2}{\mathrm{K}}^{-4}\right)=\left(5.67\times {10}^{-5}\right)\left(\mathrm{erg} {\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{K}}^{-4}\right)$

$\Rightarrow {\mathrm{n}}_1\left({10}^7\mathrm{erg}\right)\left({\mathrm{s}}^{-1}\right)\left({10}^{-4}{\mathrm{cm}}^{-2}\right)\left({\mathrm{K}}^{-4}\right)=\left(5.67\times {10}^{-5}\right)\left(\mathrm{erg} {\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{K}}^{-4}\right)$

$\Rightarrow {\mathrm{n}}_1 {10}^3\left(\mathrm{erg} {\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{K}}^{-4}\right)=5.67\times {10}^{-5}\left(\mathrm{erg} {\mathrm{s}}^{-1}{\mathrm{cm}}^{-2}{\mathrm{K}}^{-4}\right)$

$\Rightarrow {\mathrm{n}}_1=5.67\times {10}^{-8}$

So, $\mathrm{\sigma }=5.67\times {10}^{-8} \mathrm{J} {\mathrm{s}}^{-1}{\mathrm{m}}^{-2}{\mathrm{K}}^{-4}$