Question

The power of a black body at temperature $200\, K$ is $544\, W$. Its surface area is
$\left(\sigma=5.67 \times 10^{-8}\, Wm ^{-2}\, K ^{-4}\right)$

• A. $6 \times 10^{-2}\, m ^{2}$
• B. $ 6\,m^{2} $
• C. $ 6\times 10^{-6}\,m^{2} $
• D. $ 6\times 10^{2}\,m^{2} $

Answer 1

Answer: (B)

According to Stefan's law
$\frac{Q}{A l}=\sigma T^{4} $
Here $\frac{Q}{t}=544, T=200\, K$
$\sigma=5.67 \times 10^{-8} \,W m^{-2} \,K^{-4}$
$=A=\frac{Q}{\sigma t T^{4}}=\frac{544}{5.67 \times 10^{-8} \times(200)^{4}}=6\, m^{2}$