A) 225
B) 459
C) 999
D) 1899
Correct Answer: D
Solution :
[d] The energy radiated per second by a black body is given by Stefan's Law \[\frac{E}{t}=\sigma {{T}^{4}}\times A\], where A is the surface area. \[\frac{E}{t}=\sigma {{T}^{4}}\times A\pi {{r}^{2}}(\because \text{ }\operatorname{For}\,a\,sphere,=4\pi {{r}^{2}})\] Dividing (ii) and (i), we get \[\frac{E/t}{450}=\frac{{{\left( 1000 \right)}^{4}}{{\left( 0.06 \right)}^{2}}}{{{\left( 500 \right)}^{4}}{{\left( 0.12 \right)}^{2}}}=\frac{{{2}^{4}}}{{{2}^{2}}}=4\] \[\Rightarrow \frac{E}{t}=450\times 4= 1800 W\]
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