Properties Of Solids And Liquids Question 463
Question: A spherical black body with a radius of 12 cm radiates 459 W power at 599 K. If the radius were halved and the temperature doubled, the power radiated in watt would be
Options:
A) 225
B) 459
C) 999
D) 1899
Show Answer
Answer:
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 Forasphere,=4\pi r^{2}) $
Dividing (ii) and (i), we get $ \frac{E/t}{450}=\frac{{{( 1000 )}^{4}}{{( 0.06 )}^{2}}}{{{( 500 )}^{4}}{{( 0.12 )}^{2}}}=\frac{2^{4}}{2^{2}}=4 $
$ \Rightarrow \frac{E}{t}=450\times 4= 1800 W $
