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 $



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