SATHEE: Properties Of Solids And Liquids Question 463

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 $\frac{E}{t} = σ T^{4} \times A$ , where A is the surface area.

$\frac{E}{t} = σ T^{4} \times A π r^{2} (∵ F o r a s p h e r e, = 4 π r^{2})$

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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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:

Answer:

Solution:

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