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NEET 2017
Exam
NEET
Year
2017
Subject
Physics
Chapter
Thermal Properties of Matter

NEET 2017 · Physics · Thermal Properties of Matter

A spherical black body with a radius of 12cm radiates 450W power at...

A spherical black body with a radius of 12cm12cm radiates 450W450W power at 500K500K. If the radius were halved and the temperature doubled, the power radiated in watt would be

Options

  1. A225225
  2. B450450
  3. C10001000
  4. D18001800

Correct answer

D. 18001800

Step-by-step solution

By Stefan's law rate of heat radiation from a black body =\sigmaAT4= \sigmaA{T}^{4}

⇒⇒ Rate of power loss

r∝R2T4r ∝ {R}^{2}{T}^{4}

r1r2=R12T14R22T24\dfrac{{r}_{1}}{{r}_{2}} = \dfrac{{R}_{1}^{2}{T}_{1}^{4}}{{R}_{2}^{2}{T}_{2}^{4}}

=4×116= 4 \times \dfrac{1}{16}

450r2=14\dfrac{450}{{r}_{2}} = \dfrac{1}{4}

r2=1800watt{r}_{2} = 1800watt
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