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Properties of Matter question

2017 · Q156
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Properties of Matter question

2017 · Q156

NEETPhysicsProperties of MatterMCQ+4 / −1
A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be
  1. A
    450
  2. B
    1000
  3. C
    1800
  4. D
    225
View written solutionFree

Correct answer: C

Given r1 = 12 cm , r2 = 6 cm

T1 = 500 K and T2 = 2 × 500 = 1000 K

P1 = 450 watt

Rate of power loss P∝r2T4P \propto {r^2}{T^4}P∝r2T4

P1P2=r12T14r22T24{{{P_1}} \over {{P_2}}} = {{r_1^2T_1^4} \over {r_2^2T_2^4}}P2​P1​​=r22​T24​r12​T14​​

P2=P1r12T14r22T24{P_2} = {P_1}{{r_1^2T_1^4} \over {r_2^2T_2^4}}P2​=P1​r22​T24​r12​T14​​

Solving we get, P2 = 1800 watt

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