Thermal Properties of Matter - Result Question 13

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13. 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 :

======= ####13. 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 :

3e0f7ab6f6a50373c3f2dbda6ca2533482a77bed:content/english/neet-pyq-chapterwise/physics/thermal-properties-of-matter/thermal-properties-of-matter—result-question-13.md (a) 450

(b) 1000

(c) 1800

(d) 225

[2017]

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Answer:

Correct Answer: 13. (c)

Solution:

  1. (c) Given $r_1=12 cm, r_2=6 cm$

$T_1=500 K$ and $T_2=2 \times 500=1000 K$

$P_1=450$ watt

Rate of power loss $P \propto r^{2} T^{4}$

$ \frac{P_1}{P_2}=\frac{r_1^{2} T_1^{4}}{r_2^{2} T_2^{4}} $

$ P_2=P_1 \frac{r_2^{2} T_2^{4}}{r_1^{2} T_1^{4}} $

Solving we get, $P_2=1800$ watt