Thermal Properties of Matter - Result Question 13
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 :
(a) 450
(b) 1000
(c) 1800
(d) 225
[2017]
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Answer:
Correct Answer: 13. (c)
Solution:
- (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
