Thermal Properties Of Matter Ques 6
6. 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 :
[2017]
(a) $450$
(b) $1000$
(c) $1800$
(d) $225$
Show Answer
Answer:
Correct Answer: 6.(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
BETA
