Transmission Of Heat Question 237
Question: The radiation emitted by a star A is 10,000 times that of the sun. If the surface temperatures of the sun and the star A are 6000 K and 2000 K respectively, the ratio of the radii of the star A and the sun is
[EAMCET 2003]
Options:
A) 300 : 1
B) 600 : 1
C) 900 : 1
D) 1200 : 1
Show Answer
Answer:
Correct Answer: C
Solution:
$ Q\propto AT^{4}\propto r^{2}T^{4} $
$ \Rightarrow \frac{Q _{\text{star}}}{Q _{\text{sun}}}$=
$\frac{r^2 _{\text{star}}.T^4 _{\text{star}}}{r^2 _{\text{sun}}\times T _{sun}^{4}} $
$ \Rightarrow \frac{10000}{1}=\frac{r _{\text{star}}^{2}}{r _{\text{sun}}^{2}}\times {{( \frac{6000}{2000} )}^{4}} $
$ \Rightarrow \frac{{r _{\text{star}}}}{{r _{\text{sun}}}}=\frac{100\times 9}{1}=\frac{900}{1} $
BETA
