Thermal Properties of Matter - Result Question 21
21. If the radius of a star is $R$ and it acts as a black body, what would be the temperature of the star, in which the rate of energy production is $Q$ ?
(a) $Q / 4 \pi R^{2} \sigma$
(b) $(Q / 4 \pi R^{2} \sigma)^{-1 / 2}$
(c) $(4 \pi R^{2} Q / \sigma)^{1 / 4}$
(d) $(Q / 4 \pi R^{2} \sigma)^{1 / 4}$
[2012]
( $\sigma$ stands for Stefan’S constant)
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Answer:
Correct Answer: 21. (d)
Solution:
- (d) Stefan’s law for black body radiation
$ Q=\sigma e A T^{4} $
$T=[\frac{Q}{\sigma(4 \pi R^{2})}]^{1 / 4}$
Here $e=1$
$ A=4 \pi R^{2} $
