Q. 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) $\left( Q/4\pi R^{2}\sigma \right)^{- 1/2}$
C) $\left( 4\pi R^{2}Q/\sigma \right)^{1/4}$
D) $\left( Q/4\pi R^{2}\sigma \right)^{1/4}$
($\sigma$ stands for stefan’s constant)
Explanation
(d) $Q = \sigma\ e\ A\ T^{4}$
$T = \left\lbrack \frac{Q}{\sigma\left( 4\pi R^{2} \right)} \right\rbrack^{1/4}$
Here $e = 1,\ A = 4\pi R^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.