Q. The luminosity of the Rigel star is 17000 times that of the sun. Assume both to be perfectly black bodies. If the surface temperature of the sun is 6000 K, then the temperature of the star is
A) 68400 K
B) $1.02 \times 10^{8}$K
C) 12000 K
D) 68400$℃$
Explanation
(a) Luminosity of a star depends upon the total radiations emitted by the star.
The star emits 17000 times the radiations emitted by the sun.
$\therefore$ $E = \sigma T^{4}$
Hence, $\frac{E_{1}}{E} = \left( \frac{T_{1}}{T} \right)^{4}$
So, $(17000)^{\frac{1}{4}} = \frac{T_{1}}{T}$ (Given, $E_{1} = 17000E)$
${\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ T}_{1} = 6000 \times 11.4 = 68400\ K$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.