Question

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 around (Take $17000^{1/4}=11.4$ )

• A. $68400 \, K$
• B. $58400 \, K$
• C. $38600 \, K$
• D. $32600 \, K$

Answer 1

Answer: (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, $\left(17000\right)^{1 / 4}=\frac{T_{1}}{T}$ (Given, $E_{1}=17000E)$
$\, \, T_{1}=6000\times 11.4=68400 \, K$