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 $6000K$ , then the temperature of the star is around (Take $17000^{1/4}=11.4$ )

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

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, $E_1=17000E)$
$T_1=6000\times 11.4=68400K$