Question

Luminosity of Rigel star in Orion , constellation is 17000 times that of our sun .If the surface temperature of the sun is 6000 K , calculate the temperature of the star .

Answer 1

According to Stefan's law
$E=\sigma T^4$
$\therefore \frac{E_R}{E_S}=\frac{T_R^4}{T_S^4}={\left(\frac{T_R}{T_S}\right)}^4$
Given, $E_R=17000E_S;T_S=6000K;T_R=?$
$\therefore \frac{17000E_S}{E_S}={\left(\frac{T_R}{6000}\right)}^4$
or$\frac{T_R}{6000}={\left(17000\right)}^{1/4}=11.41858$
$\therefore T_R=11.41858\times 6000$
$68511.5K$
$=68512K$