Sirius,the brightest star in the night sky coverts 3.216 * 10¹⁸ kg of its mass to energy every year.How does the luminosity (power radiated)of Sirius compare to that of the sun? L_sun = 3.906 * 10²⁶ W

Question

Quizplus · Accepted Answer

We can use the formula for luminosity, which is directly proportional to the mass converted to energy per unit time. 
Let Ls represent the luminosity of Sirius and Lsun represent the luminosity of the Sun. Then:
Ls/Lsun = (mass converted to energy by Sirius per unit time) / (mass converted to energy by the Sun per unit time)
Ls/Lsun = (3.216 x 10^10 kg/year) / (4.26 x 10^9 kg/year)    (since the given mass is per year)
Ls/Lsun = 7.56

Therefore, the luminosity of Sirius is 7.56 times greater than that of the Sun. 
Using the given value of Lsun:
Ls = 7.56 x 3.906 x 10^26 W ≈ 29.6 x 10^26 W ≈ 23.5 Lsun

So, the best choice is B, which represents that the luminosity of Sirius is 23.5 times greater than that of the sun.

Sirius,the Brightest Star in the Night Sky Coverts 3