Would a star with a radius 16 times that of the Sun, but a surface temperature 0.5 times that of the Sun, be more, or less luminous than the Sun?

Answer 1

Luminosity is proportional to the square of the radius and the fourth power of the surface temperature. For the sun, L_sun ∝ R_sun²*T_sun⁴

For a star that is 16 times the radius of the sun but only 0.5 times the surface temperature, L_star ∝ (16R_sun)²*(0.5T_sun)⁴

So L_star = 16²*(0.5)⁴*R_sun²*T_sun² = 16*L_sun

So the start is 16 times more luminous than the sun.