Suppose a star has twice the surface temperature of the sun and also twice the radius. How many times larger is the rate at which this star emits energy compared to the rate at which the sun emits energy?

Question

Quizplus · Accepted Answer

The rate at which a star emits energy is given by the Stefan-Boltzmann Law: $ L = 4\pi R^2 \sigma T^4 $. If the star has twice the surface temperature (T) and twice the radius (R) of the sun, the luminosity becomes $ L = 4\pi (2R)^2 \sigma (2T)^4 = 16 \times 4\pi R^2 \sigma T^4 = 64 \times L_{\text{sun}} $. Thus, the star emits energy 64 times more than the sun.

Suppose a Star Has Twice the Surface Temperature of the Sun