Suppose that 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?
A) The star radiates at the same rate as the sun.
B) 2 times
C) 4 times
D) 8 times
E) 16 times
F) 32 times
G) 64 times

Question

Quizplus · Accepted Answer

The rate of energy emission is given by the Stefan-Boltzmann Law: $L = 4\pi R^2 \sigma T^4$. If the star has twice the temperature (T) and twice the radius (R) of the sun, the energy emission rate is $(2^2) \times (2^4) = 4 \times 16 = 64$ times that of the sun.

Suppose That a Star Has Twice the Surface Temperature of the Sun