An astronomer measures the luminosities of two stars with identical sizes,finding that star A is 256 times as luminous as star B.How are their temperatures related to each other?
A) Star A is twice as hot as star B.
B) Star A is 4 times hotter than star B.
C) Star A is 16 times hotter than star B.
D) Star A is 64 times hotter than star B.

Question

Quizplus · Accepted Answer

The luminosity of a star is proportional to the fourth power of its temperature (L ∝ T^4). If star A is 256 times as luminous as star B, then (T_A/T_B)^4 = 256. Solving for T_A/T_B gives T_A/T_B = 4, meaning star A is 4 times hotter than star B.

An Astronomer Measures the Luminosities of Two Stars with Identical