If star A has a temperature that is twice as hot as the Sun, but it has the same luminosity as the Sun, the diameter of star A must be ________ times the diameter of the Sun.
A) 16
B) 4
C) 2
D) 1/2
E) 1/4

Question

Quizplus · Accepted Answer

The luminosity of a star is proportional to its surface area and the fourth power of its temperature (L ∝ R²T⁴). If star A has the same luminosity as the Sun but twice the temperature, its radius must be smaller to compensate for the increased temperature. Specifically, if the temperature is doubled, the radius must be reduced by a factor of 4 (since (2T)⁴ = 16, and to keep L constant, R² must be 1/16, so R must be 1/4). Thus, the diameter is also 1/4 of the Sun's diameter.

If Star a Has a Temperature That Is Twice as Hot