Two stars are found to have the same luminosity.However,one star has twice the surface temperature of the other.From this information,what can you determine about their radii?
A) The hotter star has half the radius of the cooler star.
B) The cooler star has half the radius of the hotter star.
C) The hotter star has a quarter the radius of the cooler star.
D) Nothing can be determined about the radii from this information.

Question

Quizplus · Accepted Answer

The luminosity of a star is proportional to its surface area (which is related to the square of the radius) and the fourth power of its surface temperature (L ∝ R²T⁴). If one star has twice the temperature of the other but the same luminosity, it must have a smaller radius to compensate for the higher temperature. Specifically, the radius of the hotter star must be a quarter of the cooler star's radius to maintain the same luminosity.

Two Stars Are Found to Have the Same Luminosity