Two stars, Star X and Star Y, have the same radius, but Star X is twice as hot as Star Y. Based on the Stefan-Boltzmann Law, what can be said about their luminosities?

The Stefan-Boltzmann Law gives luminosity as proportional to a star’s surface area times its temperature to the fourth power: L ∝ R²T⁴. Since the stars have equal radii, only the temperature changes; doubling the temperature multiplies luminosity by 2⁴ = 16. Therefore, Star X is sixteen times as luminous as Star Y, which is choice D.

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