Two stars have the same diameter and are at the same distance from us (but in different parts of the sky.) Star A has a temperature of 4000 K, while star B has a temperature of 8000K. Which of the following statements is true: A. the two stars have the same total energy flux (luminosity) B. star B has twice the energy flux (luminosity) that star A has C. tar B has one half the energy flux (luminosity) that star A has D. star B has 16 times the energy flux (luminosity) that star A has

Answer: D. Star B has 16 times the luminosity of star A

Explanation: This is best explained by the Stefan-Boltzmann law. The Stefan-Boltzmann Law states that the power radiated by an object of area A and temperature T is

P = σ AT^4

Stars A and B have the same diameter which suggests that they have the same area, but star B is hotter than star A in the ratio of 2 to 1, meaning it has a higher temperature and radiates more. But by how much? This is calculated by taking both ratios using the Stefan-Boltzmann law.

P = (σ AT^4 of star B) / (σ AT^4 of star A)

P = (8000^4) / (4000^4) = 16

Option D is correct