Two stars,A and B,have the same emissivity,but the radii and surface temperatures are different with R_A = 0.5R_B,and T_A = 2T_B.Assuming the temperature of space to be negligible,which star radiates the most energy per unit time? A)Star A B)Star B C)Both radiate the same amount of energy per unit time. D)More information is needed in order to make a determination.

Question

Quizplus · Accepted Answer

The energy radiated per unit time by a star can be calculated using the Stefan-Boltzmann law, which states that the power radiated per unit area of a black body is proportional to the fourth power of its temperature (P = σAT^4, where σ is the Stefan-Boltzmann constant, A is the surface area, and T is the temperature). Given that Star A has twice the temperature of Star B (T_A = 2T_B), its radiated power per unit area will be 2^4 = 16 times greater. Although Star A has half the radius of Star B (R_A = 0.5R_B), its surface area (A = 4πR^2) will be 0.5^2 = 0.25 times that of Star B. Therefore, the total power radiated by Star A will be 16 * 0.25 = 4 times that of Star B, making Star A the star that radiates the most energy per unit time.

Two Stars,A and B,have the Same Emissivity,but the Radii and Surface