A particular star has a radius half that of the Sun and a luminosity equal to 60% of that of the Sun. What is the star's surface temperature? (See Box 17-4.) The surface temperature of the Sun is 5800 K.

Question

Quizplus · Accepted Answer

The luminosity (L) of a star is related to its radius (R) and surface temperature (T) by the Stefan-Boltzmann law, L = 4πR^2σT^4, where σ is the Stefan-Boltzmann constant. Given that the star's luminosity is 60% that of the Sun, and its radius is half that of the Sun, we can set up a ratio of the luminosities of the star and the Sun, considering the Sun's temperature to be 5800 K. Solving for the star's temperature with these given values, we find that the temperature must be higher than the Sun's to compensate for its smaller size and achieve 60% of the Sun's luminosity. The correct answer is 7220 K, which is derived from rearranging the equation to solve for the star's temperature, taking into account its smaller radius and given luminosity fraction.

A Particular Star Has a Radius Half That of the Sun