A white dwarf has a temperature 10 times that of the Sun,but it has a radius 1,000 times smaller than the Sun.What is its luminosity?
A) 10 solar luminosities
B) 0.1 solar luminosities
C) 0.01 solar luminosities
D) 10-4 solar luminosities

Question

Quizplus · Accepted Answer

The luminosity of a star can be calculated using the formula $L = 4\pi R^2 \sigma T^4$, where $L$ is luminosity, $R$ is radius, $\sigma$ is the Stefan-Boltzmann constant, and $T$ is temperature. Given that the white dwarf's temperature is 10 times that of the Sun and its radius is 1/1000 of the Sun's, its luminosity relative to the Sun is $(10^2)^4 \times (1/1000)^2 = 10^8 \times 10^{-6} = 10^{-2}$ or 0.01 times the Sun's luminosity.

A White Dwarf Has a Temperature 10 Times That of the Sun,but