The equation for the luminosity of a star in terms of its surface temperature is L = (surface area) $\sigma$T⁴ where $\sigma$ is the Stefan-Boltzmann constant. This suggests that when a plot is made of luminosities versus temperature A) stars of the same temperature but different radii should occupy different points on the plot. B) all stars should plot along the line. C) larger stars must have higher temperatures. D) smaller stars must have higher temperatures.

Question

Quizplus · Accepted Answer

The equation implies that luminosity is directly proportional to the surface area (which depends on the radius of the star) and the fourth power of the temperature. Therefore, stars with the same temperature but different radii (surface areas) will have different luminosities, placing them at different points on the plot.

The Equation for the Luminosity of a Star in Terms σ\sigmaσ

The Equation for the Luminosity of a Star in Terms $\sigma$