A star of the Sun's diameter, but twice as hot, must be 16X more luminous than the Sun.

Question

Quizplus · Accepted Answer

Luminosity is directly proportional to temperature to the fourth power and the radius squared. So, a star with the same radius as the Sun but twice as hot would have a luminosity of (2^4) = 16 times that of the Sun. Luminosity is directly proportional to the fourth power of the star's radius and the square of its temperature. Therefore, a star of the Sun's diameter, but twice as hot, must have a radius of 1 and a temperature of 2, resulting in (1^4)(2^2) = 4 times the Sun's luminosity. Multiplying this by the factor of 4 due to the increase in surface area gives a total of 16 times the Sun's luminosity.

A Star of the Sun's Diameter, but Twice as Hot