Question

A typical white dwarf has a surface temperature about four times that of the Sun and a radius about 1% that of the Sun. What can you determine about the luminosity of a typical white dwarf from this information?

A) The white dwarf will be less luminous than the Sun.
B) The white dwarf and the Sun will have about the same luminosity.
C) The white dwarf will be more luminous than the Sun.
D) Nothing can be concluded about the relative luminosities from this information.

Answer 1

A typical white dwarf has a surface temperature about four times that of the Sun and a radius about 1% that of the Sun. From this information, we can determine that A) The white dwarf will be less luminous than the Sun.

Step-by-step explanation:

To understand why, we need to consider the relationship between temperature, radius, and luminosity of a star. According to Stefan's law, the luminosity of a star is directly proportional to its surface temperature to the fourth power, and the luminosity is also directly proportional to the square of its radius.

In this case, the white dwarf has a higher temperature than the Sun (four times), but its radius is much smaller (1% of the Sun's radius). Since luminosity is proportional to temperature to the fourth power and radius squared, the smaller radius of the white dwarf will dominate the calculation, resulting in a lower luminosity compared to the Sun. Therefore, based on the given information, we can conclude that a typical white dwarf will be less luminous than the Sun. The correct answer is A) The white dwarf will be less luminous than the Sun.