Question

hotter than the sun
cooler than the sun
same temperature as the sun
answer bank
a k - type white dwarf
a star that is 8 times larger and 64 times more luminous than the sun
a g - type white dwarf
a star that is the same size as and 16 times more luminous than the sun
a star that is redder and just as luminous as the sun
an a - type giant star

Explanation:

1. Hotter than the Sun: An A - type giant star is hotter than the Sun. A - type stars have surface temperatures ranging from about 7,500 - 10,000 K, while the Sun's surface temperature is about 5,778 K. Also, a star that is the same size as and 16 times more luminous than the Sun must be hotter (using the Stefan - Boltzmann law $L = 4\pi R^{2}\sigma T^{4}$, where $L$ is luminosity, $R$ is radius, $\sigma$ is the Stefan - Boltzmann constant and $T$ is temperature. If $R$ is the same and $L$ is higher, $T$ must be higher).
2. Cooler than the Sun: A K - type white dwarf and a star that is redder and just as luminous as the Sun are cooler. K - type stars are cooler than G - type stars (the Sun is a G - type star). A redder star has a lower surface temperature according to Wien's law ($\lambda_{max}T = b$, where $\lambda_{max}$ is the wavelength of maximum emission, $T$ is temperature and $b$ is Wien's displacement constant).
3. Same temperature as the Sun: A G - type white dwarf has the same spectral type as the Sun in terms of surface temperature characteristics. A star that is 8 times larger and 64 times more luminous than the Sun, using the Stefan - Boltzmann law, can have the same temperature if the increase in size compensates for the increase in luminosity in a way that the temperature remains the same.

Answer:

• Hotter than the Sun: a star that is the same size as and 16 times more luminous than the Sun, an A - type giant star
• Cooler than the Sun: a K - type white dwarf, a star that is redder and just as luminous as the Sun
• Same temperature as the Sun: a G - type white dwarf, a star that is 8 times larger and 64 times more luminous than the Sun