Question

1. if a main sequence star is twice as hot as the sun, what can you infer about its luminosity? (1) it would be less luminous than the sun (2) it would have the same luminosity as the sun (3) it would be significantly more luminous than the sun (4) it would no longer be a main sequence star 13) how does mass generally change for stars along the main sequence, moving from the top - left to the bottom - right? (1) mass increases, then decreases (2) mass decreases (3) mass increases (4) mass remains relatively constant 14) based on the provided h - r diagram, what are the approximate properties of our sun? (1) spectral class m, luminosity of 0.01 (2) spectral class b, luminosity of 10,000 (3) spectral class a, luminosity of 100 (4) spectral class g, luminosity of 1 15) the star sirius b is a white dwarf. based on its position on the h - r diagram, what can be concluded about its properties? (1) it is very hot but has a very low luminosity (2) it is cool and has a very low luminosity (3) it has a temperature and luminosity similar to our sun (4) it is cool and has a very high luminosity

Explanation:

• Question 12: According to the Stefan - Boltzmann law \(L=\sigma AT^{4}\) (where \(L\) is luminosity, \(\sigma\) is the Stefan - Boltzmann constant, \(A\) is the surface area, and \(T\) is temperature). If a star is twice as hot (\(T\)) as the Sun (\(T_{star}=2T_{Sun}\)), then \(L_{star}=\sigma AT_{star}^{4}=\sigma A(2T_{Sun})^{4}=16\sigma AT_{Sun}^{4}\) (assuming similar surface areas, which is a reasonable assumption for main - sequence stars of similar size range). So it is more luminous.
• Question 13: On the Hertzsprung - Russell (H - R) diagram, moving from the top - left (hot, luminous stars) to the bottom - right (cooler, less luminous stars) along the main sequence, the mass of stars decreases. More massive stars are hotter and more luminous and are located towards the top - left of the main sequence.
• Question 14: The Sun is a G - type main - sequence star (Spectral Class G). Its luminosity is approximately \(L = 1L_{\odot}\) (where \(L_{\odot}\) is the solar luminosity).
• Question 15: White dwarfs are hot (high surface temperature, because they are the remnants of stars that have shed their outer layers and have exposed hot cores) but have very low luminosity because they are very small (small surface area). Using the Stefan - Boltzmann law \(L=\sigma AT^{4}\), a small \(A\) (even with a relatively high \(T\)) results in low \(L\).

Answer:

1. (3) it would be significantly more luminous than the Sun
2. (2) mass decreases
3. (4) Spectral Class G, luminosity of 1
4. (1) it is very hot but has a very low luminosity