Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
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Chapter 19, Problem 49Q
To determine
The surface temperature of Earth when the Sun will turn into a red giant. Use the Stefan-Boltzmann law. It is given that its luminosity increases by 2000 times of its present value while transforming into a red giant and the Earth radiates 2000 times more energy in order to maintain thermal equilibrium. The average temperature of Earth’s surface is
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When the Sun becomes a red giant, it's luminosity will be 2000 times its current value. The solar flux at Earth will also increase by a factor of 2000. Neglecting the greenhouse effect, the surface temperature of the earth is determined by thermal equilibrium: the flux of radiation absorbed equals the flux of radiation emitted. This means the Earth's surface flux must also increase by a factor of 2000. If the current average surface temperature is 58 degrees F, what will the average surface temperature be when the Sun is a red giant.
Express your answer in units of degrees Fahrenheit.
[Hint: Recall that the Stefan-Boltzmann law says that the flux F emitted by a blackbody is related to its surface temperature T (measured in Kelvins) is F=σT4 . Use this law in the form of a ratio, expressing T in Kelvins. Then convert back to Fahrenheit.]
Assume that when a certain main sequence star becomes a giant gas, its luminosity increases from L to 1000 L and its radius also increases from R to 1000 R. If the initial surface temperature is T, what approximately is the final surface temperature?
A. 0.032 T
B. 0.18 T
C. 0.0010 T
D. 0.010 T
If the nuclear fusion reaction of converting 4 H → He occurs at an
efficiency of 0.7%, and that mass is converted into energy according
to the equation E = mc2, then estimate the Main Sequence lifetime of the Sun (spectral type G2)
in years if the Sun (⊙) has a surface luminosity L⊙ = 3.839°ø1033
erg. Assume the Sun’s core (10% of the total mass) is converted
from H into He. The Sun’s mass is M⊙ = 1.9891 °ø 1033 g.
Chapter 19 Solutions
Universe
Ch. 19 - Prob. 1CCCh. 19 - Prob. 2CCCh. 19 - Prob. 3CCCh. 19 - Prob. 4CCCh. 19 - Prob. 5CCCh. 19 - Prob. 6CCCh. 19 - Prob. 7CCCh. 19 - Prob. 8CCCh. 19 - Prob. 9CCCh. 19 - Prob. 10CC
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Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, physics and related others by exploring similar questions and additional content below.Similar questions
- Appendix J lists the stars that appear brightest in our sky. Are most of these hotter or cooler than the Sun? Can you suggest a reason for the difference between this answer and the answer to the previous question? (Hint: Look at the luminosities.) Is there any tendency for a correlation between temperature and luminosity? Are there exceptions to the correlation?arrow_forwardIf the Sun were replaced by a white dwarf with a surface temperature of 10,000 K and a radius equal to Earth’s, how would its luminosity compare to that of the Sun?arrow_forwardif the nuclear fusion reaction of converting 4 H → He occurs at anefficiency of 0.7%, and that mass is converted into energy accordingto the equation E = mc2, then estimate the Main Sequence lifetime of the Sun (spectral type G2)in years if the Sun (⊙) has a surface luminosity L⊙ = 3.839×1033erg. Assume the Sun’s core (10% of the total mass) is convertedfrom H into He. The Sun’s mass is M⊙ = 1.9891 × 1033 garrow_forward
- A star such as our Sun will eventually evolve to a “red giant” star and then to a “whitedwarf” star. A typical white dwarf is approximately the size of Earth, and its surfacetemperature is about 2.5×103 K. A typical red giant has a surface temperature of 3.0×104K and a radius ~100,000 times larger than that of a white dwarf.a) What is the average radiated power per unit area by each of these types of stars?b) What is the ratio of total power radiated from the white dwarf over the power of thered giant? assume that both stars have emission e = 1arrow_forwardFor a main sequence star with luminosity L, how many kilograms of hydrogen is being converted into helium per second? Use the formula that you derive to estimate the mass of hydrogen atoms that are converted into helium in the interior of the sun (LSun = 3.9 x 1026 W). (Note: the mass of a hydrogen atom is 1 mproton and the mass of a helium atom is 3.97 mproton. You need four hydrogen nuclei to form one helium nucleus.)arrow_forward(a) The surface temperature of a star is 25,000 K and it has a luminosity about 1% that of our Sun. What kind of star is it? (B) The surface temperature of a star is 3,000 K and it has a luminosity about 104 time that of our Sun. What kind of star is it?arrow_forward
- If the Sun is well approximated by a black body with a temperature of 6,000◦ K, then how does its surface brightness compare (ratio) with the surface brightness of a 12,000◦ K star? How about a 3,000◦ K star?arrow_forwardBefore the star that became SN 1987A exploded, it evolved from a red supergiant to a blue supergiant while remaining at the same luminosity. As a red supergiant, its surface temperature would have been approximately 4000 K, while as a blue supergiant, its surface temperature was 16,000 K. How much did the radius change as it evolved from a red to a blue supergiant?arrow_forwardIn about 5 billion years, the sun will evolve to a red giant. Assume that its surface temperature will decrease to about half its present value of 6000 K, while its present radius of 7.0108 m will increase to 1.51011 m (which is the current Earth-sun distance). Calculate the ratio of the total power emitted by the sun in its red giant stage to its present power.arrow_forward
- Why do nebulae near hot stars look red? Why do dust clouds near stars usually look blue?arrow_forwardA star begins its life with a mass of 5 MSunbut ends its life as a white dwarf with a mass of 0.8 MSun. List the stages in the star’s life during which it most likely lost some of the mass it started with. How did mass loss occur in each stage?arrow_forwardA G2 star has a luminosity 100 times that of the Sun. What kind of star is it? How does its radius compare with that of the Sun?arrow_forward
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