Universe
11th Edition
ISBN: 9781319039448
Author: Robert Geller, Roger Freedman, William J. Kaufmann
Publisher: W. H. Freeman
expand_more
expand_more
format_list_bulleted
Concept explainers
Question
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
Expert Solution & Answer
Want to see the full answer?
Check out a sample textbook solutionStudents have asked these similar questions
A star such as our Sun will eventually evolve to a “red giant” star and then to a “white dwarf” star. A typical white dwarf is approximately the size of Earth, and its surface temperature is about 2.4 × 104 K. A typical red giant has a surface temperature of 3.2 × 103 K and a radius ~90000 times larger than that of a white dwarf. Take the radius of the red giant to be 6 × 1010 m.
What is the average radiated power per unit area of the red giant?_________W/m2
What is the average radiated power per unit area of the white-dwarf?________W/m2
What is the total power radiated by the red giant? _________W
What is the total power radiated by the white dwarf? ________W
Please show full work!
Thank you!
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.]
A red giant star might have radius = 104 times the solar radius,
and luminosity = 1730 times solar luminosity.
Use the data given below to calculate the temperature
at the surface of the red giant star.
Data:
solar radius R = 7 x 108 meters
solar luminosity L = 4 x 1026 watts
Stefan-Boltzmann constant
a = 5.67 x 10-8 W m² K-4
(in K)
A: 1226 OB: 1434 OC: 1678 OD: 1963 OE: 2297 OF: 2688 OG: 3145 OH: 3679
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
Ch. 19 - Prob. 11CCCh. 19 - Prob. 12CCCh. 19 - Prob. 13CCCh. 19 - Prob. 14CCCh. 19 - Prob. 15CCCh. 19 - Prob. 1QCh. 19 - Prob. 2QCh. 19 - Prob. 3QCh. 19 - Prob. 4QCh. 19 - Prob. 5QCh. 19 - Prob. 6QCh. 19 - Prob. 7QCh. 19 - Prob. 8QCh. 19 - Prob. 9QCh. 19 - Prob. 10QCh. 19 - Prob. 11QCh. 19 - Prob. 12QCh. 19 - Prob. 13QCh. 19 - Prob. 14QCh. 19 - Prob. 15QCh. 19 - Prob. 16QCh. 19 - Prob. 17QCh. 19 - Prob. 18QCh. 19 - Prob. 19QCh. 19 - Prob. 20QCh. 19 - Prob. 21QCh. 19 - Prob. 22QCh. 19 - Prob. 23QCh. 19 - Prob. 24QCh. 19 - Prob. 25QCh. 19 - Prob. 26QCh. 19 - Prob. 27QCh. 19 - Prob. 28QCh. 19 - Prob. 29QCh. 19 - Prob. 30QCh. 19 - Prob. 31QCh. 19 - Prob. 32QCh. 19 - Prob. 33QCh. 19 - Prob. 34QCh. 19 - Prob. 35QCh. 19 - Prob. 36QCh. 19 - Prob. 37QCh. 19 - Prob. 38QCh. 19 - Prob. 39QCh. 19 - Prob. 40QCh. 19 - Prob. 41QCh. 19 - Prob. 42QCh. 19 - Prob. 43QCh. 19 - Prob. 44QCh. 19 - Prob. 45QCh. 19 - Prob. 46QCh. 19 - Prob. 47QCh. 19 - Prob. 48QCh. 19 - Prob. 49QCh. 19 - Prob. 50QCh. 19 - Prob. 51QCh. 19 - Prob. 52QCh. 19 - Prob. 53QCh. 19 - Prob. 61Q
Knowledge Booster
Learn more about
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
- Using solar units, we find that a star has 4 times the luminosity of the Sun, a mass 1.25 times the mass of the Sun, and a surface temperature of 4090 K (take the Sun's surface temperature to be 5784 K for the sake of this problem). This means the star has a radius of.................... solar radii and is a .................... star (use the classification).arrow_forwardThe mass-luminosity relation describes the mathematical relationship between luminosity and mass for main sequence stars. It describes how a star with a mass of 4 M⊙ would have a luminosity of ______ L⊙. If a star has a radius 1/2 that of the Sun and a temperature 4 that of the Sun, how many times higher is the star's luminosity than that of the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125) If a star has a radius 2 times larger than the Sun's and a luminosity 1/4th that of the Sun, how many times higher is the star's temperature than that of the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125) If a star has a surface temperature 2 times lower than the Sun's and a luminosity the same as the Sun, how many times larger is the star than the Sun? (If it is smaller by a factor of 8, you would write 0.125 because 1/8=0.125)arrow_forwardAssuming stars to behave as black bodies stefan-boltzmann law to show that the luminosity of a star is related to its surface temperature and size in the following way: L = 4(3.14)R^2oT^4 where o= 5.67 ×10^-8 Wm^-2 K-4 is the stefan- boltzmann constant. Then use this expression together with the knowledge that the sun has a surface temperature of 5700k and radius 695 500km to calculate the luminosity of the Sun in units of Wattsarrow_forward
- A star with a radius 1.5 times that of the Sun has a surface temperature T=9,000 K. Calculate the luminosity of this star and express your answer in units of the Solar luminosity (the Solar luminosity = 3.84 x 1026 W and the Solar radius = 7 x 108 m)arrow_forwardThe apparent magnitude of a star is observed to vary between m = +0.4 and m = +0.1 because the star pulsates and hence continuously changes its radius and temperature. When at its peak brightness, the star’s radius has increased by a factor of two compared to its value at the mini- mum brightness. Determine the value of T+/T−, where T+ is the temperature when the star is at its peak brightness and T− is the temperature when the star is at it minimum brightness. Note: we expect T+/T− < 1 because the star’s temperature decreases as its radius increases.arrow_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 star population is composed of stars with masses in the range between 1M and 150M. The initial mass function is = 0 (M/M)-2.3, where o (Mo). The luminosity of a star = (M/M) 3.3. Calculate the percentage of the total luminosity of the stars in the population which is produced by stars with mass between 120M and 150M. scales with its mass as L/Larrow_forwardA star population is composed of stars with masses in the range between 1M and 150M. The initial mass function is = (M/M)-2.3, where = (Mo). The luminosity of a star scales with its mass as L/L = (M/M) 3.3. Calculate the percentage of the total luminosity of the stars in the population which is produced by stars with mass between 120M and 150M.arrow_forwardObservations show that stellar luminosity, L, and mass, M, are related by L x M3.5 for main sequence stars. Obtain an expression that relates the main sequence life time and the mass of a star. You should assume that the luminosity is constant throughout a star's main sequence life time, and that the amount of mass converted into energy by a star while it is on the main sequence is given by AM main sequence life time of a 20 Solar mass star given that the Sun is expected to spend 1010 years on the main sequence. Comment on the significance of your answer. fM, where f is a constant. Estimate thearrow_forward
- Many of the bright stars in the night sky are highly luminous normal blue stars (such as Acrux), and others are blue giants (such as Rigel) or red giants (such as Betelgeuse). Generally, such stars have a luminosity of 103 to 105 times that of our Sun! Ignoring any effects from our atmosphere, how bright would a star with a luminosity of 8380 solar luminosities be if it were located 620 light years from Earth? (You will need to convert some values.) W/m² For comparison, if you were 1 meter from a regular 100 W light bulb, the brightness would be 7.96 W/ m². (Since stars are not this bright, your answer should be considerably less!) Kind of amazing you can see these things, isn't it?arrow_forwardIf the surface Temperature of a star was about 11000.0 K instead of 7000.0 K what is the ratio of power per square meter of the 11000.0 K star compared to power per square meter of the 7000.0 K star? How many times greater is the magnitude of power per square meter of the 11000.0 K star compared to the 7000.0 K stararrow_forwardConsider a star for which the stellar power per unit area at distance 1 AU from the star is 3.7 kW/m^2. Assume the radius of the star is 0.005 AU (similar to Sol). What is the surface temperature of the star?arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- University Physics Volume 3PhysicsISBN:9781938168185Author:William Moebs, Jeff SannyPublisher:OpenStaxAstronomyPhysicsISBN:9781938168284Author:Andrew Fraknoi; David Morrison; Sidney C. WolffPublisher:OpenStaxStars and Galaxies (MindTap Course List)PhysicsISBN:9781337399944Author:Michael A. SeedsPublisher:Cengage Learning
- Foundations of Astronomy (MindTap Course List)PhysicsISBN:9781337399920Author:Michael A. Seeds, Dana BackmanPublisher:Cengage LearningStars and GalaxiesPhysicsISBN:9781305120785Author:Michael A. Seeds, Dana BackmanPublisher:Cengage Learning
University Physics Volume 3
Physics
ISBN:9781938168185
Author:William Moebs, Jeff Sanny
Publisher:OpenStax
Astronomy
Physics
ISBN:9781938168284
Author:Andrew Fraknoi; David Morrison; Sidney C. Wolff
Publisher:OpenStax
Stars and Galaxies (MindTap Course List)
Physics
ISBN:9781337399944
Author:Michael A. Seeds
Publisher:Cengage Learning
Foundations of Astronomy (MindTap Course List)
Physics
ISBN:9781337399920
Author:Michael A. Seeds, Dana Backman
Publisher:Cengage Learning
Stars and Galaxies
Physics
ISBN:9781305120785
Author:Michael A. Seeds, Dana Backman
Publisher:Cengage Learning