Understanding Our Universe
Understanding Our Universe
3rd Edition
ISBN: 9780393614428
Author: PALEN, Stacy, Kay, Laura, Blumenthal, George (george Ray)
Publisher: W.w. Norton & Company,
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Chapter 12.2, Problem 12.2CYU
To determine

The reason why Sun will become larger and more luminous when there is no hydrogen in its core.

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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
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.]
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.
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