As a star forms out of gravitational collapse of a cloud: it gains gravitational energy and loses kinetic energy. the star is much hotter than the initial cloud. The kinetic energy gain equals the loss in gravitational energy. the star is much hotter than the initial cloud, however, the kinetic energy gain is only half the loss in gravitational energy. the interior of the star is much hotter than the surface layers because the central density is higher.
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- Our sun, currently a yellow dwarf, will eventually evolve to a red giant star and then to a white dwarf star as shown in the figure. Assume that the sun radiates like a blackbody. Calculate the power radiated by the RED GIANT sun if its surface temperature is 3000 K.A main sequence star of mass 25 M⊙has a luminosity of approximately 80,000 L⊙. a. At what rate DOES MASS VANISH as H is fused to He in the star’s core? Note: When we say “mass vanish '' what we really mean is “gets converted into energy and leaves the star as light”. Note: approximate answer: 3.55 E14 kg/s b. At what rate is H converted into He? To do this you need to take into account that for every kg of hydrogen burned, only 0.7% gets converted into energy while the rest turns into helium. Approximate answer = 5E16 kg/s c. Assuming that only the 10% of the star’s mass in the central regions will get hot enough for fusion, calculate the main sequence lifetime of the star. Put your answer in years, and compare it to the lifetime of the Sun. It should be much, much shorter. Approximate answer: 30 million years.A window has heavy curtains in front of it. At night the curtains are closed to minimise heat loss. During the day the curtains are pulled aside exposing the glass window. How much heat is lost through the 1.0 m x 1.0 m square glass window pane that is 4mm thick when the inside temperature is 20 degree C and the outside temperature is -6 C (negative 6.0) in 12 hrs? ( 1m = 100 cm) (1m = 1000mm) %3D
- An interstellar cloud is observed at a wavelength of 2.898 µm. Estimate the temperature of the cloud.A stars wavelength is observed to be 200 nm. Calculate the approximate surface temperature of the starWhen 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.]
- -According to appendix C: radius of the sun is 7 x 10^8 mc) Derive the Schwarzschild criterion for the onset of convection in an ideal gas, namely d ln T d ln P 7-1 Y Explain all steps in your derivation, and justify any assumptions that you make. d) In a region of convective instability near the surface of a solar-type star of total mass M, the temperature and pressure are related approximately by the expression P KT5/2. Show that the temperature gradient for an ideal gas in hydrostatic = equilibrium in this convection zone is given by dT dr 2Gm(r)μ 5Rr² Further, assuming that the mass in the convection zone is small compared to M, show that at a depth h measured from the top of the convection zone, the temperature is approximately given by T = Ts + 2GMμ -h₂ 5RR² when his small compared to R, and Ts is the temperature at the top of the convection zone.