COSMIC PERSPECTIVE
9th Edition
ISBN: 9780135729458
Author: Bennett
Publisher: PEARSON
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Chapter S4, Problem 56EAP
Long-Lived Black Holes. Some scientists speculate that in the far distant future, the universe will consist only of gigantic black holes and scattered subatomic particles. The largest black holes that conceivably might form would have a mass of about a trillion 10 12 Suns. Using the formula from Problem 54, calculate the lifetime of such a giant black hole. How does your answer compare to the current age of the universe? (Hint: Your calculator may not be able to handle the large numbers involved in this problem, in which case you will need to rearrange the numbers so that you can calculate the powers of 10 without your calculator.)
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Problem 2: Black hole – the ultimate blackbody
A black hole emits blackbody radiation called Hawking radiation. A black hole with mass
M has a total energy of Mc², a surface area of 167G²M² /c*, and a temperature of
hc³/167²KGM.
a) Estimate the typical wavelength of the Hawking radiation emitted by a 1 solar
mass black hole (2 × 103ºkg). Compare your answer to the size of the black hole.
b) Calculate the total power radiated by a one-solar mass black hole.
c) Imagine a black hole in empty space, where it emits radiation but absorbs nothing.
As it loses energy, its mass must decrease; one could say "evaporates". Derive a
differential equation for the mass as a function of time, and solve to obtain an
expression for the lifetime of a black hole in terms of its mass.
Which statement concerning black hole masses and Schwarzschild radii is not true?
A. Even an object as small as you could become a black hole if there were some way to
compress you to a size smaller than your Schwarzschild radius.
B. The more massive the black hole, the larger the Schwarzschild radius.
C. For black holes produced in massive star supernovae, Schwarzschild radii are typically a
few to a few tens of kilometers.
D. In a binary system with a black hole, the Schwarzschild radius depends on the distance
from the black hole to the companion star.
Assume the observable Universe is charge neutral, and that it contains n nuclei (hydrogen plus helium nuclei, ignoring other elements). Take the helium mass fraction as 1/4. How many electrons are there in the observable Universe? Enter your answer in scientific notation with one decimal place.
Value: n = 4*1080
Chapter S4 Solutions
COSMIC PERSPECTIVE
Ch. S4 - Prob. 1EAPCh. S4 - Prob. 2EAPCh. S4 - Prob. 3EAPCh. S4 - Prob. 4EAPCh. S4 - Prob. 5EAPCh. S4 - Prob. 6EAPCh. S4 - Prob. 7EAPCh. S4 - Prob. 8EAPCh. S4 - Prob. 9EAPCh. S4 - Prob. 10EAP
Ch. S4 - Prob. 11EAPCh. S4 - Prob. 12EAPCh. S4 - Prob. 13EAPCh. S4 - Prob. 14EAPCh. S4 - Prob. 15EAPCh. S4 - Prob. 16EAPCh. S4 - Prob. 17EAPCh. S4 - Prob. 18EAPCh. S4 - Prob. 19EAPCh. S4 - Decide whether the statement makes sense (or is...Ch. S4 - Prob. 21EAPCh. S4 - Prob. 22EAPCh. S4 - Prob. 23EAPCh. S4 - Prob. 24EAPCh. S4 - Prob. 25EAPCh. S4 - Prob. 26EAPCh. S4 - Prob. 27EAPCh. S4 - Choose the best answer to each of the following....Ch. S4 - Prob. 29EAPCh. S4 - Prob. 30EAPCh. S4 - Prob. 31EAPCh. S4 - Prob. 32EAPCh. S4 - Prob. 33EAPCh. S4 - Prob. 34EAPCh. S4 - Prob. 36EAPCh. S4 - Prob. 37EAPCh. S4 - Prob. 38EAPCh. S4 - Prob. 39EAPCh. S4 - Prob. 41EAPCh. S4 - Prob. 42EAPCh. S4 - Prob. 43EAPCh. S4 - Prob. 44EAPCh. S4 - Prob. 45EAPCh. S4 - Prob. 46EAPCh. S4 - Prob. 47EAPCh. S4 - Prob. 48EAPCh. S4 - Prob. 52EAPCh. S4 - Large-Scale Gravity. Suppose Earth and the Sun...Ch. S4 - Prob. 54EAPCh. S4 - Solar Mass Black Holes. Use the formula from...Ch. S4 - Long-Lived Black Holes. Some scientists speculate...Ch. S4 - Prob. 57EAPCh. S4 - Prob. 58EAPCh. S4 - Prob. 59EAPCh. S4 - Prob. 60EAP
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