Physics for Scientists and Engineers
6th Edition
ISBN: 9781429281843
Author: Tipler
Publisher: MAC HIGHER
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Chapter 7, Problem 74P
To determine
The rate of mass gain by black hole.
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The typical core-collapse supernova has an energy budget of about 1046 J. This energy comes
from the gravitational potential energy of an inner core with mass Mic, which collapses from an
initial radius of 5 x 106 m down to the final radius of 50 km. Estimate Mic, in solar masses, for
this to be a realistic energy source of the core-collapse supernova. You may assume that the
density before the collapse is uniform.
Discuss briefly how a Type la supernova is different from a core-collapse supernova from a
massive star?
double line
The velocity curve
spectroscopic binary is shown in the sketch.
The system is viewed edge-on, i.e., with an
inclination angle of i = 90°, so that the
maximum possible Doppler shifts for this
system are observed.
for a
400
So = U, Ani
300
200
no - V Ain i
100
-100
-200
-300
400
• 1 2 3 .
S 6 7 8
10
Time (days)
Find the mass ratio, m1/m2, of the stars.
Express your answer as a fraction like a/b
Doppler Velocity
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.
Chapter 7 Solutions
Physics for Scientists and Engineers
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