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Quiz 3 for Physics 176
Professor Greenside
Tuesday, February 23, 2010
This quiz is closed book and no calculators or any other electronic devices are allowed.
All answers must be written on the supplementary blank pages. Please remember to write
your name and problem number on each extra page.
1. In a recent homework assignment, you showed (up to a constant factor) that the entropy
S
of a black
hole of mass
M
is given by
S
=
8
π
2
k GM
2
hc
,
(1)
where, to the nearest power of ten (zero signiﬁcant digits):
k
≈
10

23
J
/
K is Boltzmann’s constant,
G
≈
10

10
N
m
2
/
kg
2
is the gravitational constant,
h
≈
10

33
J
·
s is Planck’s constant, and
c
≈
10
8
m
/
s
is the speed of light.
(a)
(7 points)
Given that the energy of a black hole is its relativistic rest mass
U
=
Mc
2
, derive a
formula for the temperature
T
of the black hole in terms of its mass.
(b)
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 Spring '08
 Behringer
 Physics, Thermodynamics, Mass, Black hole

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