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PHYSICS 7B QUIZ 1 SOLUTIONS
SECTION 104
CORY SCHILLACI
1a) Because of the speciﬁc form for the ﬁrst law, the heat capacity is simply given by
(1)
C
=
∂E
∂T
.
Since we have T as a function of
M
, it’s easiest to compute
(2)
1
C
=
∂T
∂E
=
1
c
2
∂T
∂M
=

~
c
8
πGk
1
M
2
1b) Substituting back in using the temperature formula (1) and doing a small bit of algebra
leads immediately to
(3)
C
=

~
c
5
8
πGk
1
T
2
.
As many of you noticed, this heat capacity is negative!
2a) The key fact here is that
dE
=
dq
=
TdS
. Armed with this we can just integrate
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This note was uploaded on 11/19/2010 for the course LECTURE 1 taught by Professor Yildiz during the Fall '10 term at University of California, Berkeley.
 Fall '10
 yildiz
 Physics, Heat

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