4. The equation of state of a system constrains the form of the internal energy, and viceversa.
(In everything below, regard the number of particles N as fixed.)
(a) (5) Starting with the fundamental
Physics 607 Exam 2
Please show all signicant steps clearly in all problems.
1. Consider spin waves at the surface of a ferromagnetic solid, with a single polarization and
the dispersion relation = c k
Physics 607 Exam 1
Please show all signicant steps clearly in all problems.
1. We treated a diatomic molecule as a rigid rotor, but it actually stretches as it rotates
faster. If the rotations are tre
3. This problem involves a quantum ideal gas of fermions, for which a = 1 below, or bosons, for which a = !1 .
You are given the following:
! (" ! ) / kT &
#
PV 1
= ) ln % 1 + a e k
(
kT a k $
'
1
n !
Physics 607 Exam 1
Please be wellorganized, and show all significant steps clearly in all problems.
You are graded on your work, so please do not just write down answers with no explanation!
The vari
Physics 607 Exam 2
Please be wellorganized, and show all significant steps clearly in all problems.
You are graded on your work, so please do not just write down answers with no explanation!
And show
Physics 607 Final Exam
Please be wellorganized, and show all significant steps clearly in all problems.
You are graded on your work, so please do not just write down answers with no explanation!
And
+
C
V
4
V
A
4%
Si
j)
5
0
U
S
+
S
(U
>._
C
Ct
c$.
1
4
>
1%
S
C
t+
,
(U
>
C
NI
U
SI
I
I\A
4
ii
V
1
1.
V
t.

4
L
SI
;:
A.
c\H
II
:
U
U
c3
1
U
.
5%
Th
K
.c
>.
P4
&
V
ft
N
1%.
ct,
&
ft
1
+
14
I
&
\,
ft
ft

b
ft
5
H
0

ft
ft
5
4
.
II
n
rH
1

H
1
V
.,

ft
4_,
1
A
C,
J\r
t)

\
I
%1
Hi
hi
\
(%.n
H
0
1
i

1
1
( \._4_
)
4
B
iv.
44
*
L
Is
\i\
ft
+
I
4
III
1
1
L

ft
.

1
c
r4.
4,
j.
f
V
A.
U
I)
3
1
3.
ft
ft
3
A.J
ii
L
V
H
V
1
H
V
V
1
I
I
I)
ft
L r
4
1
I
ft
4
k

U
ii
4
Ij
%
rt
,
L
N
0
cfw_
H
flj
r4
LJ
4
7c
X.
1
I
II
4
II
4
4
\jc)
0
ft
4.
4
c
0
V
0
V
0
Iv
Hj
Hi
1
1
]
J4
c)
4
0
Physics 607 Final Exam
Please show all signicant steps clearly in all problems.
1. Let E, S, V, T, and P be the internal energy, entropy, volume, temperature, and pressure
of a system in thermodynamic