BE.011/2.772
Problem Set 5
Due March 17, 2004
Dill 9.1, 9.3, 9.8 and 9.10
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l
is
U
0
, and we are asked to show that this implies that
C
V
T
∂
T
V
∂
=
=
U
9.3
We are given that
V
∂
∂
0
. But we know that we can
0
. Thus,
T
E
,
p
0
T
E
,
T
f
,
This is useful, because we are likely able measure how the length of the crystal changes with the field
.
T
f
,
a) The first thing to note in this question is that we are considering
T
and
p
as variables (which we end
up holding constant). That means that we need to use the Gibbs free energy.
S
E
,
which we want. We need to first transform our equation to a new energy variable
T
9.8 The first thing to note is that if we take the cross derivatives of
dU
, we end up getting
not a function of
V
. For this, we need only prove that
permute the order of the derivatives, so we get that
.
0
SdT
Now if we take the cross derivatives we can get an expression for
Edp
0
dE
p
0
Ep
0
TdS
TS
pV
fdl
fl
Vdp
ldf
U
TS
TdS
TS
U
SdT
pdV
dU
dX
X
dU
H
G
dG
rather than
X(T,f,E)
.
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 Spring '05
 KimHamadSchifferli
 Thermodynamics, Entropy, Trigraph, ∂T V

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