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6.10
(a) We start by using the method of Jacobians to reduce the derivatives
∂
∂∂
T
V
TH
VH
TP
TV
HT
PT
VT
HV
H
P
PV
dH
T
H
T
T
V
T
V
F
H
G
I
K
J
=
()
=
⋅
⋅
=−
F
H
G
I
K
J
,
,
,
,
,
,
,
,
,
,
,,
af
Now from Table 6.1 we have that
H
P
V
T
F
H
G
I
K
J
F
H
G
I
K
J
and
H
T
CV
T
V
T
P
T
VP
V
F
H
G
I
K
J
=+−
F
H
G
I
K
J
L
N
M
O
Q
P
F
H
G
I
K
J
P
alternatively, since
HUP
V
=+
H
T
U
T
T
dP
dT
VV
V
V
F
H
G
I
K
J
=
F
H
G
I
K
J
+
F
H
G
I
K
J
F
H
I
K
V
Thus
T
V
PVVTV T
CVPT
VPV TPT
H
V
V
F
H
G
I
K
J
=
−−
+
=
−+
+
afaf
Note:
I have used
P
V
V
T
P
T
V
F
H
G
I
K
J
F
H
G
I
K
J
F
H
G
I
K
J
.
T
V
TS
VS
ST
SV
S
V
T
S
T
C
P
T
S
V
F
H
G
I
K
J
=
=
⋅
⋅
=
F
H
G
I
K
J
F
H
G
I
K
J
F
H
G
I
K
J
,
,
,
,
,
,
,
,
,
,
V
(b) For the van der Waals fluid
P
T
R
Vb
V
F
H
G
I
K
J
=
−
,
P
V
RT
a
V
T
F
H
G
I
K
J
=
−
−
+
23
2
Thus
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T
V
RTV
V
b
a V
RT V
b
CV
R
V
b
H
F
H
G
I
K
J
=
−−
−
()
++−
+−
22
2
ns
V
after simplification we obtain
T
V
aV b
RTV b
CV bV
RV bV
H
F
H
G
I
K
J
=
−
−
()+−
2
3
C
and
T
V
RT
CV b
S
F
H
G
I
K
J
=−
−
V
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 Spring '11
 Yukov

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