Правило фаз Гиббса. Уравнения Клапейрона и Клаузиса

.
.
I,
10
10
,
(T
p, p V,
V T),
f(p, T, V) = 0,
p, T
V–
-
.
,
,
.
,
,
.
C.
,
( =2).
.
.
;
,
,
,
-
,
-
.
,
( – 1)
.
,
i
= 1,
xi –
-
i–
,
(10.1).
,
,
.
,
( -1)
( -1) .
–
,
-1) +2
(10.2)
,
.
.
–
-
-
,
-1) +1
,
-1) +3
(10.3)
,
,
-
(10.4)
1
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.
.
I,
10
,
-
.
.(
-
,
,
-
).
,
-1.
,
,1
1
i
2
i
-
2,
...........(10.5)
i–
.
,
.
-
,
-1)
(10.6)
-
( -1)
+n.
,
.
,
= ( -1)
+n -
=
-1)
+n
(10.7)
(10.8)
.
,
,
,
,
(
,
;
,
)
,
-
.
,
=0.
:
0 = 1-
+2;
= 3.
(10.9)
.
n
2.
2
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.
,
.
(10.8)
,
,
I,
10
n
2,
,
-
.
,
,
,
,
=
–
)= ( )
(10.10)
+2 – 1
(10.11)
,
:
=1–
+2 = 3 –
(10.12)
,
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,
,
.
,
,
,
,
.
,
.
,
=2),
,
( =1,
( =2, =1)
( =3, =0).
,
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,
-
,
.
,
0
100
-
.
,
-
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,
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.
3
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.
.
I,
10
.
–
,
.
,
,
.
-
dG = -SdT + Vdp+
S
G
T
idn
G
p
;......V
p
(10.13)
.....(10.14)
T
.1.
( )
( ) KCl.
-
..
(G1
.
1
G
2
G
.
1,
,
G < G2,
tr
1
1
G =f( )
G = G2 .
> tr 2,
G2)
.2.
G = f( )
-
2
1
tr
1
2
G >G .
G1
S
-
G2
,
tr
,
T
,
tr
.1.
4
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.
(
,
–
.
-
,
I,
10
-
-
).
G
G1
,
.
G2
G1
G2
T
.2
,
,
.
(
,
.3),
-
,
Q
......(10.15)
dT
c
Q = TdS,
2
G
T2
dS
G
T
S
dT .......(10.16)
p
;..........(10.17)
p
,
2
cp
T
G
T2
.....(10.18)
p
(
.
.4).
5
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.
.
,
I,
10
.
-
.
,
.
«
–
»,
.
G
G1
G2
T
.3
(
,
,
)
,
.
,
,
-
,
.
,
.
,
,
.
-
.
,
.
,
dG = dG
,
(10.19)
G
(10.19)
:
G
p
dp
T
G
T
dT
P
G
p
G
dp
T
T
,
V dp -S dT = V dp -S dT
dT .......(10.20)
p
:
(10.21)
6
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.
dp
dT
S
S
S
V
V
S
V
.
,
–
10
G = 0,
-
H
......(10.22)
T V
H/T
,
I,
S = H/T.
(10.22)
dT
dp
V
V
S
S
V
S
T V
......(10.23)
H
(10.22), (10.23)
,
,
.
.
,
.
1
2
.
:
,
,
,
,
.
dp/dT
,
1
;
dT/dp
,
-
,
.
(10.22)
(10.23)
,
d /d
V=V
V >V ,
–V
, . .
.
>0
H > 0.
,
.
(
,
,
),
V <V .
.
V
>V
.
.
,
,
V ,
100 V
= 30.2 , V = 0.0188 .
,
V
.
,
7
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.
V =RT/p
dp
dT
.
I,
10
(10.24)
H p
......(10.25)
RT 2
(10.25)
d ln p
dT
(10.25)
,
H
......(10.26)
RT 2
(10.26)
(
,
,
-
).
(10.25)
(10.26)
-
.
.
–
_
.
.
3.
H
= const (T)
:
H
T 2 dT ......(10.27)
R
d ln p
H
RT
ln p
–
C......(10.28)
.
–
.
=1
const
ln p
–
H
RT
H
S
R
RT
S
R
=
.
;
,
=
.....(10.29)
....(10.30)
8
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.
ln p
(10.28), (10.30)
H
S
.
R
RT
.
(10.31)
I,
10
....(10.31)
,
lnp
lnp
= -R tg
= -R tg
1/
.4
,
-
,
.
, (10.30)
(10.31),
-
=f( ),
.
,
,
(10.30).
2.
,
(10.27)
2,
ln
2
1,
p2
p1
-
1.
H
R
1
T2
1
......(10.32)
T1
3.
,
T
H
C p dT ......(10.33)
H0
T0
Cp =
i
cpi
)-
icpi
)
(10.34)
-
9
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.
H0
lg p
a
lg T
R
2.3RT
J–
.
b
T
4.575 2
.
c
T2
4.575 6
10
J ..(10.35)
,
(
I,
,
,
,
);
a=
i
ai
)-
i
ai
)
(10.36)
b=
i
bi
)-
i
bi
)
(10.37)
c=
i
ci
)-
i
ci
)
(10.38)
.
–
.
,
-
.
-
p, T
V.
,
.
.
V =f(p, T) –
,
,
.
,
–
.
.
:
-
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,
,
,
,
.
.
:
,
,
.
-
,
.
–
.
.
,
–
.
10
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I,
10
,
.
,
– ,
-
.
–V
T – V.
(
: , ,
)
.1.5
.
.5
.
,
,
= 1,
,
– + 2 = 1 – 1 +2 = 2.
=
.
,
,
,
-
.
.
p
T
T
.
H
(V
V )
(10.39)
11
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.
.
I,
,
.
,
.
(
10
,
).
.
p
T
T
H
(V
.
(10.40)
V )
,
=
,
–
,
,
+ 2 = 1 – 2 +2 = 1).
,
.
.
.
,
.
.
.
=
–
+ 2 = 1 – 3 +2 = 0, . .
.
–
.
.
,
.
12
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