The most recent accurate measurement of the enthalpy of fusion for water to ice appears to
be that of Haida et al. (1974), who reported
∆ls HH 2O (Trw , prc ) = 6006.8 J mol 1.
*
By the relation (McGlashan 1979)
∆α HB = Tα +β ∆α SB
*
*
(14)
β
β
we find that
∆lsSH 2O (Trw , prc ) = 21.990 85 J K 1 mol 1
(15)
*
which allows the evaluation of eq 12:
* (Trw , prw ) - * (Trc , prc ) = -SB (Trc , prc )(Trw - Trc )HB (Trw , prc ) - HB (Trc , prc )
*
*
*
(16)
B
B
prw
prw
[
]
VB (Trw , p) dp +
VB (Trw , p) dp = 1.667 37 kJ mol
1
-Trw SB (Trw , prc ) - SB (Trc , prc ) +
∫
∫
*
*
*
*
prc
prc
Supercooled water
The standard-state chemical potential of supercooled water at temperatures between
0C and 46C under pressures of 1 atm can also be calculated by eq 12. In this temperature
*
range, the changes in Cp ,H 2O(l) are described by eq 10. The definite integrals needed to
make these calculations are as follows:
(
)
(
)
B(2) - 3B(3) + 6B(4) T 2 - T 2
(
)
B(3) - 4B(4) T 3 - T 3
BC4) Tf4 - Tr4
(
Tf
Cp
Cp f
Cp
rw
*
rw
Cp,H2O(l)
Cp
+
Cp f
w
+
∫
dT =
p
2Ts2
3Ts3
4Ts4
T
Trw
(
)
B(1) - 2B(2) + 3B(3) - 4B(4) T - T
T
Cp
Cp f
rw
Cp
Cp
+ 2CCp arctan f - 1
+
Ts
Ts
T
[
]
- 2CCp arctan rw - 1 + BC ) - BC ) + BC ) - BC ) + BC ) ln(Tf ) - ln(Trw )
(0
(1
(2
(3
(4
(17)
p
p
Ts
p
p
p
and
(
)
(4)
BC Tf5 - Tr5
Tf
Cp,H 2O(l) dT = BC - BC + BC - BC + BC (Tf - Trw ) +
w
∫
(0)
(1)
(2)
(3)
(4)
p
*
p
p
5Ts4
p
p
p
Trw
(
)
(
)
B(2) - 3B(3) + 6B(4) T 3 - T 3
B(3) - 4B(4) T 4 - T 4
Cp
Cp f
Cp
Cp f
rw
rw
+
Cp
+
3Ts2
3
4Ts
(
)
B(1) - 2B(2) + 3B(3) - 4B(4) T 2 - T 2
T
Cp
Cp f
rw
+
Cp
Cp
T
+ 2CCp Ts f - 1 - rw - 1 .
(18)
Ts
Ts
2Ts
11
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