80
70
60
10
0
10
20
30
50
40
Temperature (C)
Figure 6. Measured values of interfacial tension of water against its
vapor at a range of temperatures.
Water at equilibrium
The heat capacity of liquid water can be calculated accurately from the equation of state
for liquid water. The equation-of-state models for water are comprehensive and algebra-
ically complex. Fortunately, there are several computer programs available (Harr et al.
1976, Hill 1990) that can be used to calculate accurately the thermodynamic properties,
including heat capacity.
Supercooled water
As noted above, Speedy (1987) has presented equations for the various thermodynamic
properties of supercooled water. His expression for the constant-pressure heat capacity of
supercooled water is
Cp = ∑ BCn) ε n + 2CCp ε 1/2 .
(
(10)
p
n=0
The regression estimates of these parameters are presented in Table 1. Figure 7 presents the
isobaric heat capacity of water as calculated by the models of Hill (1990) and Speedy (1987).
250
200
150
100
50
60
40
20
0
20
40
Temperature (C)
Figure 7. Heat capacity of water as predicted by Hill's (1990) equa-
tion-of-state model (for t ≤ 0C) and Speedy's (1987) empirical for-
mula (for t < 0C).
9
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