application of chemicalthermodynamic information can spare the modeler from making
many tedious measurements in the laboratory. While few systems have been studied as
extensively as aqueous systems, there is a paucity of data at subzero temperatures. This
section discusses the physicalchemical properties of the solvent, water, as a pure liquid.
After a brief discussion of the relevant chemical thermodynamics, the section concludes
with a discussion of the properties of aqueous solutions at subzero temperatures.
Physical properties of liquid water
The state and movement of water in frozen and unfrozen ground is affected by several of
its physical properties, all of which change with temperature to some degree. Some of these
temperature effects are trivial, but others must be taken into account explicitly when mod-
eling solute transport.
The most up-to-date tabulations of the physicalchemical properties of liquid water
have been presented in the Journal of Physical and Chemical Reference Data (a recent cu-
mulative index is presented on page 1368 of volume 20). Many of these properties can be
modeled conveniently with the numerical equation-of-state package developed by Hill
(1990).
Most of the physical properties of supercooled water have been measured to roughly
35C. The temperature trends of these physical properties are consistent with a limiting
behavior for many physical properties of liquid water at a unique temperature, apparently
46C. Speedy (1987) fitted three properties of supercooled water--cubic expansion coeffi-
cient (α), isothermal compressibility (κT), and heat capacity at constant pressure (Cp)--to an
empirical relation:
X = ∑ BX ) ε n + 2CX ε 1/ 2 ,
(n
(3)
n=0
where X is the physical property being described. The empirical coefficients BX and CX
have been fitted to the model from experimental data. The parameter ε is a reduced temper-
ature [= (T Ts)/Ts], Ts being a limiting temperature that is assumed to be exactly 227.15 K
(46C). The fitted parameters of the Speedy model are presented in Table 1.
Table 1. Coefficients to Speedy's (1987) empirical equation for cal-
culating heat capacity, thermal expansivity, compressibility, and
viscosity of supercooled water.
Cubic expansion
Isothermal
Heat capacity at
coefficient
compressibility constant pressure Viscosity
α 103
κT
ν
Cp
1)
1 mol1)
(Pa s1)
Parameter
(K)
(bar
(J K
CX
0.80
20.0
14.2
26.312
1.802 180 3
4.120
24.952
144.565
BX )
(0
BX )
(1
0.941 698 0
1.130
128.281
1,239.075
BX )
(2
0.905 507 0
77.817
14.2
8,352.579
0.80
78.143
221.405
31,430.760
BX )
(3
54.290
64.812
48,576.798
BX )
(4
Max resid
1.2 ppm
0.2%
0.03%
1.9%
Density
Water at equilibrium
Compared with its other physicalchemical properties, the density of liquid water
changes little. Under a pressure of 0.1 MPa, the density of air-free water is at its maximum
at 3.98C. Under these conditions, the density of water is 1000 kg m3. This is the density of
5
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