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 (*C*p)--to an

empirical relation:

*X *= ∑ BX ) ε n + 2*C*X ε 1/ 2 ,

(*n*

(3)

*n*=0

where *X *is the physical property being described. The empirical coefficients *B*X and *C*X

have been fitted to the model from experimental data. The parameter ε is a reduced temper-

ature [= (*T * *T*s)/*T*s], *T*s 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

*B*X )

(0

*B*X )

(1

0.941 698 0

1.130

128.281

1,239.075

*B*X )

(2

0.905 507 0

77.817

14.2

8,352.579

0.80

78.143

221.405

31,430.760

*B*X )

(3

54.290

64.812

48,576.798

*B*X )

(4

Max resid

1.2 ppm

0.2%

0.03%

1.9%

**Density**