Generalized Clapeyron equation

 dAssm 

(

)

l

,

Sm,H 2O Sm,H 2O dT = Vml,H 2Od γ ls

By defining liquidsolid capillary pressure (Pa), pcs , as

it can be seen from eqs 60 and 68 that

Therefore, the capillary pressure of liquid water in a frozen porous medium can be

where T0 (K) is the freezing point of bulk liquid phase and ∆lsSm,H 2 O is the molar entropy of

*

melting for pure water (J K1 mol1).

Equation 77 is usually simplified by assuming that both Vml,H 2O and ∆lsSm,H 2 O are con-

*

stants, becoming

∆lsSm,H 2O

*

pcs

l

t.

(72)

=

Vml,H 2O

*

Equation 71 is often referred to as the generalized Clapeyron equation. The value of

*1

∆lsSm,H 2 O /Vm,H 2O can be calculated from physical measurements reported in the pub-

*

lished literature. Since

∆ls Hm,H 2O

*

∆lsSm,H 2O

*

(73)

=

T l+s

the molar enthalpy of melting for water measured by Haida et al. (1974), 6006.8 J mol1, can

be used. The value of Vml at 0C and atmospheric pressure is 18.0183 cm3 mol1 (Haar et al.

*

1984). The constant ∆ s m,H 2 O / Vml,H 2 O therefore is 1.2205 MPa K1.

*

l S*

Following the suggestion of Koopmans and Miller (1966), the Clapeyron equation has

long been applied to soil systems to estimate the matric potential of the liquid-water frac-

tion of frozen soils.

This argument begins with the standard definition of capillary pressure, pc (Pa):

pc = p(liquid soil water) p(ambient atmospheric pressure)

(74)

which is related to matric potential by

p

Ψ=- c

(75)

ρg

(Scheidegger 1974). A similar pressure, pi, may be defined for frozen ground to express the

pressure gradient across the ice/water interface in frozen ground

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