The Temperature Dependence of Soil Water Vapor Pressure1

JACOB W. KIJNE AND S. A. TAYLOE2

ABSTRACT

The temperature dependence of soil water vapor pres-sure was studied with a psychrometric vapor pressuretechnique in the range of 0.96 to 1.00 relative vapor pres-sures and below 0.96 with gravimetric and calorimetricheat of immersion techniques. For Millville silt loam atconstant water content, the relative vapor pressure de-creased with increasing temperature. Both differential andintegral entropy values were calculated. The differencebetween the partial molar entropy of pure free watervapor and the partial molar entropy of adsorbed waterled to the conclusion that soil water molecules are ar-ranged, on the average, less randomly than water vapormolecules. At the same time, comparison with the entropyof vaporization of pure water suggested a more randomarrangement of molecules in soil water than in free liquidwater.

THE STATE OF wATEK in the soil can be expressed asa function of three intensive variables (temperature,

pressure, and the amount of water in a unit mass of drysoil) along with a number of other composition variables.Sometimes soil bulk density is explicitly included, but fora particular soil it is frequently acceptable to combine allpertinent composition variables into a single solute vari-

able. The Gibbs or chemical potential of soil water ex-presses the state of the soil water when no external forcefields are acting. At any constant temperature, the chemi-cal potential of soil water may be expressed as a loga-rithmic function of the relative activity (4, pp. 226-227),which, in turn, is the same as the relative water vaporpressure in equilibrium with moist soil samples, assumingwater vapor acts as an ideal gas.

The effect of temperature on the relation between aque-ous vapor pressure in equilibrium with clays has beenstudied by several investigators, and the results have some-times been inconsistent (13). Vapor pressure methods inwhich samples are placed over solutions that assure dif-ferent constant relative humidities in desiccators have notalways yielded results that agree with data from calori-metric methods on the same samples.

When equilibrium is established between clay or soilwater and a constant vapor pressure and temperature, theresults are expressed in terms of the specific Gibbs freeenergy, A^tw (4, pp. 225-227), using the relation

AHW = ill = (RT/M)ln p/po [1]

where \j/ in this case is the soil water potential (19), Mthe molecular weight of water, and p and p0 are, re-spectively, the vapor pressure of soil water and the vaporpressure of pure water at the same temperature and totalpressure. Using this method on samples equilibrated indesiccators, Robins (17) presented data for Yolo loam sug-gesting that water potential decreases with increasingtemperature. The decrease was, to a first approximation,proportional to the ratio of the absolute temperatures.Klute and Richards (11), using thermocouples to measurethe vapor pressure over a soil sample, obtained a similarresult using Na-saturated montmorillonite, but found no

596 SOIL SCIENCE SOCIETY PROCEEDINGS 1964

differences when they used Chino clay soil. Martin (12),using a high vacuum technique also reported results thatwould indicate the water potential of Na- and Li-kaolinitedecreases with increasing temperature.

Results obtained in soils at a higher range of waterpotentials by the use of tensiometers to measure \jj haveshown an increase in potential with increasing tempera-tures (20, 21), in opposition to the vapor equilibrationresults.

The reason for this discrepancy is not immediately ap-parent. It may be associated, however, with the fact thatpsychrometric measurements of the soil moisture poten-tial include the influence of both solutes and of soil matrixon the water potential, while tensiometers (and pressureapparatus) measure only the matrix components and areindependent of solute effects (18).

Soane3 observed that the electrical conductivity of thesolution expressed from Millville loam in a pressure mem-brane apparatus increased somewhat with temperature.Although small at atmospheric pressure, this temperature-induced effect increased at higher air pressures that areused with pressure membrane and pressure plate appara-tus. There is also some evidence that the release of non-exchangeable ions is greatly increased as the temperatureincreases (1, 5). Either or both of these phenomena wouldexplain why the relative vapor pressure decreased withincreasing temperature while the tensiometer measured anopposite effect.

Temperature Dependence of Aqueous Vapor Pressureand Soil Moisture Tension

Two analogous ways of analyzing the temperature de-pendence of the aqueous vapor pressure were developedin an earlier paper (18) from the general theory of Hill(6). The final equations from the earlier study are givenhere as a basis for the present study. Based on solutionthermodynamics, the temperature dependence of the aque-ous vapor pressure of soil water is [eq. 22 from (18); seealso eq. 50 from (6)]:

(dp/dT), °wG - S

vwG

dir

d T [2]

where p is the aqueous vapor pressure, T is Kelvin tem-perature, SwG and vwG are the partial specific entropy andvolume of water vapor, Sw is the partial specific entropyof soil water, P is the total pressure on the system, O isthe mass of water per unit mass of dry soil, and

1 m-1*v mv7f, (9Mw /9 rk>p,T>9rr. drkWU K—I J

where F is the mass of any given component per mass ofdry soil and j and k indicate different species of the mcomponents in the system.

From adsorption thermodynamics [eq. 23 from (18);see also eq. 60 from (6)]:

S ~(dp/dT)T

wG - S *wvwG

diT_!d T [3]

where Sw° is the partial specific surface entropy of ad-sorbed water, and

"Soane, B. D. An application of a thermodynamic flowequation to water movement in unsaturated soil. UnpublishedM.S. thesis, Utah State University Library, 1958. Logan.

IT =y1 m-1

vwG k=l

where y is the amount of any given component per unitmass (or volume) of water.

The surface potential, <£, is given by [eq. 10 from (18)]:

= RT 6 d In p [4]

which must be evaluated down to zero vapor pressure.To do this requires that 6 be known as a function of psufficiently near zero that the curve may be extrapolatedthrough the origin (7).

As used here, equation [2] leads to differential thermo-dynamic quantities, and [3] leads to integral quantitiesas pointed out by Martin (12). The two terms try and7Ty are commonly known as osmotic effects.

The analogous equations for the pressure measured bya tensiometer are [Eq. 14 and 15 from (18)]:

^wf " Swvwf

and3 ,,wf - S *w

vwf

AS

vwf

vwf

[5]

[6]

where Swf and vwf are the partial specific entropy andvolume of liquid water, and Pf is the pressure on thewater inside the tensiometer. In this case, P is the atmos-pheric pressure that is on the soil water.

By comparing equations [2] and [3] with [5] and [6],we see at once that the two methods provide a quantita-tive means for differentiating between the matric andsolute influences incorporated in the vapor pressure meas-urements and the purely matric influences recorded bytensiometers (18). In addition, we have assumed that, toa satisfactory order of approximation, the adsorbent (soil-solid) surface is inert to changes in temperature between12° and 28.8°C. This assumption may cause some diffi-culties in interpreting the results in soil systems, but themeasured values are still well defined thermodynamicfunctions (6, 7, 18).

EXPERIMENTAL PROCEDUREThe relative water vapor pressure over Millville silt loam

samples, a highly calcareous soil with specific surface area of79m.2 per g. by the ethylene glycol method, with moisturecontents varying between 4.3 and 15.7%, was measured withthermocouples made according to the design of Richards andOgata (16). The sample tubes were completely immersed ina constant temperature bath controlled to a precision of ±0.001 °C. or better (10). Measurements were made in eachsample at four different temperatures. Changes in moisturecontent were avoided by keeping the sample chambers sealedat all times except when the water droplet was being placedon the psychrometer. In order to avoid the influence oftemperature on the psychrometer, calibration curves were madeover KC1 at several temperatures covering the range used inmeasurements.

The range of moisture contents that could be studied withthe psychrometric vapor pressure procedure was limited to therange of relative vapor pressures from 1.000 to about 0.94because of inaccuracies in the procedure at lower vapor pres-sures. The necessary supplemental data for the relative vaporpressure in the range from 0.000 to 0.939 were obtained fromheat of wetting measurements on samples equilibrated indesiccators containing atmospheres of different known valuesof relative humidities held constant by sulfuric acid solutions in

KIJNE AND TAYLOR: TEMPERATURE DEPENDENCE OF SOIL WATER VAPOR PRESSURE 597

Table 1—Soil water pressure (mbars) over Millville siltloam, glass beads, and sand at different moisture

contents and temperatures.

Table 2—Differential values of (Sw0 — Sw) in joules permole-degree for Millville loam at different tempera-

tures and soil moisture contents.

Moisturecontent,

4.35.46.77.78.1

11.311.715.7

T = 12.00'C.PQ » 14. 017

_ _--

13. 80613. 85313. 89314. 01314. 013

--

T = 16. 00 -C.PO= 18.173.

Millville silt loam17.24017.81317.84617.94617. 93618. 14618.13318. 159

T = 21.05-0.PO = 24. 937

23. 13323. 919

_-24.59923. 65324.85324.83924.897

T = 28. 80- O.P - 39. 594

O

36.59937.47938.419

---_

39. 39039.41239.426

Glass beads (average diameter 29 microns)7.4

0.160.220.34

14. 016

14. 01314. 01514. 016

Mean standard deviation = ±

—Sand

18. 16818. 17218. 172

.005

24.935

24.93024.93324.935

39. 590

—----

the base of the desiccators (8). The weight of each samplewas measured at various times. From the changes in weight,the moisture contents were calculated. The heat evolved whena sample was immersed in liquid water was measured incalorimeters that were modifications of those described byPierce et al. (15).

The calorimeters were placed in a constant-temperaturebath. Temperature equilibrium inside the calorimeter wasreached in about 10 hours. At that time, the temperature ofthe liquid in the calorimeter changed less than 0.001 °C. in15 minutes, which was the time required for one calibrationand the accompanying measurement. The temperature risethat resulted from the sudden immersion of the sample wasmeasured with a 100,000 ti thermistor in a Wheatstone bridgecircuit and recorded on a millivolt recorder and calibratedagainst the heat input measured electrically. Heats of wettingwere measured in this manner with a precision of ±0.05•ioules per g. soil.

2850° C

20 40 60 80 100 120

SURFACE POTENTIAL-JOULES PER MOLE

I Fig. 1—Variation of vapor pressure (mbar) with surfacepotential (joules per mole) for Millville loam at differenttemperatures.

9t 12.00 'C.0.0100.0180.0240.0300.0450.0600.0960.1200.150

Mean standard devil

93127165166177152150150150

ition for ASW la ±

16.00 -C. 21.05 'O.141146145157159164162161161

2. S joul

181175144151166164174173173

es/mole- degree.

28.80 -C.229213289166146146146146146

Units of 6 are grams water/grams dry soil,

RESULTSThe aqueous vapor pressures measured over Millville

silt loam, a sample of 29 ^ glass beads, and one of washedsand, are presented in Table 1. These values show con-sistent temperature-induced changes for the individualsamples. However, an unexpected decrease in vapor pres-sure occurred at some temperatures with the increasefrom 11.3% to 11.7% water. The decrease may havebeen related to slight differences in how the sample waspacked in the sample tube or to slight differences in thesize and shape of the vapor space in the thermocouplepsychrometer tube. However, the temperature dependencewas determined on a single sample in which the packing,shape of cavity, and moisture content was constant.

According to [2], differential values of (SwQ — Sw)may be obtained directly from a plot of vapor pressure asa function of temperature at constant moisture contentif the change in the composition of the soil solution thatresults from temperature change is assumed to be negli-gible. Since both differential and integral enthalpy values(HwS — Hw) can be calculated from the correspondingwater potential and entropy values by means of the Gibbs-Helmholtz equation A/JW = AHW — TASW, where A,u,w isobtained from [1], anything that is said about ASW values

< 30-o

7 25

uiCCO

3 20IEO-

S.

a-ui

15

10

100

12 16 20 24 28CELSIUS TEMPERATURE - DEGREES

Fig. 2—Variation of vapor pressure with temperature forMillville silt loam at different values of surface potential.

598 SOIL SCIENCE SOCIETY PROCEEDINGS 1964

Table 3—Integral values of (SwG — S,,*) in joules permole-degree for Millville loam at different surface

potentials (^>) and four temperatures.*

0t2030405060708090

100<SWG - SPW>!

12.00 'C.9072645276809079

106115

16.00 'O.10575695679828686

108116

21.05 'C.12078756183859394

110118

28.80 *C.

1598487718994

108112114119

t Mean standard deviation of AS * Is meaningless here because of a possible error IDcalculating 0 ; the maximum uncertainty Is estimated to be about ± 1 % and certainlynot more than ± 10 %.

t Units of <£ are joules/mole.§ Calculated from the values of Glauque and Stout (3).

Table 4—Integral values of (Spw — Sw*) in joules permole-degree for Millville silt loam, obtained

from heats of wetting.*

0 t9381280

16.00 -C.-1.1-2.3-18.4-37.5

*975510

21.05 °C.

-1.1-9.1-45.7-53.1

*1049976

28.80 'C.-1.1-1.8-40.1-41.1

t The standard deviation of the mean heats of Immersion from which these data werecalculated varied from ± 8% In dry soil (low £) to± 17% In the wettest soil (high *).

t The units of 0 are joules/mole.

is equally valid for AHW values; consequently, the latterare not further considered here. The differential valuesare given in Table 2.

Values of the surface potential <£ were determined bygraphically integrating the curve relating moisture contentand the natural logarithm of vapor pressure for the dif-ferent temperatures over the range from O to appropriatevalues of the vapor pressure p according to [6]. Datawere measured as low as 0.4% water, corresponding to5 mbars of vapor pressure; below this point the datawere extrapolated to zero according to Hill et al. (7).

Vapor pressure is plotted as a function of <£ for fourdifferent temperatures in Fig. 1. At selected values of <£,vapor pressure was read from each of the different tem-perature curves and used in constructing Fig. 2. The in-tegral values of (SwG — Sw*) were obtained by measuringthe slope of the curves of Fig. 2 and assuming surfaceconcentration of salts to be independent of temperature.The integral values thus obtained are presented in Table3 for four temperatures.

The integral values reported in Table 3 differ slightlyfrom those reported earlier (18) and are considered morereliable because the present values are based on psychro-metric data for high <£ values and gravimetric data forlow $ values obtained for the same soils at the same tem-peratures, while the gravimetric data for the earlier sampleswere taken at different temperatures.

Heat of wetting data were also used to determine inte-gral values of (Sw* — Spw) using equations taken fromChessick and Zettlemoyer (2) and changed to our no-tation

T(S* - S ) = [hv w pw' L aw - RT In p/p [ 7]

in which hao is the heat of wetting of the clean dry ad-sorbent, haw is the heat of wetting of the adsorbent uponwhich Naw moles of water had been preadsorbed. Thesubscript pw denotes pure free water. Appropriate <f> valuescorresponding with the moisture contents of each sample

were obtained from Table 1 and Fig. 1. The derived <£values were used with the measured heats of wetting togive entropy values form [7]. These values are presentedin Table 4.

DISCUSSIONRelative soil water vapor pressure, when calculated

from the vapor pressure data in Table 1, varies inverselywith temperature for Millville silt loam. This inverse re-lation confirms the data obtained by Robins (17) for soil,by Klute and Richards (11) for Na-saturated montmoril-lonite, and by Martin (12) for Na- and Li-kaolinite.

The differential entropy values in Table 2 show rela-tive minimum values between moisture contents of 1 and3.0%, and the integral entropy values (Table 3) showminima at <j> = 50 joules per mole. Similar minima inentropy relations are frequently observed for physical ad-sorption, and are expected whenever there is strong bind-ing of adsorbate to adsorbent. Hill and his associates (7)have predicted such minima from the BET equation (Bru-nauer-Emmett-Teller) for multilayer adsorption and shownthat they should occur near the point where one molecu-lar layer is adsorbed. Hill et al. (7) also show that thedifferential and integral values may produce completelydifferent relations with little meaning being associatedwith the differential relations.

The integral values of (SwG — Sw*) for Millville siltloam (Table 3) indicate that the entropy of water in thesoil system is less than in the gaseous state. The entropyof vaporization (SwG — Spw), where Spw is the entropy offree liquid water, is also given in Table 3 for the tem-perature used (3). All the obtained values of (SwG — Sw°),except two, are less than the entropy of vaporization.

The temperature-induced changes in the thermodynamicquantities of the soil system, which appear to result inan inverse relation between soil-moisture potential andtemperature under conditions of constant water content,may be attributed to one or more of three factors: (a)interaction between water molecules and the surface ofthe adsorbent; (b) increase in the release of exchangeableand nonexchangeable ions; (c) replacement of specific ionson the soil particles, and a consequent change in the physi-cal properties of the system.

The inverse relation between water potential and tem-perature was also observed for glass beads and sand(Table 1). These materials do not have exchangeable ionsand are supposed to be inert. Jurinak et al. (9) have no-ticed, however, that an aqueous slurry of the kind ofglass beads in this study produced a pH of 9.7. Washingwith dilute acid temporarily reduced the pH, but aftera short time, the beads assumed their original alkalinestatus. This would suggest that the solubility of the glassbeads may not be negligible.

Although the sand samples had been washed with dis-tilled water before they were used, it is still possible thatsome adsorbed impurities remained. Consequently, thereremains a finite possibility that temperature-induced os-motic effects resulted in the observed change in thermo-dynamic quantities of the soil-water system as well asof the glass beads and the sand samples.

Oster and Low (14) concluded from differential entropymeasurements on montmorillonite that water became lessorderly with increasing water content of the clay. Al-though they mentioned both swelling of the clays anddifferent ionic effects, they attributed their results en-

KIJNE AND TAYLOR: TEMPERATURE DEPENDENCE OF SOIL WATER VAPOR PRESSURE 599

tirely to changes in orderliness of water molecules of thesystem during the hydration process. The difficulty indoing this with differential entropy data has already beenpointed out (6, 7, 18, 12, 13). The changes observed byOster and Low may actually be similar to those involvedin the decrease of the difference between the entropy ofwater vapor and of soil water that occurred when thesurface potential changed from 20 to 50 joules per mole(Table 3). This would correspond to an increase in thedifference between the entropy of soil water and purewater.

Our entropy data (Table 3) for cf, = 20 at 21.05 and28.80°C. would support the hypothesis that soil watermolecules are more orderly than liquid water molecules;at all other values, the opposite is more likely. The twovalues of (SwG — Sw°) that are greater than the entropyof vaporization coincide with low surface potential wherehydration of adsorbed ions may occur. At this watercontent, hydration of ions may have had a significantinfluence on the entropy, in which case it would be in-correct to assign the entire entropy change to the condi-tion of soil water.

The difference between the entropy of soil water andthe entropy of pure water as obtained from heats of wet-ting (Table 4) reaches its maximum value for relativelydry soil (<£—>0) (surface potential <£ from 30 to 50 joulesper mole) and decreases with increasing moisture content(high (fi values).

The integral values of (Sw* — Spw), obtained fromheats of wetting, decrease to about 1 joule per mole-degree for a surface potential value of 100 joules permole. The difference between the entropy of vaporizationand the entropy values in Table 3 should also give (Sw°— Spw), which proves to be 5 to 9 joules per mole-degreefor the same value of surface potential. This apparentdiscrepancy may result from perturbations of the soil sur-face, from a temperature influence on the solubility ofsoil minerals, and hence on the solute potential whichwould be influencing the vapor pressure data even in thevery wet soils, or, more likely, a small bias could havebeen introduced in calculating <f, from [4] if the extrap-olation of the curve of moisture content vs. vapor pres-sure to the origin did not follow exactly the true relation(7). Failure of vapor pressure data and calorimetric datato give entropy data that agree has been observed before(12). The reason for such failures remains to be explained.

There are several points that suggest that the changesin the thermodynamic quantities are more likely causedby an interaction between water molecules and the sur-face of the adsorbent: first, the close similarity betweenthe observed temperature dependence of the water poten-tial in so diverse materials as Millville silt loam, glassbeads, and sand samples; second, Soane's4 observationthat the temperature-induced increase in salt concentra-tion of the soil solution of Millville silt loam is small atatmospheric pressure but increases at higher pressures;third, Jurinak et al. (9) showed that polymolecular adsorp-tion of water takes place on the surface of glass beads,even of Pyrex beads, which they had prepared and whichthey knew to be much less soluble than the commercialbeads.

Consequently, we are inclined to agree with Martin(12, 13) that quantities of the system, which were in-duced by temperature variations, can be attributed pri-

4Soane ibid.

marily to the interaction between water molecules andthe surface of the adsorbents. Osmotic effects may havean additional influence that appears to be less importantthan the interaction effect. Hence, we conclude that thedata in Table 4 from heats of wetting and the data inTable 3 from vapor pressure measurements both indicatethe soil water molecules are less orderly than free waterbut become more orderly as the moisture content of thesoil increases until in wet soil they approach the orderli-ness of pure free water molecules.