AD-751 025

THE THERMAL CONDUCTIVITY OF PURE WATERAND STANDARD SEA WATER AS A FUNCTION OFPRESSURE AND TEMPERATURE. PART I. PUREWATER

V. John Castelli, et al

Naval Ship Research and Development CenterAnnapolis, Maryland

October 1972

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NAVAL.SHIP RESEARCH AND DEVELOPMENT CENTERBethesda, Md. 20034

r4HE THERMAL CONDUCTIVITY OF PURE WATER AND STANDARDjil •SEA WATER AS A FUNCTION OF PRESSURE AND TEMPERATURE

U PART II -PURE WATER

I 4 by4 - V. John Castelli and E. M. Stanley

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0) 0 October 1972 Report 3566-11

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The The:mal Conductivity of Pure Water and Standard Sea Water as aFunction of Pressure and Temperature

4 DrLSC ar, TIV C NOT ES (Type otfreport 4ind jll u g.. .lacj

Part II - Pure Waterb AU THOR,S) (-lrst name, middle initial, last nanw¢.)

V. J. Castelli and E. M. Stanley

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yResults of the experimental observations of the thermal conductivityof pure water for the pressure range of atmospheric to 1400 bars andtemperature from 04-30"" C are presented. Data were obtained with aconcentric cylinder apparatus and have an estimated accuracy of about1%. These data are compared with those previously reported in the

3- literature. Historicail relationships proposed to describe the behaviorof the thermal conductivity are investigated, and tneir inadequacy

Ii (Authors)

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Security Classification UNCLASSIFIED14. LINK A LINK B LINK CKEY WORDS

ROLE WT ROLE WT ROLE WT

WaterThermal conductivityPressureTemperatureApparatus

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NAVAL SHIP RESEARCH AND DEVELOPMENT CENTERfit, BETHESDAMD. 20D34

THE THERMAL CONDUCTIVITY OF PURE WATERAND

STANDARD SEA WATER AS A FUNCTION OF PRESSURE AND TEMPERATURE

PART II - PURE WATER

bySV. John Castelli and E. M. Stanley

- Approved for public releasc, ,stribution unlimited.

October 1972 Report 3566-11

ABSTRACT

F Results of the experimental observationsof the thermal conductivity of pure water forthe pressure range of- atmospheric to 1400 barsand temperatures from 0o-30 C are presented.Data were obtained with a concentric cylinderapparatus and have an estimated accuracy ofabout 1%. These data are compared with thosepreviously reported in the literature. His-torical relationships proposed to describethe behavior of the thermal conductivity areinvestigated, and their inadequacy noted.

_II,

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ADMINISTRATIVE INFORMATION

Thiz report is part of Task Area SF52-552-101, Task 12874,Work Unit 1-2853-101, as described in the 1 July 1972 ProgramSummary.

The mention of proprietary products or devices by namein no way implies that they are endorsed by the U. S. Navy tothe exclusion of other similar products or devices, nor may suchmention be made in commercial advertising.

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TABLE OF CONTENTS

Pageý

ABSTRACT iiiADMINISTRATIVE INFORMATION ivINTRODUCTION 1EXPERIMENTAL INVESTIGATION 1PRECISION, ACCURACY, AND ERROR-ANALYSIS 1RESULTS 3DISCUSSION 4THEORETICAL RELATIONSHIPS 5CONCLUSIONS 7TECHNICAL REFERENCES 8LIST OF FIGURES

Figure 1 - Graph; Experimental Data for the ThermalConductivity of Pure Water as a Functionof Pressure for Various Temperatures

Figure 2 - Graph; Thermal Conductivity of Pure Wateras Determined by Equation of Least Squaresfor Experimental Data

Figure 3 - Graph; Comparison of Powell's ProposedValues for Thermal Conductivity of PureWater at Atmospheric Pressure with Resultsof these Experiments

Figure 4 - Graph; Historical Determination of theEffect of Pressure on the Thermal Conductivityof Pure Water for a Temperature of 300 C

Figure 5 - Graph; Historical Determination of theEffect of Pressure on the Thermal Conductivityof Pure Water for a Temperature of 00 C

INITIAL DISTRIBUTION

'1

I.m • • •• • n . • •• •• • • i. • •• •

[• L INTRODUCTIONA continuing part of the oceanographic research at thisUi• laboratory is the determination of the physical and chemical prop-

erties of sea water and water at pressure. Projects previouslycompleted have included viscosity and refractive index measure-ments at pressure. Most recently, measurements of the thermalconductivity of sea water and pure water have been completed inthe temperature range of 00-300 C* and the pressure range of0-1400 bars. This report is the second part of a series anddescribes the results of the experimental measurements of thethermal conductivity of pure water.

SLL EXPERIMENTAL INVESTIGATIONDetermirkations of the thermal conductivity of pure water

were conducted for temperatures of +1.830, 1.860, 10.320, 11.680,20.280, 21.760, 30.280, and 31.700 C, and nomainal pressures of10, 25, 200, 400, 600, 800, 1000, 1200, and 1400 bars.

The cleaning, filling, and experimental setup and proceduresfor the use of the special high-pressure vessel have been pre-viously described. 1 The water used for these measurements wasfreshly distilled and deionized, with a specific conductance of0.47 micromhos/cm. The purity of the water was not judged toI be extremely critical on the basis of Riedel's 2 findings whichshowed minimal effects for salt in aqueous solution.

PRECISION, ACCURACY, AND ERROR ANALYSIS

I -• Two distinct series of measurements were conducted by utilizingdifferent thermocouple junctions. Each series consisted of atleast three determinations of each data point and many determi-nations of selected "reference" data points, primarily at 10 and25 bars pressure. In almost all cases, the data resulting fromany particular series agrees to within 0.21 of the mean value.This small variation was traced to the procedure used to measurethe temperature differential. The setup required solder jointsto mate the tiermocouplo leads to the high-presaure electrical

( feedthroughs.i These joints required unsoldering and resolderingL during each assembly of the apparatus. This was observed to

cause a variation in the thermocouple electromotive force (•MW}of 0.5 uv, which is !0.2% of the approximately 130-150 uv gen-erated by the temperature gradient. The accuracy of thermocoupledifferential temperature measurement can only be estimated andis thought to be !0.5%, based upon comparison of the results

L

*Abbreviations used in this text are from the GPO Style Manual,

1967, upless otherwise noted.1 Superscripts refer to similarly numbered entries in the Tecimical

j: References at the end of the text.

S• T1

obtained with both sets of thermocouples. This estimate isbelieved to be conservative because of the short temperaturedifferential (

41 whereL = length of thermally conductive fluid path

wRe A T = t o t a l t e m p e r a t u r e d r o p o b s e r v e d e x p e r i m e n t a l l y

U V = voltage drop across the heaterI current through the heater

r= internal radius of fluid annulus

Lr = external radius of fluid annulusK = thermal conductivity of fluid

KS = thermal conductivity of silver

d = distance from inner thermocouples to inner surfaceof fluidL

d2 - distance from outer thermocouples to outer surface* ~of flu~id.

RESULTS

SIL The corrected experimenta l results o f the measurements arelisted in table 1 and shown graphically in figure 1.

THERlMAL CONDUCTIVITY (10 wATTS/C-DEGRE) R HPATU SOF 1.83*-31.70* C AND PRESSU RES TO 1400 BARS AS ME•ASURED

BY IRON- AND CURWHEL-CONSTTANTAN TIHE MOCOUPLES

1.6 103 I 0.26 30..0 I~o 1.0 S9E.7 11.70

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$G).,0 Sioo

,5 597.0

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200 S72.0 59g.0 60S.0 61S.0 S66.0 5•9's, 604.0 461.0

400 sio.. s0.. 6 $%0 %7 596.O 61 .S 621.0

60

G0 519.0 606.0

1622.0 63IS. 0

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1000 (24.0 6233 6)0.0 W1.0 64.0 622.0 619.0 6S2.0

1200r -1. 3. 647.0 6S9.S j612.0 631.0 i48.5 640.(2)MOsrdb ff - 00tata thertoc"iPle runtian-;.

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The data can be represented as a function of temperature andpressure by the equation:

K=5.5780x10-3 +4.249xl0 7 P +2.223x10 5 T-I.797x0-7T2 , (2)

where K is given in watts/cm-degree, P is the pressure in bars,and T is the temperature in 0 C. The values generated by thisequation are given in table 2 and shown graphically in figure 2.These have a standard error of ±1.5 x 10-5 watts/cm-degree, or±0.25% from the experimental data.

TABLE 2VALUES OF THE THERMAL CONDUCTIVITY (10 WATTS/CM-DEGREE)

OF PURE WATER, AS DETERMINED FROM EQUATION (2)

Gage Temperature, 0 CPressure

bars 0 10 20 30

0 557.5 578.5 595.0 608.5200 565.0 586.5 603.5 617.0

400 574.5 595.0 612.0 625.5600 583.0 603.5 620.5 634.0800 591.5 612.0 629.0 642.5

1000 600.0 620.5 637.5 650.51200 608.5 629.0 646.0 659.01400 617.0 637.5 654.5 667.5

DISCUSSION

Direct comparison of the data in table 2 with that reportedin the literature is only partly possible because most data forhigh pressure covers higher temperature ranges, and that forlower temperatures is restricted to low pressures.

SPowell's 3 review and analysis of all the atmospheric pressuredeterminations has resulted in a set of "most probable" valuesfor water. These data are shown in figure 3 in comparison to ouratmospheric values, as determined from equation (1). It can be

• i • seen that our results are systematically about 0.5%-l% lower thanthose "most probable" values cited by Powell. While the originof this discrepancy is unknown, no special effort was made toresolve this difterence since we are primarily concerned with theeffect of pressure on the thermal conductivity.

4

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Previous determinations of the thermal conductivity of waterat high pressure have been conducted by Bridgeman, Lawson,et al., and Timrot and Vargaftik; 6 however, the overlap withour data is sparce. Figure 4 shows the data of 4ridgeman (correctedin accordance with the recommendations of Riedel'), Lawson, et al.,and our results for a temperature of 300 C. All results agreeclosely with slopes of 3.7 x 10-7, 3.9 x N0-7, and 4.2 x 10-7watts/cm-degree-bar, respectively. In addition, our absoluteresults are in excellent agreement (±0.5%) with those given byLawson.

The data obtained by Timrot and Vargaftik for 00 C for pres-sures to 400 atmospheres appear in figure 5, along with ours forthe same temperature. Both sets of results agree within 1% ofeach absolutely, with slopes of 4.1 x 10-7 and 4.2 x 10-7 watts/j cm-degree-bar, respectively.

THEORETICAL RELATIONSHIPS

Relationships between thermal conductivity and other physicallymeasurable quantities have been advanced on the basis of bothempirical and theoretical groundwork.

One of the earliest relationships known was that proposedby Weber. 8 He introduced an empirical ormula which was latertheoretically deduced by Predvoditelev, and relates density (p),spec.,f!7 heat at constant pressure (C ), and molecular weight (m),and ýLhe thermal conductivity (K), to constant (A). The formulais:

K/= A. (3)

p \

The value of this constant as computed from our conducTivitydata, and values of C and p as taken from the literature, canbe seen in table 3 fop pressures up to 1000 bars. It is evidentthat this equation is not valid for the pure water system.

4Another relationship is that given by Bridgeman, relating

the thermal conductivity (K), to the density (p), the absolute.. weight of a molecule (m), the velocity of sound in the medium

(v), and the Boltzman gas constant (k), by

K~2kv..~.)2/3K= 2kv (4)

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TABLE 3VALUES OF THE CONSTANT A AS DETERMINED FROM WEBER S FORMULA

Gage Tererature, 0 CPressure

bars 0 10 20 30

0 346.6 361.9 373.9 384.0

200 355.0 368.5 380.0 389.5

400 362.7 374.6 385.5 394.6

600 369.9 380.6 390.6 399.3

800 376.5 385.9 395.3 403.7

1000 382.7 390.9 399.6 407.5

However, this relationship yields values of K only abouttwo thirds of the experimental values for thermal conductivity.Bridgeman's value of 2.02 x 10-16 ergs/degree for the Boltzmangas constant, k, is in error by almost 50% and accounts for therather close agreement between his calculated and experimentalvalues. This equation, when quoted by El'Darov,10 is given inthe slightly different form of

K = 3kv (5)

Because of the discrepancy between equations (4) and (5)r concerning the value of the constant, we decided to evaluate itsmagnitude according to our values for the thermal conductivity,such that

K m2/3-= B. (6)

Values for B are tabulated at pressures to 1000 bars, ther r limit of other available data, in table 4. It is obvious from this

table that B is constant neither with respect to temperature, norpressure.

An equation given by Vargaftik expresses the temperaturedependence of thermal conductivity of liquids as

44/3K= /3 , (7)

"tit

where K and p have their usual'meanings, and C is a constantSdependent upon pressure. Table 5 gives values of C based upon

our experiments. It is again quite evident that-this equationis not valid for the pure water system

IiTABLE 4VALUES FOR THE CONSTANT B FROM EQUATION (6)

Gage Temperature, C CPressure

bars 0 10 20 30

0 2.774 2.789 2.803 2.821

200 2.736 2.749 2.766 2.782

400 2.696 2.711 2.729 2.745

S600 2.655 2.674 2.693 2.710

800 2.615 2.638 2.659 2.677

1000 2.577 2.603 2.627 2.645

U TABLE 5VAI'IES FOR THE CONSTANT C IN EQUATION (7)

Gage Temperature, 0 C

Pressuirebars 0 10 20 30

0 179.3 172.8 167.7 163.4

200 175.0 172.6 167.3 163.0

400 178.6 172.1 166.8 162.6

600 178.1 171.6 166.4 162.1800 1177.5 171.1 165.8 161.6

100U 1176.8 170.4 165.2 161.2

CONCLUSIONS

* The reported the'mal conductivity of pure water is inexcellent agreement with historical data thus giving credence tothe design and techniques used.

F 77

.~~~~, . ...

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L * . Thermal conductivity of pure water is a direct linearfunction of pressure throughout the pressure and temperature rangeLI investigated.

* Previously proposed equations relating thermal con-ductivity to other measurable bulk properties have failed toaccurately describe the pure water system.

LiTECHNICAL REFERENCES1 - Stanley, E. M., and V. John Castelli, "The Thermal Conduc-

tivity of Pure Water and Standard Seawater as a Function ofL Pressure and Temperature," NAVSHIPRANDCEN Rept 3566, Part I(May 1972)

2 - Riedel, L., "Die Warmeleitfahigkeit von wa'ssrigen Losungenstarker Electrolyte," Chem. Ingr. Tech., Vol. 23, PP. 59-64(1951)

3 - Powell, R. W., "Thermal Conductivities and Expansion Coeffi-cients of Water and Ice," Advances in Physics, Vol. 7,pp. 276-97 (1958)

SL4 - Bridgeman, P. W., "The Thermal Conductivity of Liquids UnderPressure," Proc. Amer. Acad. Arts Sci., Vol. 59, P. 141 (1923)

5 - Lawson, A. W., et al., "Thermal Conductivity of Water at HighSPressures," J. Chem. Phys., Vol. 30, pp. 643-7 (1959)

6 -Timrot, D. L., and N. B. Vargaftik, "Thermal Conductivityof Water at High Temperatures," Zhur Tekh Fiz, Vol. 10,

U pp. 1063-73 (1940) (A transla' )n is available from associ-ated Technical Services, Inc., 855 Bloomfield Ave., GlenRidge, N. J. 07028)

7 - Reidel, L., "Neve Wgrmeleitfahigkeitsmessungen an organischenFlu*ssigkeiten," Chem. Ingr. Tech., Vol. 23, P. 321 (1951)

8 -Weber, H. F., Akad der Wissenschaften, Berlin, Phys-MathKlase, pp. 809-815 (1885)

9 -Predvoditelev, A. S., "Some invariant Quantities in theTheories of Heat Conductance and the Viscosity of Liquids,"

If Zhur Fiz Khim, Vol. 22, p. 339 (1948)L 10 - EltDarov, F. G., "The Thermal Conductivity of Non-Aqueous

Salt Solutions. II. The Mechanism of the Thermal ConductivityH• of Electrolytes," Russian Jour. of Phys. Chem., Vol. 34,No. 7, PP. 677-9 (1960)

11 - Vargaftik, N. B., Thesis, ENIN, USSR Academy of Sciences(1951)

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LI 5500 500 1000 1500

PRESSURE. BARS

Figure 1Experimental Data for the Thermal Conductivity

SIof Pure Water as a Function of Pressure for Various Temperatures

liamm m mm ]m mF ~

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U 670 300 C

LI 200 CLI 650

-'] I00 C"

LI 630

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0 50 0 1000 1500L: PRESSURE, BARS

11 Figure 2Thermal Conductivity of Pure Water as Determined by

Equation of Least Squares for Experimental Data

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560"; + POWELL:S PROPOSED VALUES

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TEMPERATUREC

S~ Figure 3Comparison of Powellts Proposed Values for

Thermal Conductivity of Pure Water at AtmosphericuPressure with Results of These ExperimentsmJiJim lmmI n I p

725

00

30

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a o BRIDGEMAN,30* CS.... ' 62.5+ LAWSON ET AL., 30° C

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PRESSURE, BARS

Figure 4Historical Determination of the Effect of Pressure

on the Thermal Conductivity of Pure Waterfor a Temperature of 300 C

580

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"PRESSURE, BARS

"Figure 5"Historical Determination of the Effeca- of Pressure

on the Thermal Conductivity of Pure Waterfor a Temperature of 00 C

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