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J. Chem. Eng. Data 1984, 29 , 245-246 2450O L ' " I ' 1 " " l " " I " " I " ~ ' " " ' ~ ~ " '

OKre t s c hm er & Wiebe+Knoebe l F. Edm is t e r- -T s onopou los Equa t i on

3

-

-1mI ~ I ~ " ~ ~ " ~ ~ ' " ~ " " ~ ~ ~ ~ ' ~ ~ ' ~ ' ~ ~ ~ ~ ~ ' ~ ' "

25 50 75 100 125 150 175 200 225TEMPERATURE, T / K - 273.15Flgure 1. Second vlrial coefflclents of ethanol. Curve Is from theTsonopoulos correlation, eq 2 and 3.lation. His value of b for ethanol is 0.0572, and the resultingline is also shown in Figure 1. We reoptimized the constant bby usingthe ive points of Kretschmer and Wlebe (5) , he hreepoints of Knoebel and Edmister (6) ,and our seven points. Wefound that with the latest physical constants ( 7 ) , the value ofb for ethanol should be 0.0532; this shift is not deemed sig-nificant in view of the scatter n Figure 1and In view of the smalldata base.GlossaryabB

parameter in eq 3, 0.0878 for ethanol ( 74 )parameter in eq 3, 0.0572 for ethanol ( 74 )second virial coefficient, m3 kmol-'

f ( O ) , f ( ' !f (2 '

P pressure, kPaPC critical pressure, kPaRT temperature, KTC critical temperature, KT , reduced temperature, T I T ,V volume, m3 kmol-'Z compressibility factor (P V IRT)

functions of reduced temperature in eq 2 (74)

gas constant, 8.31441 kPa m3 kmol-' K-'

Reglrtry No. Ethanol, 64-17-5; toluene, 108-88-3; tetramethylsiiane,75-76-3.Literature Cited

Ambrose, D. Vapor-Liquid Critical Properties"; NPL Report Chem107, NPL: Teddington. Mlddlesex TW11 OLW, UK, Feb 1980.Myers, J. E.;Hershey,H.C.; Kay, W. 8. J. Chem . Thermodyn. 1070,7 7 , 1019.Dymond, J. H.; Smith, E. 8. "The Virlal Coefficients of Pure Gases andMixtures"; Clarendon Press: Oxford, 1980.Hanks, P. A.; Lambert, J. D., unpublished results clted in ref 3, 1951.Kretschmer, C. B.; Wlebe, R. J . A m . C h e m . SOC.1054, 7 6 , 2579.Knoebel, D. H.; Edmister, W. C. J. Chem. Eng. Data 1088, 73, 12 .Kay, W. 8.;Rambosek, G.M. Ind . Eng. Chem. 1053, 45 , 221.Chun, S. W.; Kay, W. 8. ;Teja, A. S. J. Chem. Eng. Data 1081, 2 6 ,300.Barber, J. R.; Kay, W. 8. ;Teja, A. S. AIChE J. 1082, 2 8 , 134, 138,142.Lindley, D. D. Ph.D. Dissertation, The Ohlo State University, Columbus,OH, 1983.Marcos, D.H.; Lindley, D. D. ; Wilson, K. S.; Kay, W. 8.;Hershey, H. C.J. Chem. Thermodyn. 1083, 15, 1003.Swietoslawski, W. "Ebulliometric Measurem ents"; Reinhoid: NewYork, 1945.Skaates, J. M.;Kay, W. 8. Chem. Eng. Scl. 1084, 19, 431.Tsonopoulos, C. AIChE J. 1074, 2 0 , 263.Piker, K. S.; Curl, R. F.; Jr. J. Am. Chem. Soc. 1057, 7 9 , 2369.Recelved for review June 3, 1983. Accepted February 10, 1984.

Viscosity of Molten Sodium Salt HydratesS. K. Sharma," C. K. Jotshl, and Amrao SlnghDepartment of Che mic al Engineering and Technology, Panjab University, Chandigsrh- 60 0 14, IndiaViscoSny of molten sodlwn sail hydrates, NaOH.H,O,Na(CH,C00)4H20, Na2S203-5H,0,Na,CO3.10H20, andNa2HP0,*12H,O, sultabk for energy storage applicationshas been determined with a modifled Ubbeihodeviscometer. The temperature dependence shows anArrhenlw behavior whlch can be reprostented by anequation r] = A exp(EJRT), above the meltlng polnts ofthe salt hydrates studied. The values of activation energy(E,) of viscous flow are reported. ~ ~~~~~~

Hydratedsalts ( 7-3) ave been extensively investigated forthermal energy storage applications due to their high energystorage densities and low cost. Some of the salts recom-mended for this purpose show great supercooling as well asglass-forming tendencies which are undesirable. In the caseof tabular crystals, such as those of sodium acetate trlhydrate,supercooling s considerable. Viscosity is an important param-eter (4 ) ,as lt influences the crystallization of such salts. Boththe viscosity data as well as a generalized empirical corre-sponding states relationship which could be used to calculatethe viscosities of a given class of melts outside the existingexperimental range are lacking in the literature. The presentinvestigation has been designed to determine the vlscoslty of0021-9560/04/1729-0245$01.50/0

the most commonly recommended salt hydrates suitable forenergy storage applications, so that the u t i l i of each can beproperly assessed.Theoretical and Experimental Section

A modified Ubbelhode viscometer (5) has been used in thepresent investigation. The salient feature of this design is thatthe flow of meltthrough the capillary is caused by its hydrostaticpressure only.Poiseuille's equation applicable to the capillary flow is

u = q / p = at - b / t (1 )Values of the constants a and b have been calculated by usingstandard values of the density and the viscosity of carbontetrachloride and benzene, available in the literature (6). Withthe least-squares method of curve fitting, new constants A andB for the instrument are calculated. These constants havebeen used to define a new correlation between viscosity andtime, which can be represented as follows:

q = A + B t (2 )For the viscometer used, the values of constants A and Bare -0.363 and 0.0075, respectively. The accuracy of this

0 1984 American Chemical Society

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24 6 Journal of Chemical and Engineering Data, Vol. 29, No. , 1984T a b l e I. V i s c o s i t y ( 9 ) of M o l t e n Hydrated Sodium S a l t s

t e m o . "C n. CP temD. "C n . CP64.267.070.058.060.565.848.550.055.035.040.037.040.0

NaOH.H,O ( m p 64 "C)10.542 75.09.657 80.08.541Na ( CH3 C0 0 ) . 3 H2 0 m p 58 "C )5.813 70.25.315 73.54.535 75.0

Na2Sz03.5H20 m p 48 "C)9.368 60.08.877 65.07.260Na2C03.10Hz0 ( m p 33.9 "C)7.925 45.06.466 50.0

NazHP0,.12H20 ( m p 36.1 "C)4.478 45.04.410 50.0T a b l e 11. D e r i v e d V a l u e s of E ,

7.2126.0571 2 t

4.1113.6083.4556.2695.317

5.3714.4293.9273.300

sal t hydrate E,, k J / m o lNaOH.H20 34.73NaCH,C00.3Hz0 28.98NazSz03.5Hz0 30.65Na2C03-10Hz0 32.28NaZHPO4.12H20 23.43

equation has been checked by determining the viscosity ofphenol. Agreement with the literature values is within f .5%.

Salt hydrates selected for the present studies were NaOH.H20, Na(CH3COO)-3H20, a2S2O3.5H2O,Na2C03.1OH,O, andNa,HPO, 12H20. All these salt hydrates were recrystallizedfrom BDH grade samples by using doubledistilled water.Melting points of the crystallized materials were evaluated fromheating and cooling curves. These melting points were foundto be in good agreement with those reported in the literature(7). After the molten salt hydrate was transferred to the vis-cometer, it was subjected to repeated solldification and meltingcycles so as to eliminate any trapped air. The viscometer wasequilibrated for 2-3 h in the thermostat before starting theexperiment.Results and Dlscusslon

Viscosities of the selected salt hydrates at various temper-atures above their melting points are reported in Table I.Figure 1 shows the plot of log q vs. reciprocal of absolutetemperature. The linear nature of this plot confirms the Ar-rhenius behavior of these salt hydrates. The temperature in-terval is from the melting point to 20 OC above the meltingpoint, which is the range generally recommended for chargingthe storage units. Thus, it can be inferred that the viscous flow

3 L +I 1 I I

2 8 2 9 3.0 3 1 3 2 3 3i / ~ l o 3 K- ' --.+

Figure 1. Plot of log (viscosity) vs. T- ' for (1) NaOH.H,O, (2 ) Na C-H,COO.3H2O, (3 ) Na2S20,.5H,0, (4) Na,CO,-lOH,O, and (5) Na,HP-

be concluded that intermolecular hydrogen bonds, due to waterof crystallization, play an important role in the viscous flow ofthese melts.From the results of this study the temperature dependenceof the viscosity of sodium salt hydrates such as NaOH.H,O,CH3COONa.3H20,Na2S203.5H20,Na2C03.10H20,and Na2HP-

04.12H20 may be expressed by the following exponentialequations: q = (3.715 X exp(34732lRT) cP, q = (1.549X exp(28988/RT) cP, q = (9.77 X exp(30654/RT)cP, q = (2.63 X exp(32282/RT) cP, and q = (5.37 X104) exp(23436/RT) cP, respectively. The deviation from theexperimental values is f .14% .Glossarya , b constants, eq 1A , B constants, eq 2t time of flow, sT temperature, KE"Greek LettersD viscosity, CPV kinematic viscosity, cm2/s

Registry No. NaOH.H,O, 1220 0-64- 5; Na(CH3COO).3H,0, 613 1-9 0-4 :NaS,O,5H,O, 1 0102-17-7: Na,CO,. OH,O, 6 132-0 2-1; Na,HPO, 12H,O,

04*1H,O.

activation energy of viscous flow, kJ/mol

10039-32-4,Literature Cited

(1) Sharma, S.K.; Jotshi, C. K. "Proceedings of the First Na tional Work-shop on Solar Energy Storage"; Department of Chemical Engineering,Panjab University: Chandigarh, Indla, 1979; p 309.(2) Lorsch, H. G.; Kauffman, K. W.; Denton, J. C. Energy Convers. 1975,15. 1.of these melts is an activated process in which energy distri-bution can be represented by the equation(3) Telkes, M. "Solar Heat Storage"; American Society of Mechanical En-

gineers: New York, 19 64 paper 64-LA/SO L-9.(4) Andrew, V. H. I n d . Eng. Chem. 1945, 37, 782.(5) Mohan, Chander. M.Sc. Thesis, Panjab University. Chandigarh, India,(6) Tlmmerman, J. "Physico-chemical Data of Pure Organic Compounds";Elsevier: New York, 1950.(7) Weast, Robert C. "Handbook of Chemistry and P hysics", 50th ed.; heChem ical Rubber Publishing Co.: Cleveland, OH, 196 9-70.(8) Jain, S. K. J. Chem. fng.Data 1978, 23, 171.

q = A exp(E,/RT) (3) 1983, p 30.Energies of activation of viscous flow (E,) of these salt hydratesare given in Table 11. Contrary to this, hydrated salts ofcalcium nitrate, nickel nitrate, and zinc nitrate show non-Ar-rhenius behavior (8). This is most probably due to a differencein intermolecular forces between these two categories of saltmelts. Results further varieswith the number of moles of water of crystallization. I t maythat the energy of

Rece ived for review June 29, 19 83. Accepted January 31, 1984. This workhas been financially supported by Tata Energy Research Institute, Bombay(India).