The Equations for Thermophysical Properties of Aqueous Solutions of Sodium Hydroxide

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1 14th Internatonal Conference on the Propertes of Water and Steam n Kyoto The Equatons for Thermophyscal Propertes of Aqueous Solutons of Sodum Hydroxde Alexey A. Alexandrov * Department of Theoretcal Prncples of Thermotechncs, Mosco Poer Engneerng Insttute (Techncal Unversty), Mosco Krasnokazarmennaya 14, Russa * E-mal: AlexandrovAA@mpe.ru The survey of expermental data on sobarc heat capacty, vscosty and thermal conductvty of aqueous solutons of sodum hydroxde s presented. The equatons for these propertes are obtaned on base of expermental data. The equaton for sobarc heat capacty s obtaned for the regon of pressures up to 7 MPa and temperatures up to 523 K. It s vald for solutons at concentratons up to 4 mol/kg ater. The equaton for vscosty s vald for bolng solutons at temperatures up to 550 K at concentratons up to 3 mol/kg ater. The equaton for thermal conductvty s obtaned for regon of temperatures up to 400 K at pressures up to 15 MPa for solutons at concentratons up to 5 mol/kg ater. 1. Introducton The aqueous solutons of sodum hydroxde are appled n varous branches of ndustry such as poer engneerng, chemcal technology and so on. In spte of ths there s a lttle equatons for thermophyscal propertes of these solutons hch ould be sutable for usng n ndustral calculatons. The am of ths report s to present equatons for some of these propertes based on expermental data vald n regon of parameters and concentratons most mportant for poer engneerng and ones convenent for users. 2. Isobarc heat capacty Frst expermental measurements of sobarc heat capacty ere carred out at atmospherc pressures and n narro temperature nterval. Thomsen [1] fulflled measurement of heat capacty of solutons at concentratons % (t) at temperature 291 K. For more concentrated solutons at % values of heat capacty ere obtaned by Takker [2] n nterval K. In more de temperature dapason K nvestgaton as carred out by Pratt [3] for solutons th content % of sodum hydroxde. Rchards and Hall [4] measured heat capacty of solutons at concentratons % at temperatures from 288 to 293 K. Gucker and Schmnke [5] obtaned heat capacty values for solutons at concentratons % at one temperature 288 K. Investgaton n temperature dapason from 276 to 362 K as fulflled by Beretett and McCabe [6] for solutons at concentratons 4-51%. In regon of hgh concentratons from 50 to 76% measurement of heat capacty as fulflled by Wlson and McCabe [7] n range of temperatures K. At saturaton pressures for temperatures from 273 to 403 K Ackermann [8] carred out an nvestgaton for solutons at molalty mol/kg. Puchkov, Barnova and Matveeva [9] carred out the measurement of average heat capacty n nterval temperatures 25 K for solutons at concentratons from 5 to 50% n regon of temperatures K at pressures near to saturaton one. These expermental values ere descrbed by equatons hch transformed form gves the possblty to calculate a true heat capacty. Allred and Woolley [10] publshed a results of nvestgaton of dluted solutons at concentratons % n temperature nterval from 288 to 313 K as values of apparent molar heat capacty usng data for heat capacty of pure ater from [11]. Roux, Perron and Desnoyers [12] presented the results of measurement also as apparent molar heat capacty values for solutons at molalty and at temperatures K. They accepted values from [13] for heat capacty of ater. The only measurements of heat capacty of sodum hydroxde aqueous solutons n regon of elevated pressures up to 7 MPa as carred out by Smonson and Mesmer [14] n dapason temperatures from 323 to 523 K. These authors nvestgated solutons 86

2 14th Internatonal Conference on the Propertes of Water and Steam n Kyoto at molalty mol/kg and represented the results as values of rato of heat capactes of soluton and that of ater. Latter ere determned th the help of equaton of state from [15]. The uncertanty n heat capacty rato s estmated as (2-3) 10-4 Besdes data of expermental orks there are values of heat capacty calculated by Akerlof and Kegeles [16] on base of measurements of electromotve force for solutons at molalty mol/kg n temperature nterval K. After prelmnary comparson of expermental data of dfferent orks as nput values for equaton ere accepted the data of orks [10, 12, 14] and part of calculated values from [9] for parameters here another data are absent. The expermental values of apparent and relatve heat capactes of solutons ere recalculated nto values of specfc heat capacty usng ater heat capacty values used n each ork. Equaton for sobarc heat capacty of aqueous hydroxde solutons has a form j 5 5 j c c a m (1) p p, j1 0 here c p -sobarc heat capacty of soluton, kj/(kg K); c p, - sobarc heat capacty of ater, kj/(kg K); =T/T 0 ; T 0 = K; m molalty of soluton, mol/kg. The values of coeffcents a j are presented n Table 1. The data for heat capacty of ater are calculated from the equaton of state for ater lqud phase from IAPWS Formulaton IF 97 [17]. Equaton (1) s vald for solutons n the regon of concentratons up to 4 mol/kg at pressures up to 7 MPa n range of temperatures from 273 to 523 K. In ths regon t descrbes the expermental values Table 1. Values of coeffcents a j of equaton (1) a 01 = a 03 = a 11 = a 13 = a 21 = a 23 = a 31 = a 33 = a 41 = a 43 = a 51 = a 04 = a 02 = a 14 = a 12 = a 24 = a 22 = a 34 = a 32 = a 05 = a 42 = a 15 = a 52 = a 25 = j th standard devatons equal =0.032% for data [13], =0.015% for [10] and =0.074% for [12]. Values from [8] not used as nput ones have the scatter from 0.87 to +1.4% It s knon that the temperature dependence of ater sobarc heat capacty at lo temperatures has anomalous character. At atmospherc pressure t has a mnmum at temperature equals K [18]. The aqueous solutons of sodum hydroxde have analogues type of dependence for heat capacty at lo concentratons (Fg.1) th mnmum temperature decreasng hen concentraton s ncreasng. Mnmum of dependence reaches temperature equals 0ºC at molalty of soluton m=0.455 mol/kg. For more concentrated solutons mnmum of heat capacty s absent. 2. Dynamc vscosty The expermental nvestgatons of dynamc vscosty of aqueous sodum hydroxde solutons are carred out manly at atmospherc pressure also. Htchcock and McIlhennny [19] measured vscosty of solutons at molalty mol/kg n temperature dapason K. Krngs [20] nvestgated solutons at concentratons % n range of temperatures from 295 to 343 K. For solutons at molalty from to 28.7 mol/kg measurement of vscosty as fulflled by Kobus [21] n temperature dapason K. Klochko and Godneva [22] carred out measurements for solutons at concentratons from 6.21 to 71.5% n range of temperatures K. Baron and Matveeva [23] measured vscosty of solutons at concentratons from 3 to 47.6% n temperature range K and then Baron and Tscherba [24] extended the measurements n regon of more lo temperatures from 246 to 288 K for the solutons at Cp, kj/(kg*k) , Fg. 1. Temperature dependence of heat capacty of solutons: - ater, - m=0.1, - m=0.2, - m=0.3, - m=0.4 87

3 14th Internatonal Conference on the Propertes of Water and Steam n Kyoto concentratons %. Most extensve nvestgaton of vscosty of aqueous sodum hydroxde solutons as carred out by Mashovets, Puchkov, Sergaev and Fedorov [25]. They measured the vscosty of solutons at molalty mol/kg n range of temperatures from 273 to 548 K and at pressures a lttle hgher than saturaton ones. Ths ork s only one here measurements fulflled at elevated pressures. The uncertanty n ts results s estmated by authors as 1-1.5%. The data of orks [20 24] ere used as nput values for elaboraton of equaton for vscosty of solutons th moderate concentratons. Values of saturaton pressures for ork [25] ere calculated from equaton [26] The equaton for vscosty of solutons as obtaned n a form j 3 4 / b T T ln j m (2) j1 1 here -vscosty of soluton; -vscosty of ater at the same pressure and temperature; T 0 = K; values of coeffcents b j are presented n Table 2. The vscosty of ater can be calculated from equaton gven n [27]. But the vscosty n ths document s presented n dependence on temperature and densty. For ndustral calculatons t s more sutable often to have ths property as functon of temperature and pressure. Therefore an addtonal equaton s prepared for vscosty of ater ) ( exp c d (3) 1 0 here vscosty, µpa s, =(T 0 /T 1); T 0 = K; =(p p s ); p-pressure, MPa; p s saturaton pressure of ater; the values of coeffcents c and d are gven n Table 3. The values calculated from equaton gven n [28] ere Table 2. Values of coeffcents b j of equaton (2) b 11 = b 22 = b 21 = b 32 = b 31 = b 13 = b 41 = b 23 = b 12 = j 0 / Table 3. Values of coeffcents c, d of equaton (3) I c d used as nput data durng the preparaton of equaton (3). It descrbes vscosty of ater on saturaton lne th standard devaton equals =0.052% and descrbes vscosty of lqud under pressures hgher than saturaton ones th standard devaton equals =0.151%. The regon of valdty of equaton (3) ncludes temperatures up to 623 K and pressures up to 30 MPa. Equaton (2) descrbes the vscosty of solutons at molalty up to 3 mol/kg n temperature range from 273 to 548 K and under pressures up to 6 MPa. In ths regon the standard devatons of values of expermental orks are as follos: for [25] =2.05%, for [23] =2.23%, for [24] =2.17%, for [21] =1.88% and for [22] =3.37%. These devatons are rather bg and engendered by great scatter of expermental values. In Fg. 2 the temperature dependence of relatve vscosty / s shon for solutons at dfferent concentratons. It s knon that dfferent aqueous solutons of electrolytes have dfferent types of ths dependence. For some solutons relatve vscosty ncreases hen temperature ncreases, for others t decreases. It s clear from Fg. 2 that relatve / 2,2 1,9 1,6 1, Fg. 2. Relatve vscosty of solutons: - m =0.1, - m =1.0, - m =2.0, m =

4 14th Internatonal Conference on the Propertes of Water and Steam n Kyoto vscosty of lo concentrated aqueous solutons of sodum hydroxde ncreases and t decreases for more concentrated ones. 3. Thermal conductvty The expermental nvestgatons of thermal conductvty of aqueous solutons of sodum hydroxde are scant and carred out manly at atmospherc pressure also. Rdel [29] measured the thermal conductvty of solutons at concentraton % n temperature range from 274 to 353 K. Vargaftk and Osmnn [30] measured the thermal conductvty at one temperature 293 K n range of concentratons from 0 to 40%. Also at one temperature 311 K the thermal conductvty of solutons th molalty mol/kg as measured by Losencky [31]. The only nvestgaton of thermal conductvty under elevated pressures up to 15 MPa as fulflled by Gusenov [32] n temperature range from 298 to 401 K for solutons th concentratons up to 20%. The expermental data of orks [29-32] ere used as nput values for elaboraton of equaton. The equaton obtaned has a form j 3 3 j1 0 j e T / T m (4) j here -thermal conductvty of soluton, W/(m K); - thermal conductvty of ater at the same pressure and temperature; T 0 =403.0 K; m molalty of soluton, mol/kg; values of coeffcents e j are gven n Table 4. The equatons from [33] may be used for calculaton of thermal conductvty of ater here t s gven as functons of temperature and densty. Some tmes t s more sutable to calculate the thermal conductvty of ater n dependence of temperature and pressure from addtonal equaton g q (5) 0 Table 4. Values of coeffcents e j of equaton (4) E 01 = e 12 = e 11 = e 22 = e 21 = e 03 = e 31 = e 13 = e 02 = e 23 = Table 5. Values of coeffcents of equaton (5) g q here thermal conductvty, W/(m K); = (T 0 /T 1), T 0 = K; =p p s, p-pressure, MPa; p s -saturaton pressure, MPa; coeffcents g and q are presented n Table 5. The equaton (5) descrbes thermal conductvty of ater n regon of pressures up to 30 MPa and temperatures up to 623 K. Values of [33] ere used as bass for ths equaton and t descrbes these data th average square devatons equal =0.007% on saturaton lne and =0.198% for lqud under other pressures. Equaton (4) s vald n regon of pressures up to 15 MPa and temperatures from 273 to 405 K for solutons th concentraton up to 5 mol/kg. In ths regon t descrbes the expermental data th average square devatons equal =0.45% for [29], =0.43% for [30], =1.0% for [31] and =0.52% for [32] The character of change of thermal conductvty of solutons along saturaton lne s shon n Fg. 3. It s knon that ths dependence for ater has anomalous behavour. Aqueous solutons of sodum hydroxde reman that type of dependence. It can note also that heat conductvty of these solutons ncreases hen concentraton ncreases n contradcton to aqueous solutons of many others electrolytes. lamda Fg. 3. Thermal conductvty of solutons on saturaton lne: - ater, - m=1.0, - m=

5 14th Internatonal Conference on the Propertes of Water and Steam n Kyoto Delta, % Fg. 4. Devatons of vscosty values from [34] and our once: - m=1.0, - m=2.0, m= Dscusson Extensve nformaton about propertes of aqueous solutons of electrolytes s gven n reference book [34]. But t concerns manly to solutons at atmospherc pressure and at temperatures up to 100ºC. Values of heat capacty and heat conductvty from [34] agree th our ones thn ±1.5%. The dvergences of vscosty values are bgger and are shon n Fg. 4. Ne equatons presented n ths ork expand analytcal representaton of propertes of sodum hydroxde solutons n regon of hgher temperatures and pressures. Acknoledgment Ths ork s supported by Scentfc Councl of Presdent Program for Support of Scentfc Schools. Grant References [1] Thomsen, Ann. Physk, 142, 337 (1911) [2] Tucker, Trans. Roy. Soc., A 215, 319 (1915) [3] Pratt, J. Frankln Inst, 185, 663 (1918). [4] Rchards and Hall, J. Am. Chem. Soc., 15, 731 (1929). [5] F.T. Gucker and Schmnke, J. Am. Chem. Soc., 55, 1013 (1933). [6] J.W.Beretett and W.I. McCabe, Ind. Eng. Chem., 28, 558 (1936). [7] H.R. Wlson and W.I. McCabe, Ind. Eng. Chem., 34, 558 (1942). [8] T.H. Ackermann, Zesch. Elektrocheme, 62, 411 (1958). [9] L.V. Puchkov, T.A. Baranova and R.P. Matveeva, Physcal-Chemstry of Solutons, Nauka, Mosco (1972), p. 86. [10] G.C. Allred and E.M. Wooley, J. Chem. Thermodyn., 13, 147 (1981). [11] G. S. Kell, J. Chem. Eng. Data, 15, 119 (1970) [12] A.H. Roux, G. Perron and J.E. Desnoyers, Can. J. Chem., 62, 878 (1984). [13] H.F. Stmson, Am. J. Phys., 23, 614 (1955). [14] J.M. Smonson and R.E. Mesmer, J. Chem. Thermodyn., 21, 561 (1889). [15] L. Haar, J.S. Gallagher and G.S. Kell, NBS/NRC Steam Tables. Hemsphere, Washngton, DC. (1984). [16] G. Akerlof and G. Kegeles, J. Am. Chem. Soc., 52, 620 (1940) [17] Release on the IAPWS Industral Formulaton 1997 for the Thermodynamc Propertes of Water and Steam, Internatonal Assocaton for the Propertes of Water and Steam, Executve Secretary R.B. Dooley, Electrc Poer Research Insttute, Palo Alto, Ca 94304, USA [18] A.A. Alexandrov and M.S. Trakhtengerts, Thermophyscal Propertes of Water at Atmospherc Pressure, Izdatelstvo Standartov, Mosco (1977) [19] L.B. Htchcock and McIlhenny, Ind. Eng. Chem., 27, 461 (1935) [20] W. Krngs, Zet. anorg. Chem., 255, 294 (1948) [21] G.L. Kobus, Proceed. Hydrometeorolog. Insttute, 7, Odessa (1955), 113 [22] M.A. Klochko and M.M. Godneva, Z. Neorg. Chem. (Rus), 4, 2127 (1959) [23] N.M. Baron and R.P. Matveeva, Z. Prklad. Chem., 40, 673 (1967) [24] N.M. Baron and M.U. Tscherba, Z. Prklad. Chem.,42, 2128 (1969) [25] V.P. Mashovets, L.V. Puchkov, P.M. Sergaev and M.K. Fedorov, Z. Prklad. Chem., 46, 992 (1973) [26] Draft release on vapor pressure of aqueous solutons ( K), V.M. Valyashko, L.V. Puchkov, M.U. Matyushenko, V.M. Gljarov, N.V. Mlovdova, R.P. Matveeva, N.A. Gljarva, Lenngrad Technology Insttute (1986), 3 [27] Revsed Release on the IAPS Formulaton 1985 for the Vscosty of Ordnary Water Substance, Internatonal Assocaton for the Propertes of Water and Steam, Executve Secretary R.B. Dooley, Electrc Poer Research Insttute, Palo Alto, Ca 94304, USA [28] A.A. Alexandrov and A.B. Matveev, Hgh Temperature, 36, 885 (1998) [29] L. Rdel, Chem. Ing. Tech., 22, 54 (1950) [30] N.B. Vargaftk and Yu.P. Osmnn, Teploenergetka, No.7, 11 (1956) [31] Z. Losencky, J. Phys. Chem, 73, 451 (1969) [32] G.G. Gusenov, Elaboraton of measurng devces and nvestgaton of thermal conductvty of aqueous solutons of acds, alkals and porous materals saturated by flud, Thess, Makhachkala (2002) [33] Revsed Release on the IAPS Formulaton 1985 for the Thermal Conductvty of Ordnary Water Substance, Internatonal Assocaton for the Propertes of Water and Steam, Executve Secretary R.B. Dooley, Electrc Poer Research Insttute, Palo Alto, Ca 94304, USA [34] Propertes of Aqueous Solutons of Electrolytes, ed. I.A. Zaytsev and G.G. Aseev, CRC Press, Boca Raton (1999) 90

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