998
Ind. Eng. Chem. Res. 1988,27,998-1003
Estimation of the Thermodynamic Properties of Dense Gaseous D20 and T20 by a Modified Corresponding States Principle Naoki Matsunaga* and Akira Nagashima Department of Mechanical Engineering, Keio University, Hiyoshi, Kohoku, Yokohama, Kanagawa 223, Japan
A consistent set of thermodynamic property values of dense gaseous T20has been prepared by assuming the corresponding states relationship between T20and H20. The scaling for the pressure and the density has been modified at subcritical temperatures. The validity of the corresponding states principle and of the present modification has been verified in advance between D 2 0 and H20. The modification, requiring only the vapor pressure data, considerably reduces the systematic error near the saturation line. Due to the larger uncertainty in the critical constants for TzO used in the present study, the region of validity of the estimation is narrowed for T20to the reduced density range pr = p / p c S 1.1from pr 5 1.4-1.5 for D20. The values of the density, the enthalpy, the entropy, and the heat capacity a t constant pressure are given in the temperature range 4.49-1000 " C both for the saturated and superheated vapor of T20. Reliable information on the thermophysical properties of tritium oxide (T20)will be needed in the near future for the design and operation of fusion reactors. However, only a few experimental data are available for the liquid density and the vapor pressure of T20(Jones, 1952,1968; Popov and Tazetdinov, 1960; Goldblatt, 1964). With such scarcity of the experimental data in mind, the present authors intend to estimate the thermodynamic properties of T20in a wide range of temperatures and pressures. This study, succeeding the estimation of the vapor pressure and the critical constants (Matsunaga and Nagashima, 1986), deals with the prediction of the thermodynamic properties of dense gaseous T20by the corresponding states principle applied to the well-established data for H20 (for the liquid and the critical regions, the corresponding states principle does not apply well). So as to raise the accuracy of the estimates near the saturation line, a modification was introduced at subcritical temperatures. The validity of this modification was checked by applying it to the estimation of the properties of DzO, for which relatively abundant experimental data are available. Then, the thermodynamic properties of gaseous T20were predicted using our estimates of the critical constanta (Matsunaga and Nagashima, 1986). The larger uncertainty in the critical constants of T20does not seriously affect the accuracy of the estimates at lower densities. A t reduced densities p, = p / p c above about 1.1, the estimates become very sensitive to the choice of the critical constant values. Thus, the density range of validity of the corresponding states principle with H20was narrowed for TzO compared to that for D20 (p, 5 1.4-1.5), for which the critical constants are much more accurately known. In the critical region, the density limit was found to be further lowered. The estimates of the density, the enthalpy, the entropy, and the heat capacity at constant pressure of dense gaseous T20were given in the temperature range from the triple point (4.49 O C ) to 1000 "C. However, the region where the uncertainty of the estimates may be excessive was excluded. Estimation of the Thermodynamic Properties of Dense Gaseous H 2 0 Isotopes by t h e Corresponding States Principle According to the original corresponding states principle proposed by van der Waals, PUTsurfaces of various sub-
* Present address: Department of Mechanical System Engineering, Takushoku University, Tatemachi, Hachioji, Tokyo 193, Japan. 0888-5885/88/2627-0998$01.50/0
Table I. Critical Constants of HzO,DzO,and T 2 0 crit. crit. crit. temp, Tc, crit. pressure density, compressibilspecies K Pc, MPa p c , kg/m3 ity factor, 2,
H,O" DZO" TzOb
647.14 643.89 641.7
22.064 21.671 21.41
"Levelt Sengers et al. (1985).
322 356 393
0.229 0.228 0.225
*Matsunaga and Nagashima
( 1986).
stances can be generalized in terms of the reduced temperature T, = TIT,, the reduced pressure P, = PIPc, and the reduced density pr = p / p c , provided that substances have an identical value for the critical compressibility factor 2, = Pc/p$Tc. Here, Tis the absolute temperature, P is the pressure, p is the density, R is the gas constant, and the subscript c denotes the critical point. The values of the critical constants for HzO and D20 are recommended by the International Association for the Properties of Steam (IABS) (Levelt Sengers et al., 1985) and those for T20are estimated by the present authors (Matsunaga and Nagashima, 1986) (see Table I). When calculated from these critical constant values, the 2, values for D20 and T20are smaller than that for H 2 0 by 0.7% and 1.9%. This may partly be attributed to the rather large uncertainty in the critical densities, pc (A0.970 for HzO, *1.4% for D20, and f2.5% for T20). With this difference in mind, a modification of the corresponding states principle proposed by Su (1946) for the substances with different 2, values was employed in this study (as will be mentioned later, Su's method was also unsatisfactory for the near-saturation vapor state, and therefore, another modification was introduced for the subcritical temperatures). Su replaced the reduced density p, = p / p c by pri, defined as Pri
= P/Pci
(1)
where
Pc/RTc (la) Although Su's modification breaks down near the critical point, the original corresponding states principle is also found to fail in the critical region. Generally speaking, Su's modification gives better results than the original method does in a wide range of the gaseous states. The values of pc, which are rather uncertain, are not required in Su's method. There are two options when applying the corresponding states principle to the estimation of thermodynamic Pci =
0 1988 American Chemical Society
Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988 999 properties of an H20 isotope. One is to convert an equation of state for H 2 0 to that for the isotope (Trakhatengerts, 1970, Juza et al., 1974; Juza and Mare& 1978). Another method, employed here, is to obtain an estimate of a thermodynamic property of the isotope from that of H 2 0 at the corresponding state (Kesselman, 1960; Lundqvist and Persson, 1965; Juza et al., 1966). As an example, the estimation of the density of an H20 isotope, pI, at temperature T I and pressure PI from an equation of state for H 2 0 shall be considered here (the subscript I denotes the isotope under consideration). By Su’s method, the calculation proceeds as follows: (1) The temperature and the pressure of the corresponding state for H20, TH and PH, are to be calculated (the subscript H denotes the corresponding state for HzO). Since the reduced quantities TI and PIshould be identical between the corresponding states, TH and PH are calculated as
T H = T,,HT~,H = Tc,~Tr,l = Tc,~(T~/Tc,~) = TI(TC,H/TC,I)
(2)
PH= P,,HP~,H = PC,HP~,I = Pc,~(P~/Pc,~) = PI(P~,H/PC,I)
(3)
and
(2) The density of H20 at the corresponding state PH is calculated from the equation of state for H 2 0 as pH = p(TH, PH) (4)
Iterative calculation is required when the equation of state for HzO utilizes the temperature and the density as the independent variables. (3) The reduced density of HzO, pri,H,at T H and PH equals that of the isotope, pri,I, at T I and PI. Therefore, pI can be obtained as PI = Pci,IPri,I
-- Pci,IPri,H = Pci,I(PH/Pci,H) = PH(Pci,I/Pci,H)
(5)
For the derived quantities, such as the enthalpy h, the entropy s, the heat capacities c, and c , the corresponding states principle applies only to the cfepartures from the ideal gas values. The equations for estimating these excess quantities are given in the Appendix for the independent variables of the temperature and the density. The properties for the ideal gas state must be theoretically obtained for each substance from spectroscopic data. In the case of HzO isotopes, the values calculated by Friedman and Haar (1954) are usually selected.
Modification of the Corresponding States Principle for the Subcritical Vapor Region As Juza et al. (1974) pointed out, the corresponding states principle does not work well between HzO and DzO for vapor near the saturation, even when Su’s modification is applied. The same situation is expected for T20, and what is worse, the lack of experimental data for T20in this region prevents us from correcting the estimates. Since the error due to larger uncertainty in the estimated critical constants (Matsunaga and Nagashima, 1986) may further be introduced for T20, a t least the error arising from corresponding states calculation should be minimized.
Figure 1. Behavior of the reduced densities of H,O and D20in the subcritical vapor region.
Therefore, in this study, the corresponding states principle was modified so as to improve its accuracy near the saturation line. Figure 1shows the behavior of the reduced densities bfi) of the subcritical vapor of H20 and D20 at T I = 0.886 (300 OC for H 2 0 and 297 O C for D20) against the reduced pressure (PI). As shown in this figure, even when Su’s method is applied, the reduced PUTsurfaces of HzO and DzO are not congruent, though they are analogous in shape. The gap between the two PUT surfaces becomes wider with increasing pressure. Thus, the larger error of the estimates by Su’s method for D20 near the saturation line is attributed to the failure in the scaling of the pressure and the density. In such a case, correction factors for the congruity, often called the shape factors, are introduced as follows (Leach et al., 1966; Rowlinson and Watson, 1969): = pr,I/fc,p
(6)
Pri,H* = & i , I / f c , p
(7)
pr,H*
and where f,,, and f,,,are the correction factors for the congruity and the asterisk denotes the use off,,, or f,, . These correction factors, temperature dependent and slightly density dependent, are usually determined from the experimental PUTinformation (Leach et al., 1966). However, in this study, the values of f,,p and f,,, were assumed to be density independent and were determined from the saturation vapor pressure data, since no PUTdata are available for gaseous T20. The correction factor for the pressure, fc,p(Tr), is obtained from the reduced vapor pressures, P,, of the isotope and of H20 as
fc,p(Tr)= P I S , I ( /~p ~Is), H ( T r )
(8)
where
pr, = PJPC
(84
Here, P, is the saturation vapor pressure and T I = T r ,=~ is the reduced temperature. Since the compressibility factors, Z = PJpRT, of the two substances should be identical at the corresponding states (Leach et al., 1966; Rowlinson and Watson, 1969), when T I = Tr,H = T1,1,we find
fc,p(TA= fC,,(TI)
(9)
Therefore, the definition of pri,H*shall be changed as follows: Pri,H* = Pri,I/fc,p(Tr) (10) Then the present modification shall be applied to the estimation of the density of an H20 isotope ( P I ) at tem-
1000 Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988 I
Present study
!Su modif ~ ~ l i o n ) -Present sludy I Present modificat1onl 5
-.-
JGza et al
-
-
I
(1978)
I
1
-
h"
Kirillln et al (1963)
-
Present study ISu's modification) Present study lPre5ent modification Kirillin et ai (1963)
D2O
1
11978)
Jhraetal
-8-
1
-.
1
100
200
t('C)
-20
400
Figure 2. Comparison of the estimated density of the saturated vapor of D20with Hill's equation of state.
300
t(ec)
4 00
Present study 1% s m o d ~ f ~ a t i o n l study (Present modification) K i r i l l i n et a1 113631
D20
HzO. (1)The temperature and pressure of the corresponding state for HzO, T H and P H * , should be calculated. T H CUI be obtained by eq 2, while PH*is calculated as
200
Figure 3. Comparison of the estimated enthalpy of the saturated vapor of D20with Hill's equation of state.
perature TI and pressure PIfrom an equation of state for
pH*
loa
300
-Present
-.-
S" h h
Ym
J;zo
el 01
(1978)
=Pc,HPr,H*
= Pc,HPr,I/fc.p(Tr) = P C , H ( P I / P C , I ) /fc,p(Tr) = pI(pc,H/pc,I)/fc,p(Tr) = pH/fc,p(Tr)
(11)
(2) The density of HzO at the corresponding state (PH*) is calculated from the equation of state for HzO as PH* = P ( T H , p H * ) (12) (3) The reduced density of HzO at T H and PH*,P ~ , H *= p H * / p & p , should be, as shown in eq 10, equal to PriJ/fc,p(Tr) at TI and PI. Therefore, one can obtain as
0
Figure 4. Comparison of the estimated entropy of the saturated vapor of D20with Hill's equation of state.
-.-
2
PI = Pci,IPri,I
-- Pci,IPri,H*fc,p(Tr)
= Pci,I(PH*/Pci,H)fc,p(Tr) = PH*(Pci,I/Pci,H)fc,p(Tr)
Present study (Su s modification) Present study (Present modification) J h o et aI (1918)
(13)
The enthalpy (h),the entropy (s), and the heat capacities (c, and c p ) can be obtained for this modification simply by adding correction terms to the estimates obtained by Su's method (see Appendix). To check the reliability of the present modification, the estimation of thermodynamic properties of the saturated DzO vapor was carried out with the aid of an equation of state for H20 by Haar et al. (1982) (the IAF'S Formulation 1984 for the Thermodynamic Properties of Ordinary Water Substance for Scientific and General Use). The estimates were obtained by Su's method both with and without introducing the present modification. The correction factor, fc,p(Tr), between D20 and HzO was calculated from the vapor pressure equations of DzO (Hill and MacMillan, 1979) and of H 2 0 (Wagner, 1973) and was correlated into a fourth-order equation in terms of Tr as follows: fc,p(Tr) = 1 - 0.0502882(1 - Tr)- 0.465887(1 - T,)' + 1.31176(1 - Tr)3- 2.87500(1 - Tr)4(14) The ideal gas properties were calculated from the equations by Haar et al. (1982) for HzO and by Hill et al. (1982) for DzO, respectively. The resulting estimates with and without the present modification are compared with an equation of state for D20 by Hill et al. (1982) (the IAPS Formulation 1984 for the Thermodynamic Properties of Heavy Water Substance) in Figures 2-5. Equations of state in Kirillin's book (1963) and by Juza and Mareg (1978) are also in-
-10
I
I
100
200
1, 300
LOO
tree)
Figure 5. Comparison of the estimated heat capacity at constant pressure of the saturated vapor of D,O with Hill's equation of state.
3000c
resent study !Su s modification) Present study (Present modification) Kirillin et ai (1953)
-
Figure 6. Comparison of the estimated density of D,O vapor with Hill's equation of state at 300 O C .
cluded in the comparison, since these were developed with the aid of the corresponding states principle. The tolerances assigned in the International Skeleton Tables (1963) for the thermodynamic properties of HzO, adopted at the 6th International Conference on the Properties of Steam,
Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988 1001
3000c
I 4
1 2
6
8
Present study (Su s modification) Present study (Present modiltcationl K i r i l l i n et a1 (19631
-
ps
P(MPa)
Figure 7. Comparison of the estimated enthalpy of D20vapor with Hill's equation of state a t 300 "C.
1
Present study
D70 1
- 0 0061
2
-
( 5 ~ ' smod~ficotionl
Present study (Present modificotionl K i r i l l i n e l 01 119631
4
6
8
I
Pr
P(MPa)
Figure 8. Comparison of the estimated entropy of D20vapor with Hill's equation of state at 300 "C.
are also depicted. These tolerances are considered as an indication of the measure of experimental error for H20. As shown in these figures, the present modification improves the accuracy of the estimates considerably near the critical temperature for all properties, though the deviations become slightly larger at 100-200 "C. Figures 6-9 show the comparison of the estimates with Hill's equation of state on the 300 "C isotherm. These figures demonstrate that the accuracy is improved in the entire pressure range up to the saturation. The present modification can only be applied to the subcritical vapor region. Since the derivatives of f,,,( T I ) do not become zero at the critical temperature, the discontinuity of the derived properties occurs on the critical isotherm. However, the discontinuity is not so large: at 15 MPa, for example, about 4 kJ/kg for the enthalpy (h), 0.007 kJ/(kgK) for the entropy (s), and 1.5% for the heat capacity at constant pressure (c,), respectively.
Estimation of the Thermodynamic Properties of Dense Gaseous T20 In this section, thermodynamic properties will,be estimated for dense T20vapor in the manner mentioned in the preceding sections. To calculate the ideal gas properties for T20,the values of the ideal gas heat capacity at constant pressure ( c ~ by ) Friedman and Haar (1954) were correlated into the following equation:
where T is the temperature in K, c is the ideal gas heat capacity a t constant pressure in kf/(kg.K), and R is the gas constant in kJ/(kg.K).The constants for eq 15 are C1
Figure 9. Comparison of the estimated heat capacity at constant pressure of D20vapor with Hill's equation of state at 300 "C.
= 1677.92, Cz = 3394.15, C3 = -156.895, C4 = -239.1318, Cb = 104.6376, C6 = -15.642, C, = 12.53039,Cs = -975.883, and R = 0.377387 kJ/(kgK). Equation 15 is valid at temperatures from 230 to 1400 K. The constants C1and C2 have been determined so that the enthalpy (h)and the entropy (s) of the liquid are both zero at the triple point. The departures of h and s in the triple-point liquid state from those in the ideal gas condition were calculated with the aid of the present corresponding states method and of the Clausius-Clapeyron equation. The density values for the saturated liquid by Goldblatt (1964) and the saturation vapor pressure equation by the present authors (Matsunaga and Nagashima, 1986) were employed. The details of the prediction of thermodynamic properties of the saturated liquid of TzO will be described in a sequel of this paper. The estimation of thermodynamic properties was carried out for T20 using the critical constants predicted by Matsunaga and Nagashima (1986) (see Table I). The Haar-Gallagher-Kell equation of state for H 2 0 (1982) was employed also in this case. The present modification of the corresponding states principle discussed in the preceding section was applied to Su's method for the subcritical vapor region. The equations in Appendix and eq 15 were used for calculating h, s, and c,. The correction factor, fc,JT1), for T20and H 2 0 was obtained by using the vapor pressure equations for TzO (Matsunaga and Nagashima, 1986) and H 2 0 (Wagner, 1973) and was correlated with the following equation:
fc,p(T,) = 1 - 0.0822980(1 - T,) - 0.469641(1 - Tr)2+ 1.12174(1 - T,)3- 3.08149(1 - Tr)4 (16) The effect of larger uncertainty in the predicted critical constants for T20was examined by comparing the estimates with various values of T , and P,. A t low densities, the resulting estimates are rather insensitive to the change in T , and P,. The effect of the uncertainty in T, and P, was found to increase steeply at reduced densities; pr Z 1.1. In the vicinity of the critical point, the density limit tends to be further lowered. In the case of DzO, for which the values of T, and P, were determined much more accurately (Levelt Sengers et al., 1985), the density limit of the corresponding states principle is at pr = 1.4-1.5, as pointed out by previous investigators (Kesselman, 1960; Kirillin, 1963; Juza et al., 1974). The estimates of the density ( p ) , the enthalpy ( h ) ,the entropy (s),and the heat capacity at constant pressure (c,) of dense T20 vapor were calculated in the temperature range from the triple point (4.49 OC) to 1000 O C and at pressures up to 100 MPa. The region where the estimates are considered to be excessively unreliable is excluded.
1002 Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988 Table 11. Thermodynamic Properties of the Saturated Vapor of T20 T,O C T,K P,,MPa P , kg/m3 4.49 10.00 20.00 30.00 40.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00 120.00 130.00 140.00 150.00 160.00 170.00 180.00 190.00 200.00 210.00 220.00 230.00 240.00 250.00 260.00 270.00 280.00 290.00 300.00 310.00 320.00 330.00 340.00 350.00 360.00
277.64 283.15 293.15 303.15 313.15 323.15 333.15 343.15 353.15 363.15 373.15 383.15 393.15 403.15 413.15 423.15 433.15 443.15 453.15 463.15 473.15 483.15 493.15 503.15 513.15 523.15 533.15 543.15 553.15 563.15 573.15 583.15 593.15 603.15 613.15 623.15 633.15
0.000 662 0.000 983 0.001 928 0.003 591 0.006 39 0.010 90 0.017 91 0.028 45 0.043 82 0.065 65 0.095 88 0.13683 0.191 2 0.262 0 0.352 8 0.467 4 0.610 1 0.786 0.999 1.255 1.560 1.919 2.340 2.829 3.393 4.039 4.776 5.61 6.55 7.61 8.80 10.12 11.59 13.22 15.04 17.05 19.29
CP
T20
- lo-----
-~-
h, kJ/kg
0.006 33 0.009 21 0.017 45 0.031 45 0.054 19 0.089 7 0.1432 0.221 3 0.332 1 0.485 3 0.692 0.966 1.323 1.778 2.353 3.068 3.947 5.02 6.31 7.86 9.70 11.88 14.44 17.45 20.97 25.1 29.9 35.5 42.1 49.8 59.1 70.1 83.6 100 122 152 201
__
2132 2140 2156 2171 2186 2201 2216 2231 2246 2260 2274 2287 2300 2312 2323 2334 2344 2354 2362 2369 2375 2380 2383 2385 2385 2384 2380 2375 2367 2356 2341 2322 2299 2268 2229 2174 2090
6,
kJ/(kg.K) 7.68 7.56 7.36 7.18 7.01 6.86 6.71 6.58 6.46 6.35 6.25 6.15 6.06 5.98 5.90 5.82 5.75 5.68 5.62 5.55 5.49 5.43 5.37 5.31 5.26 5.20 5.14 5.08 5.02 4.96 4.90 4.83 4.76 4.68 4.59 4.47 4.32
c,,, kJ/(kg.K)
1.583 1.590 1.604 1.619 1.637 1.657 1.680 1.71 1.74 1.77 1.80 1.85 1.89 1.94 2.00 2.07 2.14 2.22 2.31 2.42 2.54 2.67 2.82 2.99 3.18 3.4 3.7 4.0 4.3 4.8 5.4 6.1 7.2 8.7 11.2 16 32
that, due to the larger uncertainty in the critical constant values employed, the density limit of the corresponding states principle for T,O is reduced to p r 5 1.1 compared with that of D 2 0 ( p , S 1.4-1.5).
Appendix. Equations for Estimating the Derived Thermodynamic Properties for an H20Isotope by the Corresponding States Principle (1) Enthalpy ( h ) . For Su's method,
0
200
4 00
600
800
1000
(-4-1)
t('C)
Figure 10. Heat capacity at constant pressure (e,) of dense gaseous
and when the present modification is further introduced,
TzO.
The resulting values are listed for the saturated vapor in Table 11. The estimated values of cp, depicted in Figure 10, show similar behavior to those of HzO and DzO. The tables of the estimated values of p , h, s, and cp for the superheated vapor of TzO are given in the supplementary material.
Conclusions The density, the enthalpy, the entropy, and the heat capacity at constant pressure of dense gaseous T20have been estimated in the temperature range 4.49-1000 "C by applying a corresponding states principle correction to the Haar-Gallagher-Kell(l982) equation of state for HzO. A modification of the corresponding states principle has been introduced a t subcritical temperatures for reducing the systematic error near the saturation line. It has been found
(A-2)
where h = h(T, p ) and P = P(T, p ) are the equations for the enthalpy and for the pressure of HzO and ho,I and ho are the ideal gas enthalpies of the isotope and of H26. (2) Entropy (s). For Su's method, %(TI,PI)
RI sl,I(TI,PlJ) + -[s(TH, RH
pH) -
sl,H(TH$P1,H)I 64-3)
and when the present modification is further introduced,
Ind. Eng. Chem. Res., Vol. 27, No. 6, 1988 1003
where s = s(T, p ) and P = P(T, p ) are the equations for , ~S1,H are the entropy and for the pressure of H20. s ~and the ideal gas entropies of the isotope and of H,O. P1,1is a reference pressure for the isotope (often set to 1 atm), and P1,H and P1,H*, the pressures for H 2 0 correspond t o P1,I, are calculated as
where P = P(T, p ) is the equation for the pressure of HzO. Registry No. TzO, 14940-65-9;DzO,7789-20-0;HzO,7732-18-5. Supplementary Material Available: Tables of the estimated densities, enthalpies, entropies, and heat capacities at constant pressure of superheated gaseous T20(12 pages). Ordering information is given on any current masthead page. Literature Cited
where c, = c,(T, p ) and P = P(T, p ) are the equations for the heat capacity at constant volume and for the pressure of HzO. cu0,1and c , ~ are , ~ the ideal gas heat capacities at constant volume of the isotope and of HzO. (4) Heat Capacity at Constant Pressure (c,). For Su’s method, the difference between cp and c, is CP,I(TI,PI) - CU,I(TI,PI)= RI T H
RH PH2 --
[
aP(TH,pH)
aP(TH, PH
aTH
apH
(A-9)
and when the present modification is further introduced,
Friedman, A. S.; Haar, L. J . Chem. Phys. 1954,22, 2051-2058. Goldblatt, M. J . Phys. Chem. 1964, 68, 147-151. Haar, L.; Gallagher, J. S.; Kell, G. S. In Proceedings of the 8th Symposium on Thermophysical Properties, Gaithersburg, June 1981;The American Society of Mechanical Engineers: New York, 1982; Vol. 11. Hill, P. G.; MacMillan, R. D. C. Znd. Eng. Chem. Fundam. 1979,18, 412-415. Hill, P. G.; MacMillan, R. D. C.; Lee, V. J . Phys. Chem. Ref. Data 1982, 11, 1-14; errata: 1983, 12, 1065. “International Skeleton Tables”. 6th International Conference on the Properties of Steam, New York, Oct 1963. Jones, W. M. J . Am. Chem. SOC. 1952, 74,6065-6066. Jones, W. M. J . Chem. Phys. 1968,48, 207-214. Juza, J.; Mareg, R.-Acta Tech. CSAV 1978,23, 1-10. Juza, J.; Mareg, R.; Sifner, 0. In Proceedings of the 8th International Conference on the Properties of Steam, Giens, France, Sept 1974, Paper VII.7, Jkza, J.; KmoniEek, V.; Sifner, 0.; Schovanec, K. Physica 1966,32, 362-384. Kesselman, P. M. Teploenergetika 1960, 7(3), 83-87. Kirillin, V. A,, Ed. In Tyazhelaya Voda-Teplofizicheskie Svoistva; Gosudarstvennoe Energeticheskoe Izdatelstvo: Moscow-Leningrad, U.S.S.R., 1963 (English translation: Heavy WaterThermophysical Properties; Israel Program for Scientific Translations, Jerusalem, Israel, 1971). Leach, J. W.; Chappelear, P. S.; Leland, T. W. Proc. Am. Pet. Znst., Sect. 3 1966, 46, 223-234. Levelt Sengers, J. M. H.; Straub, J.; Watanabe, K.; Hill, P. G. J . Phys. Chem. Ref. Data 1985, 14, 193-207. Lundqvist, B.; Persson, T. Brennst.- Wurme-Kraft 1965,17,356-362. Matsunaga, N.; Nagashima, A. Znd. Eng. Chem. Fundam. 1986,25, 115-119. Popov, M. M.; Tazetdinov, F. I. At. Energ. 1960, 8, 420-424. Rowlinson, J. S.; Watson, I. D. Chem. Eng. Sci. 1969,24,1565-1574. Su, G. J. Znd. Eng. Chem. 1946,38, 803-806. Trakhatengerts, M. S. Teploenergetika 1970, 17(5), 70-73. Wagner, W. In Meeting of the Commission Bl of the International Institute of Refrigeration, Zurich, Sept 1973; International Institute of Refrigeration: Paris, 1973; Paper 24.
Received for review March 30, 1987 Revised manuscript received September 9, 1987 Accepted December 29, 1987
