Critical parameters for 1,1,1-trifluoroethane (R-143a)

B

ELSEVIER

Fluid Phase Equilibria 125 (1996) 139-147

Critical parameters for 1,1,1-trifluoroethane (R-143a) Yukihiro Higashi *, Takeaki Ikeda Department of Mechanical Engineering, Iwaki Meisei University, 5-5-1, lino, Chuodai, lwaki 970, Japan

Abstract

Measurements of the vapor-liquid coexistence curve near the critical point were carried out for 1, l,l-trifluoroethane (R-143a) in the reduced temperature range of 0.97 < T / T c < l and in the reduced density range of 0.45 < P/Pc < 1.53. Taking into consideration of the disappearing level of the meniscus as well as the intensity of the critical opalescence, the critical temperature Tc and critical density Pc were determined. With respect to the critical pressure Pc, we calculated the value from the new vapor-pressure equation made by ourselves in order to represent the behavior of vapor-pressures near the critical point. The critical parameters determined in this paper are Tc = 345.88 + ~r K, ~r = 0.00 + 0.01 K, Pc = 431 + 3 kg m -3, and Pc = 3764 + 78.73~ r + 5 kPa. In addition, the critical exponent 13 along the coexistence curve was also discussed. Keywords: Critical state data; Vapor-liquid equilibria; Saturation properties; I, I, I-Trifluoroethane (R-143a)

I. Introduction

After the decision o f the CFCs phase out, it becomes necessary to search for new refrigerants as alternatives for CFCs and HCFCs. The new refrigerant mixtures including 1,1,1-trifluoroethane (R- 143a) as one o f the components are expected to be the alternative o f R-502, which was the present main refrigerant for the large size refrigerator. H o w e v e r the basic information on the thermophysical properties for R-143a and their mixtures is very restricted. Especially although the critical parameters, i.e. critical temperature Tc, critical density Pc, and critical pressure Pc, are very important not only for understanding the thermodynamic state surface but also for developing the correlations and predictions for the thermophysical properties with the help o f the principle o f corresponding states, only two reports can be available for R-143a. Mears et al. (1955) determined the critical parameters for R-143a as T c = 346.25 + 0.5 K, Pc = 434__+ 10 kg m -3 and Pc = 3760 + 70 kPa. Recently Fukushima (1993)

" Corresponding

author.

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Y. Higashi. T. Ikeda / Fluid Phase Equilibria 125 (1996) 139-147

determined the critical parameters for R-143a as T¢ = 345.97 + 0.03 K, Pc = 429 + 3 kg m -3 and Pc = 3769 + 5 kPa. In the present paper, the critical parameters for R-143a have been determined by visual observation of the meniscus disappearance. In addition, the correlations of the vapor-liquid coexistence curve as well as that of the vapor pressure near the critical point are formulated.

2. Experimental apparatus The experimental apparatus for measuring the vapor-liquid coexistence curve and for determining the critical parameters of fluid had been previously described in detail (Okazaki et al., 1983; Higashi, 1994). This apparatus is composed of three pressure vessels. The optical cell with two Pyrex glass windows was used for observing the change of the meniscus behavior of the sample refrigerant. The optical cell was a SUS-304 barrel-type cylindrical vessel and its inner volume was about 12 cm 3, which was calibrated by filling water. The expansion vessel and the supplying vessel was used to change the sample density in the optical cell without new sample charge. The inner volumes of the expansion vessel and the supplying vessel are about 9 cm 3 and 79 cm 3, respectively. The experimental apparatus was installed in the thermostated silicone-oil bath. The temperature in this bath was controlled within + 5 mK. The temperature measurement was conducted with a 25 1~ standard platinum resistance thermometer calibrated against ITS-90. The uncertainty of the temperature measurements depended upon the precision of the thermometer and the temperature fluctuation in the thermostated bath. In the present study, the uncertainty of the temperature measurements was estimated to be within ___10 mK. The sample density was calculated from the sample mass and the inner volumes of the pressure vessels. The uncertainty of the sample density in the optical cell was estimated to be within + 0.3-1.4 kg m - 3 The sample of R-143a was furnished from Asahi Glass Co. Ltd., Japan. The manufacturer stated that the sample purity of R-143a was 99.995 mass.%. In this R-143a, the water content was less than 5 ppm. This sample was used without further purification.

3. Measurements of the vapor-liquid coexistence curve in the critical region The vapor-liquid coexistence curve near the critical point for R-143a was measured by the observation of the meniscus disappearance. The experimental data are shown in Table 1. Eight data of saturated vapor densities and seven data of saturated liquid densities were obtained in the temperature range from 336.62 K to the critical temperature and in the density range between 195 and 661 kg m-3. The uncertainty of the temperature measurements is estimated to be within _ 10 mK. The uncertainties of each density measurement is different because the expansion procedure was introduced to change the sample purity. Therefore the uncertainty of the density measurements is represented in Table 1. Fig. 1 shows the distribution of the vapor-liquid coexistence curve data in the critical region on the temperature-density plane. Only one data set exists excluding the present data. Fukushima (1993) had

Y. Higashi, T. lkeda / Fluid Phase Equilibria 125 (1996) 139-147

141

Table 1 Experimental results along the vapor-liquid coexistence curve near the critical point for R-143a Temperature (K)

Density (kg m-3)

336.621 342.042 342.889 345.179 345.479 345.735 345.865 a 345.882 " 345.883 a 345.880 a 345.853

195.8 + 0.8 249.3 + 0.3 262.4+ 1.4 330.7 +__1.3 345.4 _ 0.6 374.5 + 1.2 416.8 + 1.3 427.7___ 1.4 431.7 + 0.8 435.3 + 0.5 487.8 +_0.5 524.5 + 0.9 544.1 +0.6 599.1 _+ I.I 661.2 + 0.7

345.407

345.120 343.166 339.63 ~ a Measured by observing the critical opalescence.

reported the experimental data o f the v a p o r - l i q u i d coexistence curve near the critical point. H e had adopted the same procedure for measuring the coexistence curve. Although a small temperature difference can be found, the present data are almost in agreement with F u k u s h i m a ' s data.

4. Determination of the critical parameters 4.1. C r i t i c a l t e m p e r a t u r e

Tc

T h e meniscus disappearance temperatures o f three experimental results at the top o f the coexistence curve, e.g. 345.882 K at the density o f 427.7 kg m -3, 345,883 K at the density o f 431.7 kg m -3, and

1348

R-i 43a

342 ................. o.<° E~

',

-"";i ...........................

~_ 340

............

!

,~- .......... ~ =

......................

338 ................... i" ~D

,

33~00'='

,~

200

. . . . . . .

300

ii........... ~i ............. !

.......................

,,

i. . . . . . . . . . . . . . . . . . . . . . . . . .~. ;

/'.

Fuku~ima

•

Critical Point i

400

...............

,,,I

. . . . . . .

500

600

700

Density (kg/m a) Fig. i. Vapor-liquid coexistence curve data for R-143a near the critical point.

Y. Higashi, T. Ikeda / Fluid Phase Equilibria 125 (1996) 139-147

142

345.880 K at the density of 435.3 kg m-3, were in good agreement within experimental uncertainty of temperature. Furthermore for these three experimental results, the critical opalescence was observed to be the typical critical phenomenon when the meniscus had disappeared. From the present results, the critical temperature Tc for R-143a was determined as follows: T~ = 345.88 + t5r K

(l)

6 r = 0.00 + 0.01 K

(2)

The uncertainty of the critical temperature was determined in consideration of the accuracy of the thermometer bridge, the experimental uncertainty of the temperature measurement, and the temperature fluctuation in the thermostated bath.

4.2. Critical density p~ For pure substances, the critical point can be defined as the point at which the meniscus disappears at the center level in the optical cell. Moreover the critical point can be also be defined as the point at which the critical opalescence of the liquid phase is observed as intensely as that at the vapor phase just before the meniscus disappears. In the present observation of the meniscus disappearance for R-143a, the critical opalescence was observed at four data points of the densities between 416.8 kg m -3 and 435.3 kg m -3. The meniscus for the densities of 416.8 kg m -3 and 427.7 kg m -3 descended with increasing temperature but disappeared prior to reaching the bottom of the optical cell. Whereas that for the density of 435.3 kg m -3 ascended with increasing temperature but disappeared prior to reaching the top of the optical cell. In the case of the density of 431.7 kg m -3, the meniscus was unchanged at the center of the optical cell with increasing temperature and finally disappeared at that level. On the basis of these observation of the meniscus disappearance, the critical density for R-143a is experimentally determined as follows. Pc = 431 + 3 k g m -3

(3)

4.3. Correlation of the vapor-liquid coexistence curve With respect to some halogenated hydrocarbons, one of the authors had reported the correlation of the vapor-liquid coexistence curve in the critical region by the following function (Higashi et al., 1984)

p+=p¢(I+Do]AT*['-"+D,]AT*[+D2IAT*[~-"+a'+BoIAT*I~+B~[AT*[ ~+a')

(4)

Where A T * = ( T - T c ) / T ~ is the reduced temperature difference, ot and 13 indicate the critical exponents for the specific heat at constant volume along the critical isochore and for the density along the coexistence curve, respectively. The exponent A~ stands for the first symmetric correlation-toscaling exponent in the Wegner expansion. In the present paper, the values of these exponents are quoted from the literature by Levelt Sengers and Sengers (1981). D 0, D I, D E, B 0 and B I indicate the

Y. Higashi, T. Ikeda / Fluid Phase Equilibria 125 (1996) 139-147

143

Table 2 C o e f f i c i e n t s in Eq. (4) Tc ( K ) Pc (kg m - 3) a 13 At DO D I D2 B0 Bi

345.88 (fixed) 430.59 0.1085 ( f i x e d ) 0.325 (fixed) 0.50 (fixed) 40.83606 - 82.52955 98.73731 1.747254 1.129734

coefficients. The upper sign " + " of B0 and B~ corresponds to the saturated liquid, while the lower sign " - " corresponds to the saturated vapor. Furthermore in Eq. (4), the critical density Pc is treated as an adjustable parameter determined from the experimental data of the vapor-liquid coexistence curve.

Six coefficients including the critical density in Eq. (4) were determined by weighted least-squares fitting exclusively to the present measurements. The coefficients determined are given in Table 2. The critical density determined analytically, which is 430.59 kg m - 3 , is in good agreement with that determined experimentally to be 431 kg m-3.

4.4. Critical pressure Pc The critical pressure Pc could not be determined directly from this experimental apparatus. Thus, in the present paper, the critical pressure was calculated as the extrapolation from the vapor-pressure correlation with the aid of the Tc value given in Eq. (1). The vapor-pressure correlation for R-143a

3800

3eoo ....R - ~ , 3 a - ............................I............~ ~.................... A

3400 .............................................. ~...................................

n v

3200 ....................................... ', ....... ;;~--~ .................... i ................. th t,D

o

~

B

D. 2600 .......... ,~".................... ~.................. 2400

~©'

325

'

i

330

335

,

,

(3 Znang i

340

, i 345

350

Temperature (K) Fig. 2. V a p o r p r e s s u r e s for R- 143a n e a r the critical p o i n t

Y. Higashi, T. lkeda / Fluid Phase Equilibria 125 (1996) 139-147

144

Table 3 Coefficients in Eq. (5) Tc (K) Pc " (kPa) ct Ai A2 A3 A4

345.88 (fixed) 3763.63 0.1085 (fixed) - 7.23490 33.82027 - 27.47321 45.14764

was formulated based on the vapor-pressure data near the critical point. In Fig. 2, the vapor-pressure data near the critical point, which we could obtain from the publication, are shown on the pressure-temperature plane. Four sets of experimental data of the vapor pressures for R- 143a, namely those by Fukushima (1993), Widiatmo et al. (1994), Guiliani et al. (1995) and Zhang et al. (1995) could be obtained in the temperatures above 325 K ( T / T c > 0.94). Using these data sets, the vapor-pressure correlation near the critical point for R- 143a was formulated. As the functional form of the vapor-pressure correlation near the critical point, the correlation proposed by Levelt Sengers et al. (1983) was adopted.

(5)

P~= Pc'(l + AIIAT'I+ A2IAT'I 2-~' + A3IAT'I 2 + A4IAT'I 3)

where Pc* indicates the adjustable parameter corresponding to the critical pressure and a indicates the critical exponent. Five coefficients, Pc" and A~-A 4 in Eq. (5), were determined by weighted least-squares fitting, and are summarized in Table 3. Fig. 3 shows the deviation plots of the vapor pressure for R-143a against Eq. (5). It is found the present correlation represents the three kinds of data set by Fukushima, Guiliani et al. and Zhang et ai. within the uncertainty to be -t-0.1%.

0.4 l 0.3

+

0.2

............

~ . . . . . .

Ip ...............

t . . . . .

4

.............

~,~ o.+ o I~ ~

8~

i"

'

I

+"

O(

~,,.(~) i -0.1 -0.2

,

,

i

W~iatmo

I

I

I

330 M

I

I

I

i

I

i '

325 •

*~t ,+ .~ ~, "~

J---I,

..... i. . . . . . . .

: ,

335

.

.

I

i ,

.

,

340

Temperature (K) Fukushima

•

Giullllni

i

.

345

.

350 O

Zhang I

Fig. 3. Deviation plots of the vapor pressures for R-143a against Eq. (5)

145

Y. Higashi, T. Ikeda/ Fluid Phase Equilibria 125 (1996) 139-147 101

R-143a t~

y

'9-

.........

+

1 0 -I 1 0 .4

, ,,,,I

. . . . . . . .

10-3

1 0 .2

1 0 "~

/T- T C //T C Fig. 4. Temperature dependence of the difference in coexisting densities.

On the basis of this correlation, the critical pressure for R-143a was determined as 3764 kPa. The uncertainty of the critical pressure ~Pc depends upon the uncertainty of the critical temperature and the accuracy of the vapor-pressure correlation. Taking into consideration of these factors, the critical pressure for R-143a was determined finally as follows: Pc = 3764 + 78.736 r + 5 kPa

(6)

5. Critical exponent B The critical exponent 13 along the coexistence curve can be determined on the basis of the power law representations

( p + - p - ) / 2 pc --- nl AT "I

(7)

where AT ° = ( T - Tc)/T~ is the reduced temperature difference, p+ and p - are the saturated liquid and vapor density, respectively. Coefficient B stands for a critical amplitude. The critical exponent 13 can also be represented by another power law representation for the saturated densities as follows. ( P -- P c ) / P c = BI A T " I t3

(8)

The relation between logKp + - P - ) / P c l and IoglAT'l with respect to Eq. (7) is shown in Fig. 4, whereas that between logKp - Pc)/Pcl and loglAT*l with respect to Eq. (8) is shown in Fig. 5. The

100 . . . . . . . . . . . . . .

t

~'~J

i

1 0 "1 10-4

.....

t 10-3

. . . . . . .

1 10-2

" •

R-143a . . . . . 1 0 -1

/T-T C /['l- C Fig. 5. Temperature dependence of the reduced density difference.

146

Y. Higashi, T. Ikeda / Fluid Phase Equilibria 125 (1996) 139-147

power law representations by Eqs. (7) and (8) suggest that the experimental results may be fitted by a straight with a gradient equivalent to the critical exponent 13. For R-143a, the values of 13 and B in Eq. (7) were obtained as 13 = 0.346 and B = 2.0606, respectively, as a result of least-squares fittings. Furthermore the values of 13 and B in Eq. (8) were obtained as 13 = 0.341 and B = 1.9038 for saturated vapor and as [3 = 0.350 and B = 2.1920 for saturated liquid. As for the critical exponent 13, Higashi (1989) had reported that the experimental value of 13 seemed to be larger than the theoretical value to be 0.325. The same conclusion can be also confirmed for R-143a.

6. Nomenclature A0, Al, A2, A3 Coefficients in Eq. (5) Coefficients in Eq. (4) B0, BI Coefficients in Eq. (4) Do, Di, D2 Pressure (kPa) P Critical pressure (kPa) Pc Vapor pressure (kPa) P, T Temperature (K) Tc Critical temperature (K) ot Critical exponent in relation to the specific heat at constant volume 13 Critical exponent along the coexistence curve Critical amplitude along the coexistence curve B ml First symmetric correction-to-scaling exponent AT* Reduced temperature difference = ( T - Tc) / T c Uncertainty of critical temperature (K) ~r Density (kg m -3) P p+ Saturated liquid density (kg m -3) pSaturated vapor density (kg m-3) Critical density (kg m -3) Pc

Acknowledgements The authors are greatly indebted to Asahi Glass Co. Ltd., Tokyo, Japan for kindly furnishing and analyzing the sample and to Messrs H. Takashima, J. Ohshima and K. Sakashita, lwaki Meisei University, for their valuable assistance in this experiment.

References M. Fukushima. 1993. Measurements of vapor pressure, vapor-liquid coexistence curve and critical parameters of HFC-143a. Trans. JAR, 10 (1): 87-93 (in Japanese).

Y. Higashi. T. Ikeda / Fluid Phase Equilibria 125 (1996) 139-147

147

G. Guiliani, S. Kumar, P. Zazzini and F. Polonara, 1995. Vapor pressure and gas phase PVT data and correlation for 1,1, l-trifluoroethane (R143a). J. Chem. Eng. Data, 40 (4): 903-908. Y. Higashi, M. Uematsu and K. Watanabe, 1984. Determination of the vapor-liquid coexistence curve and the critical parameters for Refrigerant 502. Int. J. Thermophys., 5 (1): 117-129. Y. Higashi, 1989. Correlation of the saturated densities for halogenated hydrocarbons and their mixtures. Proc. 2nd Asian Thermophysical Properties Conference, Sapporo, pp. 525-530. Y. Higashi, 1994. Critical parameters for HFCI34a, HFC32 and HFCI25. Int. J. Refrig., 17 (8): 524-531. J.M.H. Levelt Sengers and J.V. Sengers, 1981. How close is "close to the critical point?" In: H. J. Raveche (ed.), Perspectives in Statistical Physics. North-Holland, Amsterdam, Chap. 14. J.M.H. Levelt Sengers, B. Kamgar-Parsi and J.V. Sengers, 1983. Thermodynamic properties of isobutane in the critical region. J. Chem. Eng. Data, 28 (4): 354-362. W.H. Mears, R.F. Stahl, R. Orfeo, R.C. Shair, L.F. Kells, W. Thompson and H. McCann, 1955. Thermodynamic properties of halogenated ethanes and ethylenes. Ind. Eng. Chem., 47 (7): 1449-1454. S. Okazaki, Y. Higashi, Y. Takaishi, M. Uematsu and K. Watanabe, 1983. Procedures for determining the critical parameters of fluids. Rev. Sci. Instrum., 54 (1): 21-25. J.V. Widiatmo, H. Sato and K. Watanabe, 1994. Saturated-liquid densities and vapor pressures of I,l,l-trifluoroethane, difluoromethane, and pentafluoroethane. J. Chem. Eng. Data, 39 (2): 304-308. H.L. Zhang, H. Sato and K. Watanabe, 1995. Vapor pressures, gas-phase PVT properties, and second virial coefficients for l,l,l-trifluoroethane. J. Chem. Eng. Data, 40 (4): 887-890.