Second and third virial coefficients for the R41+N2O system

Fluid Phase Equilibria 225 (2004) 69–75

Second and third virial coefficients for the R41+N2O system G. Di Nicolaa , G. Giuliania , F. Polonaraa,∗ , R. Stryjekb a b

Department of Energetics, Universit`a Politecnica delle Marche, Ancona, Italy Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland

Received 7 April 2004; received in revised form 22 July 2004; accepted 23 July 2004

Abstract As a part of our ongoing research program on the PVTx measurements by the Burnett method for HFC + hydrocarbon and/or inorganic compound systems, in this work the experimental results for the nitrous oxide (N2 O) + fluoromethane (R41) system will be described. The system was chosen as an alternative refrigerant mixture. The thermodynamic properties of both mixture constituents are well known from the literature, but no experimental results have been published so far on the PVTx properties of this specific binary system. PVTx measurements were performed for the binary N2 O + R41 system for four isotherms (283, 303, 323 and 343 K). In total, 17 runs were performed in a pressure range from 4600 to 150 kPa. The second and third virial coefficients along with the second and third cross-virial coefficients were derived from experimental results. The experimental uncertainty in second and third virial coefficients is estimated to be within ±2 cm3 /mol and ±500 cm6 /mol2 , respectively. © 2004 Elsevier B.V. All rights reserved. Keywords: Burnett method; PVTx; Virial coefficients; R41; N2 O

1. Introduction Nitrous oxide is an inexpensive and widely available gas. It is largely used as weak anaesthetic gas and for surgical purposes. It is also used in the dairy industry as a mixing and foaming agent as it is non-flammable, bacteriostatic and leaves no taste and odour. It is also used in auto racing to speed engines and in diving to prepare divers for nitrous-like effects. For its thermophysical properties, it can also be suggested as a refrigerant. Fluoromethane is a hydrofluorocarbon used in the refrigeration industry as a constituent in several binary or ternary mixtures substituting difluorochloromethane (R22). The main drawback of this refrigerant fluid lies in its flammability and far from negligible global warming potential (GWP), despite zero ozone depletion potential (ODP). However, a combination of fluoromethane and N2 O might make it possible to achieve the

basic requirements for industrially-applicable blends, in particular for low-temperature applications like cascade cycles. The Burnett apparatus was calibrated using helium, and its performance was confirmed by measurements for pure N2 O and R41. The values of the virial coefficients for N2 O and R41 were adopted from our previous measurements [1,2] as the same sample was used in the present study. In a first attempt to study the properties of the R41 + N2 O system, the PVTx property was measured by the Burnett method, and virial coefficients were derived from the experimental data collected. To our knowledge, no experimental PVTx data are reported in the literature for this specific binary system.

2. Experimental section 2.1. Reagents

∗

Corresponding author. Tel.: +39071 2204 432; fax: +39071 2204 770. E-mail address: [email protected] (F. Polonara).

0378-3812/$ – see front matter © 2004 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2004.07.011

N2 O and R41 were supplied by Sol SpA and Lancaster Inc., respectively; their purity was checked by gas chromato-

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graphic analysis, using a thermal conductivity detector. It was found to be 99.99% for the N2 O and 99.9% for the R41 on an area–response basis. 2.2. Apparatus

Fig. 1. Schematic view of the experimental apparatus. Legenda: (1): nitrogen reservoir, (2): vacuum pump (Vacuubrand, mod. RZ2), (3): precision pressure controller (Ruska, model 3981), (4): gas lubricated dead weight gage (Ruska, model 2465), (5): vibr. cylinder pressure gage (Ruska, model 6220), (6): digital temperature indicator (Corradi, RP 7000), (7): electronic null indicator (Ruska, model 2416), (8): stirrer, (9): heater, (10): cooling coil connected with an auxiliary bath, (11): differential press. transducer (Ruska, model 2413), (12): measurement chamber (VA ), (13): expansion chamber (VB ), (14): magnetic recirculating pump, (15): Pt resistance thermometer (Tersid, Pt 100), (16): vacuum pump for VB (Vacuubrand, model RZ2), (17): charging fluid reservoir, (18): Pt resistance thermometer (Hart Scientific, Pt 25) V1 , V2 , V3 , V4 constant volume valves, (19): digital pressure indicator (Ruska, model 7000)

The experimental apparatus is reported in Fig. 1. It is the same as the one described elsewhere [3–5] and used with only minimal modifications already described [6]. It consists of two pressure vessels, the measurement chamber, VA , and the expansion chamber, VB , both spherical in shape, with a volume of approximately 70 and 35 cm3 , respectively, plus some auxiliary systems for filling and mixing the compounds in the Burnett vessels, and for controlling and measuring the pressure and temperature. The vessels are made of Invar, given its excellent corrosion resistance and low thermal-expansion coefficient. The four-valve arrangement enables the vessels VA and VB to be filled or emptied separately and, in addition to the expansion experiment, allows for the compounds in the Burnett vessels to be mixed using a magnetic recirculating pump. The packing surfaces of valves V1 and V4 are exposed to the expansion volume VB and the packing surfaces of valves V2 and V3 are exposed in the opposite direction of the volumes VA and VB . Thus, the principal volume VA and its fixtures are all-metal to prevent contact between the sample gas in vessel VA and the Teflon packing throughout the lengthy Burnett experiment, except for the time it takes to reach thermal equilibrium after expansion. The measurement vessel is connected to a diaphragm-type differential pressure transducer (Ruska Model 2413), coupled to an electronic null indicator (Ruska Model 2416). The

Fig. 2. Experimental second virial coefficients for N2 O against reduced temperature, T/Tc , where Tc = 309.6 K is the critical temperature [13]. (䊉): present work; (♦): [7]; (): [8];(–): [9]; (): [10]; (): [11]; (): [12].

G.Di Nicola et al. / Fluid Phase Equilibria 225 (2004) 69–75

pressure on either side of the diaphragm is balanced with nitrogen by means of a precision pressure controller (Ruska Model 3981), and the pressure is read by a digital pressure gauge (Ruska Model 7000). The vessels with the magnetic pump and the pressure transducer are immersed in a thermostatic bath filled with about 45 l of silicon oil. The temperature of the bath is kept constant by means of a Proportional Integrative Derivative (PID) device, controlled by a computer to which the temperature measurement system is also connected. The temperature control and acquisition system relies on two platinum resistance thermometers calibrated according to ITS 90 at the Istituto Metrologico G. Colon-

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netti (IMGC), of Turin. A Hart Scientific Pt 25  resistance thermometer (mod. Hart 5680) and a Tersid Pt 100  resistance thermometer are used, respectively, for temperature measurement and control. Both thermometers are connected to a digital temperature indicator (Corradi, RP 7000). The Burnett constant, N, defined as the ratio of the volumes of cell A and the sum of the volumes of cells A and B at zero pressure, was determined using gaseous helium measurements. After taking measurements at several isotherms, the constant was found to be N = 1.4945 ± 0.0001 for series from 1 to 14 and N = 1.4961 ± 0.0001 for series 15 and 16.

Fig. 3. Experimental third virial coefficients for N2 O against reduced temperature, T/Tc , where Tc = 309.6 K is the critical temperature [13]. (䊉): present work; (): [11].

Table 1 Second and third virial coefficients for N2 O and R41 Series

1 2 3 4 5 6 7 8 9 10 11 12 13 14

N2 O

R41

T/K

B/cm3 ·mol−1

C/cm6 ·mol−2

T/K

B/cm3 ·mol−1

C/cm6 ·mol−2

283.51 283.50 304.09 304.10 314.42 314.41 324.78 324.79 335.18 335.16 345.58 345.52 364.36 364.36

−150.3 −151.1 −127.3 −128.4 −119.1 −119.2 −109.9 −111.2 −101.5 −100.1 −95.0 −95.5 −82.7 −81.3

6410.51 6911.01 5376.18 5670.57 5471.23 5466.06 4776.90 5427.21 4387.63 3774.42 4223.44 4428.41 3540.37 2943.91

303.15 303.15 313.15 323.15 323.15 333.15 333.15 343.15 343.15

−196.1 −197.5 −182.2 −169.0 −169.5 −158.0 −157.1 −146.0 −144.7

16100 16330 14750 13480 13740 12830 12510 11400 10930

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Table 2 Experimental pressures measured during Burnett expansions and regressed compressibility factors of the N2 O (1) + R41 (2) system Series 1 (T/K = 283.53) (x1 = 0.4332)

Series 2 (T/K = 283.52) (x1 = 0.5103)

Series 3 (T/K = 283.39) (x1 = 0.5702)

Series 4 (T/K = 283.53) (x1 = 0.7587)

P (kPa)

z

P (kPa)

z

P (kPa)

z

P (kPa)

z

3127.5 2384.2 1733.1 1223.9 848.6 581.1 394.9 266.9 179.9

0.6829 0.7793 0.8479 0.8963 0.9302 0.9536 0.9701 0.9816 0.9903

2974.4 2230.5 1605.8 1126.9 778.0 531.4 360.4 243.4 163.7

0.7137 0.8012 0.8633 0.9069 0.9373 0.9584 0.9728 0.9837 0.9902

2783.0 2053.7 1463.6 1020.4 701.4 477.8 323.4 218.1 146.8

0.7468 0.8250 0.8800 0.9184 0.9450 0.9635 0.9763 0.9858 0.9931

3492.1 2657.2 1928.2 1359.9 941.9 644.6 437.9 296.0 199.4

0.6883 0.7840 0.8515 0.8990 0.9320 0.9548 0.9710 0.9823 0.9907

Series 5 (T/K = 304.12) (x1 = 0.2406)

Series 6 (T/K = 304.12) (x1 = 0.4961)

Series 7 (T/K = 304.10) (x1 = 0.7188)

Series 8 (T/K = 304.12) (x1 = 0.8163)

4427.0 3522.1 2642.5 1907.3 1340.6 927.7 634.6 430.7 291.6

4316.4 3296.8 2407.6 1704.2 1183.7 811.6 551.8 373.0 251.2

4635.8 3539.0 2580.8 1827.2 1269.2 871.3 592.9 401.9 271.8

3493.6 2534.0 1787.7 1238.5 848.0 575.9 389.2 262.2 176.2

0.5939 0.7073 0.7943 0.8582 0.9029 0.9353 0.9577 0.9731 0.9862

0.6722 0.7686 0.8402 0.8902 0.9255 0.9500 0.9668 0.9783 0.9863

0.6730 0.7690 0.8395 0.8897 0.9250 0.9505 0.9682 0.9825 0.9945

0.7814 0.8484 0.8960 0.9292 0.9523 0.9682 0.9793 0.9876 0.9934

Series 9 (T/K = 324.78) (x1 = 0.2491)

Series 10 (T/K = 324.78) (x1 = 0.3502)

Series 11 (T/K = 324.77) (x1 = 0.5530)

Series 12 (T/K = 324.77) (x1 = 0.7497)

4613.6 3453.7 2492.7 1754.7 1214.2 830.4 563.8 380.8 256.4

3973.7 2897.4 2053.6 1427.6 979.4 666.3 450.8 303.8 204.1

4446.8 3254.2 2310.6 1608.1 1104.4 751.6 508.4 342.6 230.3

4153.3 2992.7 2103.6 1453.6 993.5 674.3 455.1 306.2 205.6

0.7054 0.7904 0.8540 0.8999 0.9321 0.9542 0.9698 0.9805 0.9881

0.7656 0.8356 0.8865 0.9225 0.9474 0.9648 0.9771 0.9856 0.9915

0.7592 0.8316 0.8839 0.9208 0.9466 0.9643 0.9764 0.9849 0.9909

0.7952 0.8578 0.9025 0.9335 0.9550 0.9703 0.9804 0.9872 0.9921

Series 13 (T/K = 345.25) (x1 = 0.2790)

Series 14 (T/K = 345.58) (x1 = 0.4514)

Series 15 (T/K = 345.75) (x1 = 0.6300)

Series 16 (T/K = 345.74) (x1 = 0.7278)

4645.0 3365.2 2375.9 1647.8 1129.1 767.3 518.5 349.2 234.6

4621.4 3323.7 2334.7 1613.2 1102.7 748.2 505.2 340.0 228.3

3431.9 2404.3 1658.3 1131.7 766.9 517.2 347.7 233.3 156.3

4924.6 3528.9 2471.7 1704.5 1163.3 788.4 531.7 357.5 239.8

0.7787 0.8445 0.8925 0.9265 0.9503 0.9667 0.9779 0.9859 0.9915

0.7971 0.8581 0.9023 0.9333 0.9549 0.9698 0.9802 0.9874 0.9927

0.8690 0.9107 0.9398 0.9595 0.9728 0.9815 0.9872 0.9908 0.9932

0.8104 0.8688 0.9104 0.9393 0.9590 0.9724 0.9811 0.9869 0.9906

Series 1–14: N = 1.4945. Series 15 and 16: N = 1.4961.

3. Experimental procedure and uncertainties 3.1. Experimental procedure To measure the system components, the classical Burnett experimental procedure was followed, repeating expansions until low pressures were achieved. When measuring mixtures, the two vessels were separately filled with different compounds. Then the sample was mixed to homogenize the composition with the aid of the magnetic pump while the

expansion valve was kept open. A sample for composition measurement, collected during the first expansion, was used for gas chromatographic analysis. The gas chromatograph calibration was performed as described elsewhere [6]. 3.2. Experimental uncertainties The uncertainty in the temperature measurements is due to the thermometer and any instability of the bath. The stability of the bath was found to be less than ±0.015 K and

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Table 3 Experimental and calculated second and third virial coefficients for the N2 O (1) + R41 (2) system Series

T/K

x1

Bm exp (cm3 mol−1 )

Bm calc (cm3 mol−1 )

dBm (cm3 mol−1 )

Cm exp (cm6 mol−2 )

Cm calc (cm6 mol−2 )

dCm (cm6 mol−2 )

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16

283.53 283.52 283.39 283.53 304.12 304.12 304.10 304.12 324.78 324.78 324.77 324.77 345.25 345.58 345.75 345.74

0.4332 0.5103 0.5702 0.7587 0.2406 0.4961 0.7188 0.8163 0.2491 0.3502 0.5530 0.7497 0.2790 0.4514 0.6300 0.7278

−177.5 −173.8 −168.1 −155.4 −167.1 −146.0 −136.5 −129.6 −140.1 −132.8 −120.1 −110.8 −116.2 −107.3 −100.6 −99.1

−177.9 −171.7 −167.5 −157.1 −167.4 −146.0 −134.2 −131.0 −140.5 −132.0 −119.1 −111.7 −120.1 −109.4 −101.4 −98.4

0.3 −2.1 −0.6 1.7 0.3 0.0 −2.3 1.4 0.5 −0.8 −1.1 1.0 3.9 2.1 0.8 −0.7

8360 8100 7060 5720 10250 7220 6540 5180 8360 7090 5310 4110 5970 4800 3800 4460

8720 7670 7020 5890 10380 7180 6010 5810 8510 7060 5070 4300 5990 4660 4200 4170

−360 430 40 −170 −130 40 530 −630 −150 30 240 −190 −20 140 −400 290

the uncertainty of the thermometer was found to be less than ±0.010 K in our temperature range. The total uncertainty in the temperature measurements was thus lower than ±0.03 K. Any uncertainty in the pressure measurements is due to the transducer and null indicator system and to the pressure gauge. The digital pressure indicator (Ruska, mod. 7000) has an uncertainty of ±0.003% of the full scale. The total uncertainty in the pressure measurement, also influenced by temperature fluctuations due to bath instability, was found to be lower than ±1 kPa. The uncertainty of the mixture’s composition was found to be constantly lower than 0.5% in mole fraction.

For N2 O, 14 runs, along seven isotherms in a pressure range from 5200 to 170 kPa, were performed. Experimental PVT data are reported elsewhere [1]. The second and third virial coefficients were derived and a good consistency was found after comparison with data in the literature [7–12], as shown in Figs. 2 and 3. For R41, 90 experimental points along five isotherms (nine sets in all) were collected in the temperature range from 303 to 343 K and for pressures from 125 up to 4200 kPa. All experimental data, together with the comparison with literature, were reported elsewhere [2]. Here, a summary of the derived second and third virial coefficients for both pure fluids is reported in Table 1. These results were adopted in the present work because the same samples were used for the mixture.

4. Results for N2 O and R41 5. Results for the mixtures

The experimental PVT measurements obtained in previous papers [1,2] were used to derive the second, B, and third, C, virial coefficients of the virial equation:
 RT B C P= 1+ + 2 (1) V V V

For the N2 O + R41 system, 144 experimental points along 16 sets and four isotherms were collected within a temperature range from 283.5 to 345.7 K and a pressure range from 150 to 4900 kPa. The experimental findings are given in Table 2, together with the compressibility factor values, z. The virial coefficients for the mixtures were found by applying the same procedure as for pure compounds. The values of the second and third virial coefficients (Table 3), along with the virial coefficients for the pure compounds (smoothed as a function of reduced temperature) were used to derive

In the regression, each run was treated separately and (dP)2 was used as an objective function, applying the Burnett constant from the helium calibration. The pressure distortion of the Burnett cells was taken into account, as explained elsewhere [3–5]. Table 4 The averaged second and third virial coefficents for the N2 O (1) + R41 (2) system T/K

B11 (cm3 mol−1 )

B12 (cm3 mol−1 )

B22 (cm3 mol−1 )

C111 (cm6 mol−2 )

C112 (cm6 mol−2 )

C122 (cm6 mol−2 )

C222 (cm6 mol−2 )

283.5 304.1 324.8 345.6

−150.6 −128.4 −109.8 −94.8

−156.3 −129.7 −105.3 −91.5

−226.8 −195.2 −167.3 −143.0

6640 5700 4880 4160

3820 5720 2990 4560

8560 6090 5490 2290

18640 16020 13470 10990

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Fig. 4. Second virial coefficients for the N2 O (1) + R41 (2) system against the mole fraction at temperatures, T: (), 283.5; (), 304.1; (), 324.8; (), 345.7. The lines represent the trend of the second virial coefficients.

cross-virial coefficients. The results are shown in Table 4. The second cross-virial coefficients were calculated from the expression: B12 =

Bm − x12 B11 − x22 B22 2x1 x2

(2)

for each experimental datum point. Next, the B12 values found for each temperature were averaged; the averaged B12 values, given in Table 4, were used to calculate the deviations of Bm

from the experimental values shown in Table 3. Likewise, the third cross-virial coefficients, C112 and C122 , were determined by combining data for each temperature from the equation: Cm = x13 C111 + x23 C222 + 3x12 x2 C112 + 3x1 x22 C122

(3)

keeping the pure third virial coefficients and the different experimental compositions as fixed values. The averaged values of the third cross-virial coefficients are included in Table 4.

Fig. 5. Third virial coefficients for the N2 O (1) + R41(2) system against the mole fraction at temperatures, T: (), 283.5; (), 304.1; (), 324.8; (), 345.7. The lines represent the trend of the third virial coefficients.

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Using these values, the third virial coefficients for the mixtures were recalculated for each point. The results, together with the deviations, are also given in Table 3. The overall AAD for Bm was evaluated at 1.2 cm3 /mol, while the AAD for Cm was 237 cm6 /mol2 . For the system being plotted against the mole fraction in Figs. 4 and 5, respectively, the second and third virial coefficients show a slightly positive and a slightly negative deviation, respectively, from the ideal for the second and third virial coefficients. It should be noted that the cross-virial coefficients, we found, depend slightly on the empirical expressions used for the approximation of the virial coefficients of the system constituents.

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Subscripts m relates to mixture i, j, k components r reduced property c critical property

Acknowledgments This work was supported by MIUR, Ministry of Instruction, University and Research and by the Government of Regione Marche.

References 6. Conclusions This work reports the experimental findings for the N2 O + R41 system obtained with the Burnett method. The performance of the apparatus was checked by means of measurements for the mixture constituents and a good consistency was observed between the virial coefficients obtained and those reported in the literature. The N2 O + R41 system was studied over four isotherms, deriving second and third crossvirial coefficients. List of Symbols P pressure V molar volume B second virial coefficient N number of experimental points n number of mixture components z compressibility factor T temperature R gas constant C third virial coefficient x mole fraction V molar volume

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