Isotherms for the He-Ar system at -130, -115, and -90°C up to 700 atm

Physica

52 (1971) 79-91 o North-Holland

ISOTHERMS

FOR

Publishing

THE

He-Ar

AT - 130, - 115, AND -90°C J. A. PROVINE* University

Co.

SYSTEM

UP TO 700 ATM

and F. B. CANFIELD

of Oklahoma, Norman,

Oklahoma,

USA

Received 7 September 1970

Synopsis A Burnett apparatus was used to obtain compressibility factors and virial coefficients for helium, argon, and four mixtures at -90, - 115, and - 130°C. The pressures for the first two isotherms ranged from 2 to 700 atmospheres for both pure components and all mixtures. For the - 130°C isotherm the pressures for the pure argon and mixtures ranged from 2 atmospheres to slightly below saturation pressure.

1. Introduction. Compressibility factors and virial coefficients are presented for helium, argon, and four mixtures at -9O”C, -115”C, and - 130°C. The pressure ranges from 2 to 700 atmospheres for the first two isotherms for all runs. For the - 130°C isotherm the pressure for the pure argon and mixtures ranges from 2 atmospheres to slightly belaw saturation pressure. These results complement those reported by other investigators for the helium-argon system at higher temperatures. Tanner and Massonl) report seven isotherms between 25°C and 174°C up to 125 atmospheres with two mixtures at each isotherm. Kalfoglou and Miller2) present six isotherms between 30°C and 500°C at pressures up to 80 atmospheres with seven mixtures at each isotherm. Blancett et ~2.~) give 50°C O”C, and -50°C isotherms at pressures from 2 to 700 atmospheres for the same four mixtures presented here. Data for pure helium and argon are reported only for consistency and for purposes of calculating interaction virial coefficients. Many investigators have reported compressibility data for the pure components. These investigations are too numerous to list here. 2. Experimental method. These data were obtained using the experimental method proposed by Burnett 4). This apparatus is described in detail in previous publications 375-a). Other modifications to reduce licjuid nitrogen t Present address: Continental Oil Co. Ponca City, Oklahoma. 79

P (atm)

10.2350

5

5 7

1.00857

1.00547

6.7072

6.5260 A (A.717

16.0812

6

1.01344

16.5018

10.5111

, fb-l?CA

25.3409

8

1.02113

25.9776

1 -,.-.l_

40.1491

9

1.03335

41.0726

103.696

105.243 64.1145

171.286

12

1.13782

172.476

10

292.968

16

1.22966

291.262

11

532.773

22

1.39831

517.529

1.05292

1.00316

3.2039

8

1.08476

1.00494 4.7844 3.0567

18 24

1.00489 1.00312

5.0154

6

1.00422

1.00270

5.1751

3.3076

65.3857

1.00774

7.4963

15

1.00765

7.8587

5

1.00661

8.1045

1 flc-lAfl/.

1.00636

1.00996

1.01562

1.02456

1.03877

1.06158

1.09880

1.16129

1.27115

16 19

16

18

22

26

28

31

36

49

6.2969 4 n?n.?

9.8748

15.5183

38.7807 24.4677

61.9877

100.452

166.533

286.98

1.00650 1 00415

1.01019

1.01602

1.02525

1.04001

1.0639 1

1.10338

1.17063

1.29105

3 4

4

5

6

7

7

9

15 11

18

3 4

1.01214 11.7636

16

1.01199

12.3324

5

1.01036

12.7103

1.52399

4 3

1.01910 18.5064

19

1.01883

19.4043

7

1.01626

19.9741

1

5

1.03017

29.2318

23

1.02965

30.6433

8

1.02560

529.402

6

1.04793

46.4584

27

1.04691

48.6876

9

1.04048

49.9187

31.4930

69

7

1.07687

1.47902

9 7

1.12518

74.5963

30

121.792

34

1.12071 1.07478

78.1040

10

127.269

12

129.293

1.10382

1.20887

1.06447

15 12

1.36266

79.7981

21

1.67237

690.706 360.132 204.454

76 62 43

1.61944 1.34063 1.19910

701.742 371.683 212.730

20 14

o(Z). 105

24

Z = Pv/RT

u(Z) .105

Z = Pv/RT

1.28801 1.17033

P (atm)

1.51135

o(Z)-105

675.389

Z = Pv/RT

143.15 K

158.15 K

factors

368.318 214.196

100.OOOh Helium

P (atm)

183.15 K

Compressibility

TABLE I *

0

0)

1.02105

1.01325

1.00839

1.00533 1.00340

1.00217

19.1184

12.1779

7.7709

3.1738

1.00697

1.00444

1.00283

1.00181

10.1402

6.4742

4.1369

2.6449

proportional

1.01099

15.9067

factors

1.01742

* Weighting

1.02780

25.009 1

1.07401

100.692

39.4733

1.12562

164.875

1.04493

1.22356

280.052

62.6974

1.42890

511.031

4.9643

1.03375

47.6138

30.0997

1.09140

122.715

1.05491

1.15775

203.384

75.9150

1.57663

1.28827

676.277

353.613

to (3 + Prj)-2

1.65812

all data.

19

1.00187

2.1093

14

2 3

1.00324 5.1588 3.298 1

15

1.00293

1.00458

1.00132

2

1.00511 1.00206

3 2

1.00810 12.6531 8.0746

1.01132 19

3

1.01292 19.8639

1.00719

4 1.02086

31.2777

5 4 1.03431 49.5 103

6 1.05806

79.1306

8 1.10258

128.839

10 1.39624 1.19306

398.314 217.821

29 24

32

37

45

57

67

92

17

13

15

20

26

30

34

41

51

63

75

107

1.01790

1.02853

1.07637 1.04611

1.13171

1.24178

1.48566

1.00223

1.00348

1.00546

1.00858

1.01351

1.02142

1.03429

1.09375 1.05586

1.16515

1.31265

were used in treating

2.5093

3.9242

7

6.1405

5

9.6175

15.0873

23.7227

37.4523

59.5138

95.6791

157.178

269.416

503.655

2.9856

4.6695

7.3098

11.4560

17.9819

28.3081

44.7778

71.4028

115.543

192.277

338.466

667.956

5 4

6

8

9

10

11

14

19

22

5

5

5

5

7

8

9

10

12

15

19

26

11

tn

1.00866

1.00497

1.00296

1.00180

1.00112

i nnn7n

38.7362

24.7092

15.7876

10.0958

6.4580

A 1’217

9.8820

14 6.3289 A flr;X

15.4230

24.0608

37.5268

58.5947

17

20

23

26

0.99809 00~17~ n

0.99711

0.99571

0.99385

0.99181

0.99094

8 R

11

14

17

19

25 21

1.01589

0.99587

60.9325

92.0363

32

1.02128

147.522

39

1.06592 1.03112

155.988 96.6011

31

37

1.11217

53

1.40318

13

10

251.088

1.00053

3.1516

11

495.171

1BOO84

45

1.00135

7.6947

4.9240

18

15

62

1.00218

12.0250

21

1.38761

1.00361

18.8063

24

1.15212

1.00615

29.4489

28

263.365

1.01091

35

495.512

1.02048

72.8561

1.09040

1.04131

189.904

116.120

46.2121

1.21615

43

74

51

1.5797 1

330.827

Helium

rJ(Z). 105 P (atm)

2.4750

3.8637

6.029 1

9.404 1

14.6573

22.8205

35.4989

55.2362

86.4019

138.178

0.99872

0.99801

0.99693

0.99531

0.99292

0.98957

0.98534

0.98139

0.98259

1.00583

Z = Pv/RT

P (atm)

Z = Pv/RT

o(Z) .105

2 = Pv/RT

671.262

59.35%

P (atm)

143.15 K

158.15 K

183.15 K

TABLE I $ (continued)

9

6

7

10

13

15

17

20

25

28

o(Z). 105

LI

1.31733 1.03402 0.96821 0.96038 0.96737 0.9763 1 0.98373 0.98915 0.99288 0.99537 0.99701 0.99807

301.905 173.629 108.838 69.9629 45.1953 29.1701 18.7867 12.0761 7.7513 4.9702 3.1855

488.410 245.328 147.000 93.3320 60.1627 38.8538 25.0590 16.1255 10.3593 6.6468 4.2609 2.7305

71

58 39 34 28 24 22 20 17 14 11 10 14

44 38 31 26 23 20 18 14 11 10 13 471.152 217.937 129.040 85.4114 57.8188 38.7185 25.5770 16.7195 10.8486 7.0049 4.5087 2.896 1

1.18161 0.85493 0.79116 0.82013 0.86693 0.90786 0.93830 0.95944 0.97362 0.98295 0.98903 0.99295

t Weighting factors proportional to (3 + P,5)-2 were used in treating all data.

1 .tabYJl

1.09102 0.98035 0.96021 0.96439 0.97331 0.98140 0.98749 0.99175 0.99462 0.99652 0.99776

014..YJu

488 314 276 222 200 192 178 151 117 89 97 146 61.5804 40.9799 27.0113 17.6427 11.4436 7.3886 4.7556 3.0540 1.9600

73.6126 49.1401 32.5543 21.3507 13.8902 8.9870 5.7918 3.7228 2.3907

0.87981 0.91517 0.94247 0.96185 0.97504 0.98380 0.98954 0.99327 0.99568

0.86259 0.90029 0.93137 0.95410 0.9698 1 0.98035 0.98729 0.99181 0.99473

29 26 29 33 37 40 43 45 46

36 24 27 31 35 38 41 42 44

0.99043

0.99385

12.0481

7.7767

5.0041

3.2146

0.96840

0.97950

0.98677 - -_. ._

6.9212

0.95172

25.4411

10.7318

0.92736

38.7233

16.5746

0.85308

0.89378

86.9052

58.2890

0.8203 1

0.98513

18.5848

130.547

0.97699

28.4761

1.23657

0.96459

43.2329

0.85488

0.91933 0.94607

64.9073

480.256

0.88335

96.6950

212.540

0.81832

0.84233

146.742

1.53885

0.89806

251.604

Helium

2 = Pv/RT

673.728

21.99%

P (atm)

183.15 K

16 .^

22

28

32

35

40

47

50

57

91

16

14

18

24

29

32

36

41

49 47

62

115

u(Z)~105

3.4280

5.3152

8.2059

12.5821

19.0833

28.4710

41.4389

58.2855

79.6751

113.428

202.535

677.175

P (atm)

0.98677

0.97937

0.96787

0.95006

0.9227

0.88139

0.82105

0.73936

0.64710

0.58973

0.67412

1.44262

1

30

22

29

40

49

55

57

61

67

65

84

198

1.9280

2.9965

4.6446

7.1708

10.9944

16.6802

24.8977

36.2558

2.3620

3.667 1

5.6760

8.7381

13.3442

20.1111

29.7113

42.6382

0.99120

0.98629

0.97866

0.96688

0.94877

0.92125

0.88010

0.82034

0.98920

0.98319

0.97386

0.95949

0.93750

0.90428

0.85519

0.78534

Z = PvIRT

P (atm)

Z = Pv/RT o(Z) .105

143.15 K

158.15 K

TABLE I t (continued)

21

21

19

18

16

13

11

12

20

19

18

16

14

10 12

14

u(Z).105

~

0.95470

0.97079

0.98121

0.98794

11.7382

7.6412

4.9436

3.1864

85

t Weighting

factors

proportional

0.98926

2.8406

0.95957

0.97395

0.93751

16.0343

10.5051

0.98326

0.90409

6.8249

25

0.85459

24.1577

4.4098

27

0.78434

51.1609 35.6771

2.6671

4.1286

6.3586

9.7123

14.6420

21.6219

30.8931

41.8848

52.4855

60.1068

72.3768

343.9010

2.9466

4.5572

7.0072

10.6772

16.0381

2.3.5342

33.2928

54.5344 44.4484

61.6081

83.5805

647.730

1.59250

0.98383

0.97482

0.96086

0.93936

0.90647

0.85684

0.78357

0.67993

0.54544

0.39989

0.30820

0.93719

0.98212

0.97216

0.95676

0.93304

0.89686

0.84246

0.76275

0.65159

0.51169

0.36985

0.32115

to (3 + PTj)-2 were used in treating

10 14

12

17

20

23

29

0.69250

70.5673

28

0.59232

28

57

13

11

18 14

21

2.3

24

26

28

26

30

94.2986

1.01460

0.93010

17.8632

0.54722

0.89300

26.7921

136.106

0.83853

39.2912

394.316

0.76248

55.8203

0.57021

101.864

0.66628

159.893

76.1874

1.50767

0.57297

657.367

all data.

29

35 27

44

51

58 55

60

57

45

40

132

26

23

34

45

54

59

64

66

59

47

45

247

30.3901

0.67337

0.88421 0.92502 0.95165 0.9689 1 0.98004

8.8420 5.8225 3.7946 2.4567

0.82245

0.73078

0.97532

0.96158

0.94032

0.90762

0.85776

0.78291

13.2030

19.1872

26.6933

3.0288

4.6645

7.1265

10.7467

15.8673

22.6192

66

114

108

98

86

72

58

54

109

102

92

79

65

52

Helium

Helium

59.35%

Helium

80.00%

100%

Composition

2.4650806

328.78934

13 795.749 -_. _-- --

4

36 462.861

5

3

2 744.0613

4

2

10.246538

240.83183

1410.5876

4

2

123.69844

3

12.271634

2

Bx

3

k

183.15 K

2 150. -- ___

24.5

0.141

3 951.

232.

4.39

0.0399

36.2

1.60

0.0279

@k)

Virial

4

3

2

3423

6

13 037.747 _- _ .- --

405.85040

- 4.1004249

056.5

-233621.59

11 029.173

152.22850

9.6572578

1 896.4162

112.98310

12.662644

Bk

158.15 K

(cc/g mol)k-1

5

4

3

2

4

3

2

k

coefficients

TABLE II *

._ .__

703.

12.3

0.0939

1 010 000.

78 500.

2 220.

27.7

0.181

77.1

3.72

0.0738

O(Bk)

4

3

2

4

3

13 400.376

413.83618

- 6.1746247

4 766.3382

255.54634

7.2977738

9 693.2153

5 2

1 143.1125

146.78233

12.127116

Bk.

4

3

2

k

143.15

K

674.

13.7

0.0954

26.7

0.987

0.0141

1 300.

93.1

2.15

0.0247

@k)

Argon

Helium

series.

t Virial coefficients,

100%

21.99%

526 000. 15 800 000. 179 000 000.

-2

81 212 245.

-494

5

6 7

111.59

145 000 000.

-

not that

accurate,

are expressed

12 800 000.

though

12 310 159. -

420 000.

- 7 050 250.3 217 391 120.

1 036 023 900.

-44

6 730.

90 391.637

digits

to allow

accurate

calculation

31 600 000 000.

- 425 167 990 000.

to eight

3 230 000 000.

133 000 000.

2 770 000.

31 700.

194.

0.524

2 470 000.

195 000.

5 560.

66.1

0.315

92 200.

5 800.

38 552 947 000.

1 110 709 200.

084.186

2 229.9070

0.184 53.3

- 77.870274

82 134 809.

135 893.06 - 5 776 047.8

462.81321

- 49.550057

-372

17 661.667

1 286.9467

5

4

- 56.479549

703 060.

567 866.7

8 510.

45 253.027

4

68.0

- 28.752386

0.259

1 060 000.

831.31611

6

1 990. 75 100.

2

12 323 874.

5

3

14 281.530

- 340 730.28

4

2

2 363.1502

-94.044109

1 507.7540

-53.415305

of Z by summing

3

2

3

the virial

149.

0.565

21.0

0.0969

aa

J. A. PKOVINE

usage and to increase bath cryostat 3. Results.

AND

the heat transfer

F. B. CANFIELD

rate to the Burnett

cell in the gas

are given by Provines). Isotherms

were measured

for pure helium,

pure argon,

and

four mixtures having compositions of 21.99, 41.05, 59.35, and 80.00 mole percent helium in argon. These are the recommended compositions after examination

of mass spectrographic

and molecular

weight

analysis

of the

experimental gas mixtures. Two runs were made for each pure component and each mixture for the -90, - 115, and - 130°C isotherms. The method used to reduce the Burnett data to compressibility factors and virial coefficients has been described previously 10). The results are presented in tables I, II, and 111. Table I lists the observed pressures and the compressibility factors calculated from the virial coefficients along with the standard deviations in the compressiblity factor. Table II presents the virial coefficients for each isotherm with their standard deviations. Table III contains the information necessary to calculate the compressibility factor from the Burnett constants using the following equation,

where Pi is the observed pressure for the jth expansion, Zo/Pois the run constant, N, is the cell constant, and cj is a pressure-distortion correction of the form:

The constants ak and bk are given in table IV. Although the method of Hall and Canfieldia) generally was used for treating the data, certain variations were made for some of the runs at - 115°C and - 130°C. The - 115°C isotherm which is slightly above the critical temperature of argon gave some unexpected results. For two mixtures (59.35% He and 41.05% He) the results indicated a change in composition had occurred for one of the two runs. It is thought that this is due to the phenomenon of fluid-fluid phase separation coupled with incomplete mixing with the magnetic pump after the first expansion. This phenomenon is an equilibrium that exists between two separate, distinct gas phases that occur at high pressures in a region that for most systems would be a region of homogeneous fluid mixtures. This phenomenon has been observed experimentally by Streettir) at temperatures slightly below the critical

Helium

Helium

41.05%

21.99%

1.5624775

143.15

a) Cell constants were not adjusted

during treatment

“f

1 990

838

“)

1 080

“)

6 460

650

521

577

664

45.159399

406.73647

436.01653

54.287840

469.40729

437.81290

85.344567

432.42335

424.92747

402.83797

428.93728

413.01121

433.34338

446.87397

(PO/Z,) 1

0.0279

0.629

0.244

of these runs because of the small number

36.472193

366.95112

388.64174

44.202546

388.37653

69.961120

398.73433

370.75670

137.37712

352.89039

357.09704

285.27560

339.01874

357.63875

347.37650

360.17590

370.11305

(POP-O) 2

of data points.

equation.

0.0231

0.516

0.219

0.00506

0.286

0.0167

1.63

0.158

0.0385

0.131

0.156

0.0199

0.205

0.0562

0.0410

0.155

0.0545

u(Po/Zo) 2

of Z from the Burnett

0.00599

0.644

0.324

0.0196

0.195

0.197

0.258

0.0686

0.0495

0.202

0.0712

fJ(~O/~O)l

to eight digits to allow accurate calculation

1.5624775

1.5622752

1.5623030

1.5624775

1.5620088

are expressed

“f

808 2 200

1.5625218

“)

1.5620835

1.5624775

143.15

1 060 2 020

158.15

1.5620016

158.15

183.15

1.5622774

183.15

“)

1.5624775

1.5624775

1.5624772

143.15

678 1.5637869

1.5623533

158.15

183.15

1.5622529

143.15

1.5619351

117

917

254

190

733

251

o(Nms) . lo7

constants

1.5623561

1.5623027

1.5623731

1.5624923

1.5625505

1.5623632

NC02

1.5628770

690

950

247

185

773

265

o(Nml) . lo7

158.15

183.15

1.5617856

1.5621135

143.15

1.5623644

1.5624628

143.15

158.15

1.5625762

183.15

1.5623974

158.15

N 021

183.15

TK

t Values of Zs/Ps and N, though not accurate,

100% Argon

Helium

59.35%

80.00% Helium

100% Helium

Composition

Burnett

TABLE IIIt

90

J. A. PROVINE

AND F. B. CANFIELD TABLE IV

Coefficients

for equation

(2)

a3( 1011)

a4( 1014)

-3.22 -2.92 -3.13

2.22 0.818 2.40

0.00801 -3.08 -1.03

h

bz(l0’)

b3( 10’1)

b4( 1014)

1.00 1.00 1.00

-4.66 -4.22 -4.51

T”K

al

183.15 158.15 143.15

1.00 1.00 1.00

T”K 183.15 158.15 143.15

a2(107)

3.49 1.28 3.77

0.126 -4.85 - 1.62

temperature of argon starting at 576 atm. Therefore for these mixtures the runs were treated individually and the results for the first runs are not reported. The - 130°C isotherm also required some variation for certain mixtures in the data treatment procedure. For the first runs for the 80.00 and 59.35% He mixtures, the gas-liquid phase boundary was apparently crossed for the initial pressure, so that the two runs were for mixtures of slightly different composition. These runs were also treated separately, and the results for the first run are not reported. Since the runs for the 4l.O5o/o helium mixture, and the pure argon had to be started at the 21.99% helium mixture, pressures slightly less than the saturation pressure, these runs had fewer data points than the others. Preliminary attempts at fitting these runs indicated that there were too many adjustable parameters for the number of data points. Therefore for these runs the values of the cell constants obtained from the 100% helium runs were used and held constant in the Newton-Raphson determination of the run constants and virial coefficients. 4. E~v_m.

The standard

deviations

listed in tables

I, II, and III

for the

compressibility factors, virial coefficients, and Burnett constants were calculated from a propagation of errors analysis. Hall and Canfieldie) give the form of the equation used and a discussion of the development of the equation. The standard deviations for the Burnett constants seem reasonable as indicated by the fact that the deviations for the cell constants are of the same magnitude as the difference between the cell constants for each isotherm. Acknowledgment. This research is part of a long-range study of the volumetric behavior of gaseous mixtures at low temperature. The project is wholly supported by grant GK-633 from the National Science Foundation.

ISOTHERMS FOR THE He-Ar SYSTEM

91

The authors express their appreciation to the staff of the University of Oklahoma Computer Laboratory and Continental Oil Company Computer Department for their contribution of machine time.

REFERENCES 1) 2) 3) 4) 5) 6) 7) 8) 9) 10) 11)

Tanner, C. C. and Masson, I., Proc. Roy. Sot. Al26 (1930) 268. Kalfoglou, N. K. and Miller, J. G., J. Phys. Chem. 71 (1967) 1256. Blancett, A. L., Hall, K. R. and Canfield, F. B., Physica 47 (1970) 75. Burnett, E. S., J. Appl. Mech., Trans. A.S.M.E. 58 (1936) A136. Blancett, A. L., Ph. D. Dissertation, University of Oklahoma, Norman, Oklahoma (1966). Hall, K. R., Ph. D. Dissertation, University of Oklahoma, Norman, Oklahoma (1967). Hall, K. R., Blancett, A. L. and Canfield, F. B., Cryo. Tech. 5 (1969) 98. Hall, K. R. and Canfield, F. B., Physica 47 (1970) 219. Provine, J. A., Ph. D. Dissertation, University of Oklahoma, Norman, Oklahoma (1969). Hall, K. R. and Canfield, F. B., Physica 47 (1970) 99. Streett, W. B., Trans. Faraday Sot. 65 (1969) 696.