Experimental pVT data and thermodynamic properties of nitrogen up to 1000°C and 5000 bar

Physica

66 (1973) 3.51-363

0

North-Holland

EXPERIMENTAL PROPERTIES

Pub&h&g

pVT DATA

OF NITROGEN

AND

THERMODYNAMIC

UP TO 1000°C AND

P. MALBRUNOT* Laboratoire

Co.

5000 BAR

and B. VODAR

des Hautes

Pressions,

92, Bellewe,

France

C.N.R.S.

Received 9 October 1972

Synopsis The values of the density of nitrogen measured with an accuracy of 0.3 % in the high-temperature high-pressure range of 1000°C - 5000 bar are presented and a comparison with data of other workers is discussed. Although this comparison is limited due to lack of data beyond 4OO”C, the good agreement is an interesting test of the validity of the experimental method used. Then the results of computation of the main thermodynamic functions which can be derived from these experimental values are given in the same range of temperature and pressure; in addition, the principle and the accuracy of this computation are analysed.

1. Introduction. In recent years, the important improvements of several theories of the equilibrium state of fluids, mainly in the area of the dense fluids1v2) have led to a reawakening of interest in the experimental data of liquids and dense gases. Our contribution consists of an extension of the experimental knowledge of the equilibrium behaviour of dense gases from room temperature to the hightemperature range. First we made measurements on nitrogen up to 5000 bar and 1000°C. Our constant-volume method, apparatus and corrections have been previously described3*4). We used the data of Michels et ~1.~) to determine the filling density of our apparatus; more exactly, with a computer, we interpolated the results of these authors (for the temperatures 5O”C, 100°C: and 150°C) to obtain coincidence with the initial pressures of our measurement runs. In refs. 3 and 4 we also described the method for deriving the pressure p, density Q and temperature T from the observed data; moreover, we estimated the different errors and concluded that our experimental data have an accuracy of 0.3 ‘A_ 2. Results. Our experimental values of the density of nitrogen are listed in table I for the ten isotherms between 200 and 1000°C. The regulating apparatus3v4) allows measurements at temperatures so close to round values (differences of the * Present address: Laboratoire France.

de Physique Appliquee,

351

Place E. Bataillon, 34, Montpellier,

P. MALBRUNOT

352

AND

B. VODAR

TABLE I

Experimental results of the densities of nitrogen Q at different pressures p and temperatures 200 “C P

300 “C

@-3)

P

(bar)

(g cm

(bar)

758.8 997.3 1415 1807 2213 2651.2 3021.4 3371 3604 3996 4026 4537 4942

0.3661 0.4247 0.5082 0.5691 0.6194 0.6642 0.697 0.725 0.7423 0.7689 0.7708 0.8007 0.8222

984 1062 1227 1417 1784 1965 2256 2630 2864 3175 3537 3820 4117 4310 4807

(g

0.26306 0.29259 0.34255 0.3715 0.41637 0.46767 0.51182 0.5313 0.55406 0.5721 0.61041 0.63209 0.65854 0.6901

P (bar)

800 “C P (bar) 842.5 1115.5 1376.2 1626.5 1800 2124 2437 2892 3212 3546 3741 4100 4433 4853

895.1 1060 1210 1463 1791.5 2118.2 2308.5 2693 2817 3113 3373 3717 4160 4490 4813

0.24607 0.29318 0.31963 0.34294 0.37123 0.41622 0.43705 0.46949 0.51421 0.53676 0.59135 0.66153 0.72967 0.87556

P (bar)

0.2037 0.2484 0.2863 0.3196 0.3414 0.3800 0.4152 0.4621 0.4917 0.5194 0.5343 0.5601 0.5833 0.6099

P (bar) 923 1266.4 1530 1791 1983 2337 2675 2884 3158 3494 3722 4062 4446 4817

0.30735 0.3422 0.37162 0.41663 0.46731 0.5103 0.5325 0.57234 0.58405 0.6103 0.63181 0.65847 0.68986 0.71065 0.72872

(g cl%3)

948 1230 1456 1619 1828.5 2206 2623 2924 3387 3761 4062 4420 4801

0.23976 0.28552 0.31924 0.34213 0.36997 0.41611 0.46171 0.49141 0.53231 0.56183 0.58396 0.60891 0.63278

1000 “C

900 “C e (g cmp3>

(g cme3)

700 “C (g czl-3)

861.6 1121.5 1283 1435.2 1632.5 1974.5 2144 2421 2825 3034.3 3522 4016 4346 4796

e

P

(bar)

600 “C (g cil-3)

825 971.5 1245 1420 1718.5 2106 2487.3 2673 2907 3108 3591 3900 4300 4802

cl%)

0.36532 0.3824 0.41644 0.45213 0.51124 0.5362 0.57164 0.6108 0.63276 0.65982 0.68887 0.70971 0.72954 0.74125 0.76889

500 “C P (bar)

400 “C

(g cl%) 0.2009 0.2521 0.2863 0.3177 0.3400 0.3798 0.4161 0.4372 0.4630 0.4915 0.5090 0.5334 0.5606 0.5854

P (bar) 785 877.5 1050.2 1340.7 1960.6 2172 2543 2911 3127.5 3403 3774 4007 4392 4803

e (g cmm31 0.1618 0.1774 0.2041 0.2439 0.3173 0.3407 0.3803 0.4172 0.4374 0.4613 0.4905 0.5076 0.5351 0.5628

p YT DATA AND THERMODYNAMIC TABLE

PROPERTIES

OF Nz

353

II

... fitted to the data of table I, and Coefficients of the polynomials Q = C,, + C,p + Czp2+ errors (maximum and RMS values) of the fitting. The units are g cmw3 for the density e and bar for the pressure p 200°C Degree

co C,

c2 c3 c4 G c6

6 0.11119 0.41031 -0.10159 -0.34627 0.69258 -0.15196 0.10388

x x x x x x

10-a 10-e IO-l4 lo-l4 10-l’ 1O-21

c9

Max. % RMS %

Degree

co Cl c2 c3 c4 2

0.04 0.02

300°C

400 “C

9

6

0.74647 x 0.37947 x -0.10278 x 0.21630 x -0.46945 x 0.49304 x 0.97536 x 0.14786 x -0.96444 x 0.11253 x 0.02 0.015

10-I 10-a 1O-6 l&i0 lo-l4 10-1s 1O-22 1O-26 1O-2g 1O-32

500°C

600°C

700°C

6

6

9

0.58455 0.29219 -0.55465 -0.17927 0.35857 -0.88458 0.70130

x x x x x x x

10-I 1O-3 lo-’ lo-l4 10-14 lo-Is lo-a2

0.40428 0.29145 -0.64975 -0.33870 0.67746 -0.20538 0.21032

x x x x x x x

10-l 1O-3 lo-’ lo-I4 lo-l4 10-I’ 1O-21

c8 c9

Degree

co

C1 C2 c3

C4 C5 c6

2

c9

Max. % RMS %

x x x x x x x

0.41233 0.25767 -0.62862 0.14332 -0.20345 0.26431 -0.99444 0.16750 0.62292 -0.23519 0.015 0.006

x x x x x x x x x x

0.08 0.04

0.05 0.03

800°C

900°C

1000°C

9

9

9

0.30549 0.23988 -0.36954 -0.88399 0.54544 0.61285 -0.76678 -0.30934 0.13462

x x x x x x x x

10-l 1O-3 lo-’ lo-” 10-14 lo-‘s 1O-21 10-29 1O-24

-0.63299 x 1O-33 0.1 0.04

-0.41974 x 0.38535 x -0.16598 x 0.34794 x 0.18125 x -0.38450 x -0.68236 x 0.91696 x 0.14724 x -0.24381 x 0.25 0.1

10-l 1o-3 lo-’ 1O-15 lo-r4 10-1s 1O-25

0.04 0.02

ct

Max. % RMS %

0.67468 0.31900 -0.58238 -0.91168 0.18234 -0.19507 0.23765

10-I 1O-3 1O-6 lo-‘0 lo-i4 10-19 1O-21 1O-25 lo-” 1O-32

-0.72570 x 0.26893 x -0.71296 x -0.42766 x 0.15599 x -0.68472 x 0.18405 x -0.38983 x 0.54921 x -0.33571 x 0.2 0.07

10-r 1O-3 lo-’ lo-lo lo-l4 1O-18 10-22 1O-25 1O-3o 1O-33

1O-2 1O-3 1O-7 lo-I1 10-13 10-l’ 1O-2o 1O-24 1O-28 10-32

354

P. MALBRUNOT

AND B. VODAR

order of 0.1 K) that isotherms might be obtained, without errors, by a simple linear correction. To facilitate the use of these results, particularly interpolations, the coefficients of the polynomials which fit them as precisely as possible, are presented in table II with the accuracy of the fitting. The practical procedure of this polynomial approximation is the well-known “least-squares method” with the help of Legendre polynomials. Obviously, these polynomials have neither the characteristics nor the significance of the virial expansion. Moreover, they are valuable only in the strict boundaries of the basic data and may not be extrapolated. On the other hand, their calculation does not need accurate low-density data and numerous and well-divided experimental points as the virial-coefficients determination doeP). In fig. 1 is shown a generalized compressibility diagram extracted from our measurements, the reduced temperature T, = TIT, and pressure pr = p/p= being formed with the critical parameters given by Din7), i.e., T, = 126.2 K and pc = 33.95 bar. The comparison with the values given by Nelson and OberP) shows

Fig. 1. Representation of isotherms in generalized charts: plot of compressibility factor 2 = p/@RT ~etws reduced pressure pr for various reduced temperatures T,; ------: data of Nelson and Obert ; -: present data.

a mean difference of 2 ‘4 up to 700 “C and of 4 ‘A to 1000 “C, which is quite understandable given the approximate character of this representation. One can thus reasonably claim that our curves agree with those of Nelson-Obert and for lack of something better, extend them to a reduced pressure of 140 in the range of

pVT DATA

reduced

temperatures

AND THERMODYNAMIC

from 4 to 10. Nevertheless,

be required for a complete dense-fluid range.

study

PROPERTIES OF Nz

results

of this representation

355

on several gases would in the high-temperature

3. Comparison with other experimental results. To our knowledge, there are no experimental data covering our range of measurements, and so this comparison will be relatively limited. The comparison with the results of Michels is of little interest since they are our fiducial data. The results of Benedictg) between - 185 and 200°C and up to 5000 atm were not taken into account because the common range is too limited; furthermore, Robertson”) made a detailed comparison of Benedict’s data with his own results, the range of which is more appropriate. 3.1. Results of Tsiklis and Robertson and Babb. The results of Tsiklis”) and of Robertson and BabblO) up to 400°C and 10000 bar are those which are nearest ours. Tsiklis and his collaborators evaluate the errors in their measurements to be 0.5”C (i.e., less than 0.1 ‘A) for the temperature, 0.3 oA for the density and 20 bar for the pressure (i.e., 1% to 0.4% from 2000 bar to 5000 bar). This lack of precision in their pressure measurements over a wide area is regrettable as the simplicity and absolute character of their method would have permitted very precise measurements. In this connection, the replacement of their manganin gauge with a pressure balance would be an interesting improvement. Robertson and Babb estimate 0.2% to be the final precision of their measurements. This value seems to us to a limit mainly governed by the temperature. The relative precision of 0.2% which they give corresponds to an absolute error of the order of 0.1 “C which seems an overestimate of the accuracy of the chromelalumel thermocouples they used, despite frequent and carefully made calibrations against the platinum resistance thermometers which they were able to make. The direct use of such thermometers, which is possible in their case, would seem preferable; a remark applying equally to the measurements of Tsiklis and his collaborators who also used chromel-alumel thermocouples. In table III we have given a comparison with these various results. Our first conclusion is that on the whole, the agreement is acceptable taking into account the accuracy of the measurements and the differences which exist between the data of Tsiklis and those of Robertson and Babb. It should be said that our data are not sufficiently precise to decide between these authors. In fact, this difference is mainly explained, as Robertson and BabblO) indicate, by the approximation made by Tsiklis of the linearity of the response of his manganin gauge. According to the work of Boren”) and that of Atanov13) this approximation may result in varying errors. Those errors present a maximum of 18 bar towards 3500 bar and increase again at high pressures to reach 70 bar towards 10000 bar. Besides, not knowing any details about the operating method,

356

P. MALBRUNOT

AND B. VODAR

TABLEIII Comparison

with the results of Tsiklis”)

A, = (ea”th0rS -

~Tsiklls)/@authors

in

%,

and the results of Robertson &

=

d,

1500 2000 2500 3000 3500 4000 4500 5000 Mean relative deviation in % Max. relative deviation in %

0.15 0.05 0.07 0.1 -0.1 - 0.24 -0.26 -0.32

(&thors

3oo

-

d,

and Babb’O)

@Babb)/@authors

in

d,

%

4oo

d,

-0.3 -0.12 -0.01 -0.06 0.18 0.54 0.7 0.44

-0.6 -0.4 - 0.28 - 0.04 0.07 0.43

0.15

0.3

0.3

0.25

0.55

0.6

-0.3 -0.18 0.1 0.07 0.01 0.02

-0.32 -0.05 -0.16 -0.26 0.05 0.36 0.22 0.58

- 0.25 -0.18 -0.01 0.15 0.02 0.17

0.15

0.10

0.25

0.30

0.2

0.6

it is difficult to determine how to record the reproducibility of the manganin gauge in the course of the two successive measurements which the experimental method of Tsiklis demands. Let us return to the comparison with our own data. The differences at 200°C and 300°C from the results of the authors cited have an erratic character and on no occasion exceed the values permissible in view of the respective accuracies. Therefore no particular significance is attributed to the fact that our values seem nearer those of Tsiklis at lower pressures and those of Robertson at higher pressures. At 400°C this behaviour is more pronounced and leads us to conclude that below 2500 bar our densities appear systematically lower. A possible explanation is that the temperature gradient along the piezometer (bulb which contains the gas sample) is generally more important in this range of pressures than at higher pressures. This fact is also quahtatively in agreement with the estimation of the convective heat transfer which we have made with regard to the insulation of the heaters14). For this same reason, it is very probable that the difference between the high temperatures of the junctions of the thermocouples and the temperature of the piezometer is in this case relatively large. So, the improvement, provided for in ref. 4, which consists in enclosing the junctions of the thermocouples into the piezometer wall will allow us to avoid this inconvenience. At high pressures in our region, the comparison of our results and those of Robertson seems to indicate that a re-examination of the data of Tsiklis at 400°C would be desirable.

pVT DATA

In summary, with totally cannot

AND THERMODYNAMIC

PROPERTIES OF N,

it can be said that the agreement

different

methods

is sufficient

357

of our results with those obtained

to show that the validity

of our method

be questioned.

3.2. Work of Saurel. This is a direct comparison since we have both used the same principle of measurement. It is, however, more limited than the preceding comparison as our region does not extend to that of our predecessor. In table IV, we have added to the data of Saurel15) those which Kessel’man16) obtained by extrapolation up to 700°C and 1000 bar of the data existing at lower temperatures*. Up to 7OO”C, the agreement of the data is very acceptable and the isotherms fit together quite well. This is an interesting verification of the reproducibility of the method because, although the methods are the same, our apparatus is completely different from that of Saurel (heater, controller, temperaturemeasuring circuits, pressure balance, etc.). TABLEIV Comparison K: Kessel’man,

AS

=

with the results of SaureP)

(@authors

-

@Saurel)/@authors

in

800 (789.5 atm) 4

300 400

- 0.08

and Kessel’man16)

%,

AK

=

(@authors

-

@K)/@aUlhorS

in

%

1000

900 (888.91 atm)

(986.9 atm) AK

AK

As

-0.8 - 0.04

-0.5

- 1.25 -0.6

AK

-1.45 -0.95 -0.9

500

0.35

0.45

-0.4

-0.4

600

0.4

0.55

-0.5

-0.2

-0.85

700 800

0.2 -0.15

0.25

-0.7 -1.10

-0.35

-1.5

At 8OO”C, a notable difference appears. Since the comparison concerns only two points it would be rash to draw precise and definitive conclusions from it. It is here more difficult to attribute the differencies to the temperature measurement, since our heating technique is the same as Saurel’s. One possible cause of error in the case of our predecessor could result from his measuring circuits being less protected than ours. Only a verification with more experimental points and under still better temperature-measuring conditions, will be able to decide upon this dif* Although this author cites the work of Saurel, he does not state explicitly whether he has actually used Saurel’s results to find the parameters of his extrapolating equation. If this is so, the good agreement which has been etablished is not significant but in the contrary case it would be particularly interesting.

P. MALBRUNOT

358

AND B. VODAR

ference between the results of Saurel and ours. This is the more necessary since the results of Kessel’man (with the usual reservations for calculations involving extrapolations) seem to confirm at 1000 bar that the values of our densities are slightly too low as was already apparent of Tsiklis and of Robertson and Babb.

at 400°C by comparison

with the results

3.3. Mathematical correlation of’the experimental data. Coleman”) attempts with a least-squares fit technique to find such a correlation of the thermodynamic properties of nitrogen. As he included the results of Saurel, Tsiklis and Robertson in the basic data of his equation, the comparison of his values with ours gives about the same rest_& up to 400°C. On the other hand, his extrapolation up to 1000°C and 10000 bar allows a more significant comparison. The agreement is relatively good mainly at the highest pressures of our range: better than 1% above 2500 bar and better than 2 % below. So, Coleman’s extrapolation appears to be reasonable and our results seem to be located in the expected range of values. However, there is an exception in the neighbourhood of 1000 bar where a deviation of the order of 3 ‘A exists. In fact, this disagreement is the logical consequence of the one we have underlined in the preceding comparison. 4. Calculation of the thermodynamic functions. 4.1. Entropy. Following usual practice we computed the entropy with the help of Maxwell’s formula

(igT =-(Zl Thus, the entropy

%T= -[

S,,,

for the pressure p and the temperature

T is

~(~)pdp] +s,, Pi

T

where pi = 100 atm (Le., 101.325 bar) and S, is the entropy at temperature T and pressure p, . To obtain these “initial conditians” we use: (i) the absolute entropy values for 100 atm tabulated by Hilsenrath et aI.18); (ii) some data of Saurel to extrapolate ours to 100 atm. This last choice seemed to us the most coherent since Saurel has used the same principle of measurement as we have used. These calculations have been performed by exact mathematical operations on polynomials similar to those presented table II. Thus, for the present calculation of the entropy we used two polynomials, one giving V as a function of T and another one giving (aV/aT), as a function of p. Of course, the derivatives of these polynomials should be equal to the derivatives of the physical quantities which they represent. In the present case the first derivatives of the thermo-

5.400 5.172 5.030 4.928 4.850 4.785 4.73 4.684 4.642 4.604

Authors

200

4.5966

4.6766

4.7725

Tsiklis’

5.623 5.400 5.260 5.158 5.080 5.017 4.965 4.920 4.878 4.841

Authors

300

4.8395

4.9186

5.0145

Tsiklisa

a Deviation from our values: mean 0.1 %, max. 0.25 %.

500 1000 1500 2000 2500 3000 3500 4000 4500 5000

e\ (bar)

t (“0

Entropy S in J g-‘K-l,

5.810 5.591 5.452 5.352 5.275 5.212 5.160 5.115 5.075 5.040

Authors

400

5.0441

5.1203

5.2147

Tsiklis”

error 0.8%. Comparison

TABLEV

5.972 5.757 5.620 5.520 5.442 5.380 5.330 5.285 5.244 5.209

500

6.116 5.903 5.766 5.667 5.590 5.528 5.477 5.433 5.394 5.359

600

with Tsiklis’s resultslg)

6.247 6.036 5.900 5.801 5.724 5.663 5.612 5.569 5.530 5.495

700

6.367 6.157 6.022 5.923 5.847 5.785 5.735 5.692 5.654 5.619

800

6.477 6.269 6.134 6.035 5.959 5.898 5.848 5.806 5.767 5.733

900

6.519 6.371 6.236 6.138 6.062 6.002 5.952 5.910 5.872 5.837

1000

t

H

865.00

5000

1278.85

1324.55

1369.75

4000

4500

5000

623.45

623.10

622.05

619.30

617.10

617.40

619.40

625.85

646.85

657.35

U

864.6

777.5

H

700

1486.30

1441.85

1396.65

1349.15

1302.00

1256.60

1212.60

1168.80

1125.20

1077.35

262.10

261.95

260.15

260.30

260.65

262.55

268.55

H

996.0

907.40

817.50

1610.05

1564.65

1519.10

1471.30

1424.65

1377.85

1332.75

1289.05

1246.15

1196.20

H

800

348.50

347.0

346.45

346.35

345.65

348.75

354.15

361.70

371.85

391.25

u

799.70

799.35

797.10

792.35

788.50

787.55

786.30

791.55

815.15

826.40

U

1111.70

1067.35

1022.25

976.65

931.25

886.75

843.70

802.75

763.10

722.70

H Authors

1737.15

1692.40

1646.60

1598.50

1550.40

1504.00

1458.35

1412.40

1366.15

1312.75

H

900

1125.90

1036.0

946.0

Tsiklisb

H

400

895.40

895.90

891.85

886.35

880.75

877.40

874.40

879.50

899.95

914.00

U

434.40 434.70

433.15

431.50

431.70

434.65

440.45

448.55

460.05

476.40

U

with Tsiklis’s resultsig)

b Deviation from our values : mean 1.3 %, max. 1.5 %.

708.10

709.00

707.00

702.80

699.60

700.45

702.40

707.30

726.00

737.90

U

989.05

945.45

900.85

855.80

811.10

766.80

723.80

682.90

643.60

605.85

Tsikli?

H

300

error: 1.2% for H, I .5 % for Cr. Comparison

Authors

’ Deviation from our values: mean 0.6%, max. 0.8%.

1185.80

1140.40

2500

1232.25

1096.15

2000

3000

1053.20

1500

3500

966.40

1011.80

500

600

1000

P (bar)

H

824.80

4500

t P-2

736.20

692.00

3000

780.60

648.05

2500

3500

604.95

2000

4000

563.90

1500

687.7

290.65

277.10

311.15

u

525.90

H Tsiklisa

492.30

Authors

200

503 1000

e (bar)

1(“Cl

Enthalpy H and energy U in J g-l,

TABLE VI

1186.60

1859.45

1814.60

1768.65

1719.75

1670.90

1623.55

1577.15

1530.35

1484.65

1429.35

H

1000

986.10

985.85

980.45

974.30

965.00

958.65

957.00

960.00

985.65

1002.75

U

516.45 518.05

1140.95 1231.80

514.60 515.10

1094.55

517.00

520.95 514.90

526.70 960.50 1048.65

547.25

918.35 1003.85

562.10

877.60

U

839.90

H

500

pYT DATA AND THERMODYNAMIC

PROPERTIES OF N2

361

dynamic functions are monotonic. To take this criterion into account we used the following simple procedure: we calculated the slopes of the successive straightlines joining the experimental data; then, we eliminated the data which lead to a change of the direction of the variation of these slopes. (However, the differences between these values and the calculated ones, are taken into account for the determination of the polynomial-fitting uncertainty.) The results are reported in table V. 4.2. Enthalpy equation

and energy.

For the calculation of the enthalpy we used the

(-gT = v- T& Thus, the enthalpy Ho,= at pressure p and temperature T is

where pi = 100 atm and Hi is the enthalpy at temperature T and pressure pi (from ref. 18). The energy is then calculated from the equation U = H - pV. The results are given in table VI. 4.3. Specific heats and speed of sound. The specific heat at constant pressure C,, the specific heat at constant volume C, and the speed of sound c have been determined with the relations

and

The results and the average errors are presented in tables VII, VIII and IX. 4.4. Comparison with other results. It would be particularly interesting to make a comparison of our calculated results with direct experimental data. Unfortunately, such measurements are so difficult to perform at high temperatures and high pressures that they are nonexistent. Only the comparison with the calculated results obtained by Tsiklis and Polyakovlg) from their pVT data is possible. This is reported in table V. Since our respective procedures are different the good agreement proves the consistency of these calculations. Moreover, this

362

P. MALBRUNOT

AND

B. VODAR

agreement allows one to estimate the uncertainty of the thermodynamic functions of nitrogen up to 400°C and 5000 bar. It is of the order of 1 ‘A for the entropy and 1.5 % for the enthalpy. TABLEVII Specific heat at constant pressure C,, in J g-’ K-‘, x

200

300

400

500

600

700

error 2% 800

900

1000

500

1.170

1.150

1.140

1.145

1 170

1200

1.210

1.225

1.230

1000

1.195

1.175

1.165

1.165

1.190

1.220

1.235

1.240

1.245

2000

1.208

1.177

1.20

1.25

1.245

1.248

1.252

1.217

1.185 1.195

1.178

3000

1.185

1.184

1.208

1.238

1.252

1.255

1.258

4000

1.233

1.206

1.193

1.191

1.212

1.243

1.258

1.262

1.265

5000

1.247

1.218

1.203

1.196

1.217

1.249

1.264

1.268

1.272

TABLEVIII Specific heat at constant volume C, in J g-l K-l, x

error 2%

200

300

400

500

600

700

800

900

1000

500

0.760

0.790

0.795

0.803

0.806

0.795

0.805

0.818

0.825

0.829

0.808 0.832

0.809

0.776

0.769 0.782

0.782

1000 2000

0.820

0.820

0.821

0.837

0.856

0.870

0.874

0.882

3000

0.872

0.850

0.867

0.914

0.874

0.896

0.892 0.926

0.911 0.952

0.920

4000 5000

0.853 0.890

0.963

0.930 0.976

0.888 0.939

0.960

0.925

0.898

0.930

0.962

0.990

1.003

1.020

1.035

800

900

1000

817 1024

866 1087

1130 1219 1308 138.5

1192 1244 1280 1336

0.825

0.988

TABLEIX Speed of sound c in m s-l, x 500 1000 2000 3000 4000 5000

error 2.5 %

200

300

400

500

600

700

608

660

735

765

788

830 1083 1288 1481

688 843 1067 1264

712

830 1103 1315

834 1035 1240

945 1064 1192

988 1118 1230

1448 1618

1406 1565

873 1054 1204 1358 1514

1322 1456

1325 1422

1514 1686

1654

pyT DATA AND THERMODYNAMIC

PROPERTIES

OF N2

363

5. Conclusion. The significance of our results is the extension of the experimental data into an unexplored range. They are expected to be valid since they agree with results obtained with totally different methods as well as with the extrapolations of these other results. The domain of interest in our data for practical applications is extensive : physical phenomena in compressed gases for which knowledge of the density is required, fluids mechanics, thermal engineering, chemical engineering, etc. From a theoretical view point our results allow a particularly significant confrontation with the numerous recent theories developed on the basis of statistical mechanics. We shall deal with this subject in a forthcoming article.

Acknowledgment. cul des Laboratoires gramming.

We wish to thank Mr. L.Varion of the “Bureau de Calde Bellevue” for his essential assistance in computer pro-

REFERENCES 1) 2) 3) 4) 5) 6)

Rowlinson, J.S., Liquids and Liquids Mixtures, sec. ed., Butterworths (London, 1969). Verlet, L. and Weis, J. J., Phys. Rev. A5 (1972) 939 and references cited therein. Malbrunot, P., These, Paris, 1970. Malbrunot, P. and Vodar, B., High Temp. - High Pressures 3 (1971) 225. Michels, A., Wouters, H. and De Boer, J., Physica 3 (1936) 585. Levelt-Sengers, J. M. H., Proc. of the Fourth Symp. on Thermophysical Properties, Maryland, April 1968, ed. by A.S.M.E. 7) Din F., Thermodynamic Functions of Gases, vol. 3 Butterworths (London, 1961). 8) Nelson L.C. and Obert, E.F., Trans. A.S.M.E. 76 (1954) 1057. 9) Benedict, M., J. Amer. Chem. Sot. 59 (1937) 2224 and 2233. 10) Robertson, S.L. Babb, S.E., J. them. Phys. 50 (1969) 4560. 11) Tsiklis, D.S. and Polyakov, E.V., Dokl. Akad. Nauk SSSR 176 (1967) 308. 12) Boren, M.D., Babb, S.E. and Scott, G. J., Rev. sci. Instrum. 36 (1965) 1456. 13) Atanov, Yu.A. and Yvanova, E.M., Symposium on the Accurate Characterisation of High Pressure Environment, N.B.S. Gaitesburg, Maryland, 1968, ed. N.B.S. Spec. Publ. no 326 (1971). 14) Malbrunot, P., Meunier, P. and Vidal, D., High Temp. - High Pressures 1 (1969) 93. 1.5) Saurel, J., These, Paris, 1958. 16) Kessel’man, P.M., Kotlyareskii, P.A. and VoIashin, A.P., lnzhen.-fiz. Zh. 8 (1965) 35; J. of Eng. Phys. 8 (1965) 24. 17) Coleman, D., Ph.D. Thesis, Univ. of Idaho, 1971. 18) Hilsenrath, J. and Col., Tables ofThermal Properties of Gases, N.B.S. Circular no 564 (1955). 19) Tsiklis, D.S. and Polyakov, E.V., Russian J. phys. Chem. 41 (1967) 1697.