Volume 96, Number 6, November-December 1991
Journal of Research of the National Institute of Standards and Technology [J. Res. Nat!. Inst. Stand. Technol. 96, 725 (1991)]
Molar Heat Capacity (Cv) for Saturated and Compressed Liquid and Vapor Nitrogen from 65 to 300 K at Pressures to 35 MPa
Volume 96 J. W. Magee National Institute of Standards and Technology, Boulder, CO 80303
Number 6
November-December 1991
Molar heat capacities at constant volume (C,) for nitrogen have been measured with an automated adiabatic calorimeter. The temperatures ranged from 65 to 300 K, while pressures were as high as 35 MPa. Calorimetric data were obtained for a total of 276 state conditions on 14 isochores. Extensive results which were obtained in the saturated liquid region (C^^^' and C„) demonstrate the internal consistency of
Glossary a,b,c,d,e
c.
a
C„
a
Vbamb
Vr, P P. AP T Tc TuT2
Ar
Q Go N P PP-
the Cv (fi,T) data and also show satisfactory agreement with published heat capacity data. The overall uncertainty of the Cy values ranges from 2% in the vapor to 0.5% in the liquid. Key words: calorimeter; heat capacity; high pressure; isochorlc; liquid; measurement; nitrogen; saturation; vapor. Accepted: August 30, 1991
ticular, the heat capacity at constant volume {Cv) is related to P(j^T) by:
Coefficients for Eq. (7) Molar heat capacity at constant volume Molar heat capacity in the ideal gas state Molar heat capacity of a two-phase sample Molar heat capacity of a saturated liquid sample Volume of the calorimeter containing sample Molar volume, dm' • mol"' Pressure, MPa Vapor pressure Pressure rise during a heating interval Temperature, K Critical-point temperature Temperature at start and end of heating Interval Temperature rise during a heating Interval Calorimetric heat energy input to bomb and sample Calorimetric heat energy input to empty bomb Moles of substance in the calorimeter Fluid density, mol • dm"' Saturated liquid density Chemical potential
Jo
(1)
where C? is the ideal gas heat capacity. Consequently, Cv measurements which cover a wide range of {P, p, T) states are beneficial to the development of an accurate equation of state for the substance. The amount of experimental data on the calorimetric properties of nitrogen is very limited. Measurements of Cv are mostly confined to atmospheric pressure. Only two published works concern Cv measurements at elevated pressure. First, Voronel et al. [1] obtained 69 experimental values of Cv at temperatures from 106 to 167 K at densities close to the critical density, with an emphasis on the temperature variation of Cv near the critical point (126.2 K). However, these authors give neither the pressures nor the densities at which the measurements were performed. Thus, comparisons with the Cv data of Voronel et al. are difficult at best. In the only other experimental study at elevated pressures, Weber [2] performed measurements at temperatures from 91 to 242 K using the same calorimeter as used in this work. The combined works of Voronel et al. and Weber
1. Introduction Accurate measurements of thermodynamic properties, including heat capacity, are needed to establish behavior of higher order temperature derivatives of an equation of state P(p, T). In par725
Volume 96, Number 6, November-December 1991
Journal of Research of the National Institute of Standards and Technology compare these measurements with published data and with predictions from published equations of state.
leave gaps in the Cv surface between the triple point (63.15 K) and 91 K, and for temperatures above 242 K. Published experimental results for the heat capacity of the saturated liquid (C„) are more available than those for Cv at elevated pressures. When combined, the data of Weber [2], Giauque and Clayton [3], and Wiebe and Brevoort [4] range from 65 to 125 K. However, none of these works spans the entire temperature domain for saturated liquid nitrogen. Thus, we cannot be certain how the various data will intercompare. In this work, the goals include extending the published data for Cv to temperatures as low as the triple point, and also to near ambient temperature. A second goal is to measure Ca over temperatures from the vicinity of the triple point to that of the critical point, and to
2.
Experimental
The apparatus in Fig. 1 has a long history dating to its original construction for liquid hydrogen calorimetry. Its mechanical details remain essentially unchanged since they were described by Goodwin [5]. Instrumentation, however, has been changed extensively. The older instruments were replaced with electronic versions, each equipped with an IEEE-488 standard interface for two-way communication with a microcomputer. The arrangement of the new instruments is shown in Fig. 2.
Access Tubes
Outer Vacuum Tube
Refrigerant Tubes
Inner Refrigerant Tanl
% J-mol-i-K-i -0.49 -0.24 -0.23 -0.10 0.01 0.16 0.32 0.67 1.06 1.27 1.43 1.54 -0.79 -0.29 -0.05 0.09 0.32 0.58 1.00 1.27 1.59 1.70 1.17 -0.60 -0.40 -0.13 -0.15 0.23 0.40 0.41 0.62 0.95 1.39 1.68 1.62 1.19 -0.76 -0.42 -0.15 -0.17 0.06 0.04 0.43 0.72 1.07 1.60
59.99 60.84 61.66 62.64 63.69 64.81 66.00 67.37 68.85 70.36 72.10 74.29 60.49 62.73 65.29 66.70 68.24 69.87 71.72 73.65 75.98 78.80 82.41 60.99 62.19 63.60 65.00 66.76 68.50 70.22 72.14 74.28 76.70 79.41 82.57 86.99 61.91 63.64 65.56 67.52 69.79 72.04 74.66 77.34 80.22 83.57
Volume 96, Number 6, November-December 1991
Journal of Research of the National Institute of Standards and Technology Table 4.
T K 66.1756 9.0867 71.9548 74.7849 77.5788 69.2774 72.6946 76.0585 72.6097 75.5013 78.3559 81.1743 83.9583 72.0307 74.9320 77.7934 80.6178 83.4075 77.0893 80.0185 82.9065 85.7558 88.5715 85.2388 88.2096 91.1399 94.0353 96.8947 99.7227 102.5197 92.3233 95.3475 98.3344 101.2850 104.2006 107.0820 109.9340 112.7578 105.7600 108.8264 111.8576 114.8599 117.8323 120.7784 123.6977 126.5950 129.4678 132.3201 135.1429 137.9433 112.3409 115.9124 119.4468 122.9472 126.4129 129.8462 133.2459 136.6150 119.3182 122.9365
Experimental single-phase heat capacities
P mol-dm"' 30.9599 30.8819 30.8328 30.8035 30.7869 30.8813 30.8246 30.7943 30.3311 30.2825 30.2515 30.2318 30.2188 30.3444 30.2907 30.2568 30.2352 30.2209 29.5526 29.5055 29.4743 29.4528 29.4368 28.1342 28.0972 28.0717 28.0522 28.0364 28.0232 28.0104 26.5920 26.5632 26.5439 26.5288 26.5166 26.5049 26.4947 26.4840 24.2453 24.2371 24.2317 24.2259 24.2205 24.2140 24.2071 24.1991 24.1907 24.1817 24.1724 24.1626 22.1595 22.1468 22.1408 22.1381 22.1302 22.1242 22.1177 22.1102 20.2246 20.2050
P MPa 8.5838 14.4587 20.2568 25.9553 31.5376 14.9188 21.7709 28.4964 11.8026 17.2998 22.6862 27.9586 33.1070 10.7150 16.2231 21.6323 26.9234 32.0913 8.6948 13.7919 18.7781 23.6465 28.3997 6.0948 10.4732 14.7565 18.9399 23.0260 27.0294 30.9381 3.1853 6.9012 10.5495 14.1182 17.6147 21.0309 24.3895 27.6783 4.8752 7.7000 10.4814 13.2159 15.9078 18.5546 21.1602 23.7239 26.2495 28.7374 31.1832 33.5919 3.1882 5.6836 8.1621 10.6204 13.0294 15.4143 17.7654 20.0821 3.7560 5.7012
N mol 2.2520 2.2477 2.2456 2.2449 2.2452 2.2478 2.2454 2.2449 2.2073 2.2051 2.2042 2.2042 2.2046 2.2080 2.2054 2.2044 2.2042 2.2045 2.1502 2.1481 2.1471 2.1468 2.1469 2.0469 2.0453 2.0446 2.0443 2.0442 2.0444 2.0446 1.9345 1.9334 1.9329 1.9327 1.9328 1.9329 1.9331 1.9333 1.7648 1.7650 1.7653 1.7657 1.7660 1.7663 1.7665 1.7667 1.7668 1.7669 1.7669 1.7670 1.6131 1.6128 1.6130 1.6135 1.6136 1.6138 1.6140 1.6141 1.4727 1.4717
rbomb
Ar
cm'
K
72.739 72.785 72.832 72.879 72.927 72.789 72.844 72.901 72.773 72.818 72.864 72.910 72.956 72.764 72.809 72.855 72.901 72.947 72.759 72.802 72.846 72.889 72.933 72.756 72.795 72.835 72.874 72.914 7X953 72.993 72.748 72.783 72.819 72.855 72.890 72.926 72.961 72.997 72.791 72.822 72.852 72.883 72.913 72.944 72.975 73.005 73.036 73.067 73.098 73.128 72.793 72.823 72.852 72.883 72.913 72.943 72.974 73.004 72.815 72.841
2.9305 2.8898 2.8506 2.8157 2.7814 3.4450 3.3915 3.3428 Z9139 2.8762 2.8386 2.8076 2.7718 2.9234 2.8824 2.8466 2.8122 2.7793 2.9544 2.9149 2.8759 2.8404 2.8069 2.9975 2.9579 2.9212 2.8869 2.8548 2.8259 2.7951 3.0508 3.0172 2.9797 2.9451 2.9134 2.8842 2.8541 2.8304 3.0766 3.0460 3.0164 2.9831 2.9560 2.9311 2.9064 2.8807 2.8633 2.8364 2.8135 2.7945 3.5832 3.5489 3.5135 3.4780 3.4438 3.4128 3.3829 3.3532 3.6281 3.6044
733
Q/^T JK-'
JK-i
107.357 108.710 110.186 111.573 112.954 108.863 110.553 112.208 107.734 109.104 110.564 111.831 113.210 107.377 108.874 110.217 111.579 112.913 106.205 107 J84 108.936 110.320 111.676 104.445 105.825 107.095 108.360 109.573 110.653 111.823 102.476 103.613 104.856 106.022 107.127 108.191 109.272 110.181 100.935 101.875 102.853 103.887 104.861 105.701 106.567 107.485 108.096 109.073 109.817 110.542 98.547 99.454 100.436 101.363 102.298 103.165 104.003 104.893 97.117 97.697
29.273 31.377 33.368 35.254 37.044 31.512 33.868 36.079 33.811 35.720 37.530 39.245 40.874 33.419 35.350 37.179 38.912 40.557 36.736 38.550 40.266 41.892 43.434 41.602 43.239 44.788 46.257 47.648 48.970 50.225 45.396 46.902 48.328 49.677 50.956 52.169 53.322 54.419 51.619 52.880 54.074 55.207 56.283 57.306 58.279 59.206 60.090 60.934 61.738 62.506 54.260 55.593 56.849 58.032 59.149 60.204 61.201 62.145 56.804 58.029
Co'
Adj."
Cv
t.y.calc
J-mol-'-K-■J 1.28 1.24 1.22 1.21 1.22 1.23 1.21 1.21 1.16 1.16 1.16 1.18 1.20 1.17 1.16 1.16 1.17 1.19 1.06 1.07 1.08 1.10 1.12 0.89 0.91 0.93 0.95 0.97 1.00 1.02 0.73 0.75 0.77 0.79 0.81 0.83 0.86 0.88 0.55 0.57 0.59 0.61 0.63 0.65 0.67 0.69 0.70 0.72 0.74 0.75 0.41 0.43 0.45 0.46 0.48 0.50 0.52 0.54 0.31 0.33
33.26 33.09 37 95 32.76 32.58 33.11 32.91 32.69 32.29 32.11 31.97 31.76 31.62 32.29 32.16 31.97 31.80 31.64 31.24 31.08 30.91 30.79 30.68 29.82 29.70 29.56 29.44 29.32 29.18 29.10 28.79 28.59 28.48 28.36 28.25 28.14 28.08 27.96 27.39 27.18 27.03 26.95 26.87 26.74 26.66 26.64 26.47 26.52 26.47 26.43 27.04 26.76 26.57 26.39 26.25 26.12 26.00 25.95 27.06 26.62
Diff.''
% 31.76 31.98 32.13 32.18 32.17 32.00 32.15 32.19 31.30 31.41 31.46 31.45 31.39 31.27 31.40 31.45 31.45 31.41 30.51 30.57 30.60 30.58 30.53 29.39 29.37 29.35 29.31 29.26 29.20 29.12 28.46 28.35 28.28 28.23 28.17 28.11 28.04 27.97 27.28 27.11 27.00 26.92 26.85 26.78 26.71 26.64 26.58 26.51 26.45 26.39 27.02 26.59 26.35 26.19 26.07 25.97 25.88 25.80 27.03 26.41
4.526 3.33 2.49 1.76 1.25 3.34 2.30 1.53 3.06 2.17 1.61 0.99 0.73 3.14 2.38 1.62 1.10 0.73 2.34 1.62 1.02 0.67 0.46 1.46 1.12 0.70 0.41 0.20 -0.07 -0.05 1.13 0.86 0.70 0.48 0.27 0.13 0.14 -0.04 0.40 0.26 0.11 0.12 0.08 -0.13 -0.18 -0.03 -0.43 0.04 0.09 0.17 0.07 0.64 0.85 0.76 0.71 0.57 0.46 0.58 0.08 0.80
Volume 96, Number 6, November-December 1991
Journal of Research of the National Institute of Standards and Technology Table 4.
T K 126.5253 130.0849 133.6139 137.1129 140.5803 147.4210 150.8021 127.3163 131.4649 135.5815 139.6662 126.4530 130.6765 134.9085 139.1213 143.3060 147.4574 130.2059 134.5362 138.8786 143.2083 147.5123 132.0747 136.5879 141.1204 145.6394 150.1322 132.5996 137.3223 142.0505 146.7525 151.4228 156.0526 160.6436 165.1919 169.6996 174.1710 178.6041 183.0001 187.3635 191.6890 195.9802 200.2466 204.4752 210.0585 218.3924 226.6318 234.7910 242.8663 250.8702 258.8035 266.6768 274.4971 282.2634 289.9925 297.6971 305.4009 130.8320 135.8440 140.8426
Experimental single-phase heat capacities—Continued
P raol-dra"* 20.1948 20.1876 20.1808 20.1750 20.1679 20.1529 20.1443 18.2448 18.2238 18.2155 18.2082 16.2966 16.0985 16.0823 16.0846 16.0869 16.0876 14.1938 14.2878 14.3485 14.3826 14.4028 11.7620 11.9194 11.9827 12.0146 12.0316 10.2076 10.1724 10.1587 10.1507 10.1446 10.1406 10.1369 10.1336 10.1302 10.1264 10.1225 10.1189 10.1153 10.1125 10.1105 10.1079 10.1060 10.1008 10.0959 10.0911 10.0834 10.0801 10.0748 10.0694 10.0636 10.0578 10.0524 10.0466 10.0405 10.0343 8.3415 8.2185 8.1615
P MPa 7.6456 9.5802 11.4985 13.4013 15.2807 18.9728 20.7859 5.2548 6.9785 8.7087 10.4320 3.8154 5.0768 6.4036 7.7470 9.0928 10.4346 4.4025 5.4914 6.6081 7.7332 8.8591 4.4567 5.3117 6.1771 7.0439 7.9074 4.3573 5.0568 5.7565 6.4513 7.1397 7.8212 8.4954 9.1617 9.8204 10.4716 11.1153 11.7521 12.3825 13.0069 13.6259 14.2391 14.8466 15.6420 16.8298 17.9990 19.1453 20.2847 21.4044 ?.7„5096 23.6003 24.6790 25.7471 26.8042 27.8527 28.8964 3.9188 4.4754 5.0222
N mol
Kbomb
Ar
cm»
K
e/AT J-K-i
J-K-'
1.4715 1.4715 1.4716 1.4717 1.4717 1.4717 1.4716 1.3291 1.3280 1.3279 1.3279 1.1869 1.1729 1.1721 1.1726 1.1732 1.1736 1.0340 1.0412 1.0459 1.0487 1.0505 0.8569 0.8686 0.8735 0.8760 0.8775 0.7437 0.7413 0.7405 0.7401 0.7399 0.7398 0.7397 0.7397 0.7396 0.7395 0.7395 0.7394 0.7393 0.7393 0.7394 0.7394 0.7395 0.7394 0.7394 0.7395 0.7393 0.7395 0.7395 0.7395 0.7395 0.7394 0.7394 0.7394 0.7394 0.7393 0.6076 0.5988 0.5948
72.867 72.893 72.920 72.947 72.974 73.028 73.055 72.848 72.874 72.901 72.928 72.834 72.856 72.879 72.902 7Z926 7Z951 72.849 7Z870 72.892 72.914 72.936 72.854 72.874 72.894 72.915 72.935 72.855 72.874 72.893 72.912 72.932 72.952 72.972 72.992 73.012 73.032 73.052 73.072 73.092 73.112 73.132 73.152 73.172 73.198 73.239 73.279 73.319 73.359 73.399 73.439 73.479 73.519 73.558 73.598 73.638 73.679 72.846 72.864 72.883
3.5761 3.5480 3.5169 3.4894 3.4628 3.4039 3.3782 4.1564 4.1314 4.1031 4.0666 4.2098 4.2449 4.2317 4.2110 4.1806 4.1517 4.3099 4.3446 4.3393 4.3162 4.2922 4.4820 4.5294 4.5279 4.5080 4.4773 4.7041 4.7362 4.7206 4.6912 4.6574 4.6183 4.5785 4.5417 4.5066 4.4733 4.4369 4.4042 4.3729 4.3382 4.3119 4.2886 4.2636 8.4399 8.3530 8.2747 8.1942 8.1251 8.0608 7.9993 7.9311 7.8800 7.8414 7.7978 7.7563 7.7187 5.0045 5.0201 4.9925
98.407 99.139 99.966 100.687 101.401 102.823 103.547 95.609 96.084 96.688 97.462 94.283 93.387 93.468 93.845 94.410 95.028 92.049 91.257 91.358 91.743 92.214 88.512 87.555 87.530 87.872 88.395 84.345 83.715 83.850 84.319 84.904 85.575 86.222 86.855 87.610 88.099 88.735 89.342 89.907 90.510 91.024 91.478 91.925 92.646 93.507 94.275 95.062 95.797 96.445 97.065 97.777 98.376 98.751 99.164 99.611 100.111 79.223 79.040 79.288
59.185 60.276 61.307 62.281 63.203 64.903 65.689 59.432 60.685 61.860 62.964 59.162 60.452 61.672 62.820 63.898 64.911 60.312 61.568 62.756 63.874 64.924 60.863 62.138 63.343 64.474 65.535 61.015 62.338 63.581 64.743 65.829 66.844 67.795 68.686 69.523 70.311 71.055 71.757 72.423 73.054 73.653 74.225 74.769 75.456 76.421 77.311 78.136 78.902 79.617 80.285 80.912 81.500 82.054 82.577 83.075 83.551 60.498 61.933 63.271
734
CB"
Adj."
Cv J-moI-'-K-
Ci.,ca]c
■'
0.35 0.36 0.38 0.39 0.41 0.44 0.45 0.25 0.27 0.28 0.30 0.17 0.19 0.20 0.22 0.23 0.24 0.15 0.16 0.17 0.18 0.19 0.12 0.13 0.14 0.15 0.15 0.11 0.11 0.12 0.12 0.13 0.13 0.14 0.14 0.15 0.15 0.16 0.16 0.17 0.17 0.18 0.18 0.19 0.20 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.27 0.28 0.29 0.30 0.09 0.09 0.10
26.30 26.05 25.89 25.70 25.55 25.33 25.28 26.97 26.39 25.95 25.69 29.41 27.89 26.93 26.25 25.78 25.43 30.54 28J6 27.18 26.40 25.79 32.14 29.13 27.56 26.57 25.90 31.27 28.73 27.26 26.33 25.66 25.19 24.77 24.42 24.30 23.89 23.75 23.61 23.48 23.43 23.31 23.15 23.01 23.06 22.90 22.72 22.66 22.60 22.51 22.46 22.60 22.63 22.40
V.75 22.16 22.15 30.73 28.48 26.84
Diff."
% 26.04 1.01 0.94 25.80 1.01 25.63 0.81 25.50 0.65 25.38 25.19 0.57 0.69 25.10 0.41 26.86 0.90 26.15 0.84 25.73 0.93 25.45 29.79 -1.26 0.21 27.83 0.96 26.67 0.99 25.99 0.92 25.55 0.74 25.24 30.34 0.67 1.33 27.98 26.72 1.70 1.59 25.98 1.14 25.49 31.55 1.86 28.63 1.75 27.08 1.74 1.49 26.17 25.58 1.24 31.44 -0.55 28.59 0.47 0.79 27.05 26.12 0.82 25.50 0.63 25.04 0.57 24.69 0.34 24.40 0.08 0.61 24.15 23.94 -0.21 23.76 -0.05 23.60 0.08 23.45 0.10 23.33 0.47 23.21 0.44 23.11 0.18 23.02 -0.02 22.91 0.65 0.58 22.77 0.29 22.65 22.55 0.47 0.60 22.47 0.53 22.40 22.33 0.56 1.40 22.28 22.24 1.74 0.91 22.20 0.39 22.16 0.12 22.13 22.11 0.21 31.55 -2.69 0.04 28.47 26.86 -0.08
Volume 96, Number 6, November-December 1991
Journal of Research of the National Institute of Standards and Technology Table 4.
T K 145.7985 150.7101 155.5657 160.3678 165.1232 169.8250 174.4834 179.1053 183.6860 190.3080 199.2457 208.0556 216.7534 225.3505 233.8541 242.2773 250.6135 258.8895 267.1020 275.2560 283.3544 291.4014 299.4287 307.4412 127.3144 132.7254 138.0861 143.3730 148.5902 153.7331 158.8084 163.8194 168.7682 173.6621 178.5030 183.2876 188.0301 192.7??2 197.3785 201.9963 206.5742 211.1170 215.6256 225.9475 234.7724 243.4888 252.1201 260.6670 269.1402 277.5386 285.8948 294.1859 302.4355
Experimental single-phase heat capacities—Continued
P mol-dm"^ 8.1292 8.1089 8.0962 8.0871 8.0808 8.0756 8.0714 8.0673 8.0631 8.0587 8.0544 8.0502 8.0455 8.0409 8.0362 8.0314 8.0268 8.0217 8.0167 8.0116 8.0065 8.0018 7.9968 7.9916 6.0901 6.1679 6.1711 6.1676 6.1628 6.1594 6.1569 6.1554 6.1542 6.1533 6.1525 6.1519 6.1506 6.1498 6.1487 6.1476 6.1467 6.1455 6.1443 6.1421 6.1397 6.1378 6.1352 6.1324 6.1297 6.1271 6.1237 6.1206 6.1171
P MPa 5.5589 6.0866 6.6057 7.1162 7.6198 8.1153 8.6044 9.0873 9.5638 10.2509 11.1748 12.0803 12.9687 13.8425 14.7024 15.5501 16.3857 17.2106 18.0258 18.8314 19.6284 20.4184 21.2024 21.9817 3.2938 3.7382 4.1600 4.5679 4.9645 5.3516 5.7305 6.1022 6.4671 6.8261 7.1796 7.5277 7.8706 8.2091 8.5435 8.8742 9.2013 9.5246 9.8447 10.5756 11.1968 11.8087 12.4110 13.0049 13.5919 14.1718 14.7451 15.3127 15.8745
N mol
V^^ cm^
0.5926 0.5913 0.5905 0.5900 0.5897 0.5895 0.5893 0.5892 0.5890 0.5889 0.5889 0.5889 0.5889 0.5888 0.5888 0.5888 0.5887 0.5886 0.5886 0.5885 0.5884 0.5884 0.5883 0.5882 0.4435 0.4493 0.4497 0.4495 0.4493 0.4492 0.4491 0.4491 0.4491 0.4492 0.4492 0.4493 0.4493 0.4494 0.4494 0.4494 0.4495 0.4495 0.4495 0.4496 0.4496 0.4497 0.4497 0.4498 0.4498 0.4498 0.4498 0.4498 0.4497
72.902 72.920 72.939 72.958 72.977 72.996 73.015 73.034 73.053 73.080 73.118 73.156 73.193 73.231 73.269 73.306 73.344 73.381 73.419 73.456 73.493 73.531 73.568 73.606 72.831 72.850 72.868 72.886 72.904 72.922 72.941 72.959 72.977 72.995 73.013 73.031 73.050 73.068 73.086 73.104 73.122 73.140 73.157 73.199 73.235 73.270 73.306 73.341 73.377 73.412 73.447 73.483 73.518
^T K 4.9437 4.8982 4.3486 4.7965 4.7509 4.7024 4.6666 4.6259 4.5857 9.0408 8.9245 8.8087 8.6985 8.6044 8.5230 8.4479 8.3741 8.3097 8.2442 8.1783 8.1280 8.0823 8.0399 7.9875 5.4232 5.3865 5.3243 5.2530 5.1815 5.1152 5.0505 4.9947 4.9387 4.8845 4.8418 4.7966 4.7514 4.7141 4.6762 4.6439 4.6119 4.5784 4.5517 8.9395 8.8400 8.7463 8.6624 8.5795 8.5140 8.4513 8.3925 8.3413 8.2861
"Derived from Eq. (3). Co=dQo/dT. *" Equation (6). ' Reference [8]. •*100(Cv-C,c.ic)/a.
735
G/A7-
Co* JK-'
Adj."
JK-' 79.989 80.696 81.440 82.299 82.975 83.729 84.377 85.022 85.724 86.587 87.626 88.670 89.692 90.566 91.372 92.085 92.764 93.448 94.122 94.784 95.267 95.733 96.127 96.620 73.354 73.729 74.524 75.465 76.438 77.392 78.312 79.120 79.975 80.791 81.426 82.111 82.818 83.461 84.077 84.619 85.171 85.692 86.159 87.304 88.190 88.958 89.740 90.456 91.088 91.647 92.204 92.662 93.249
64.513 65.668 66.740 67.739 68.673 69J46 70.365 71.136 71.864 72.855 74.093 75.214 76.237 77.177 78.044 78.848 79.595 80.292 80.944 81.556 82.129 82.670 83.183 83.674 59.431 61.052 62.544 63.915 65.178 66.343 67.421 68.422 69.354 70 773 71.038 71.802 72.522 73.200 73.843 74.453 75.032 75.583 76.109 77.239 78.134 78.959 79.725 80.437 81.100 81.720 82.303 82.851 83.370
0.10 0.11 0.11 0.11 0.12 0.12 0.13 0.13 0.14 0.14 0.15 0.16 0.16 0.17 0.18 0.19 0.19 0.20 0.21 0.22 0.22 0.23 0.24 0.24 0.08 0.08 0.08 0.08 0.09 0.09 0.10 0.10 0.10 0.11 0.11 0.11 0.12 0.12 0.12 0.13 0.13 0.13 0.14 0.14 0.15 0.16 0.16 0.17 0.18 0.18 0.19 0.19 0.20
c.
Cy^'
J-mol-'-K--1 26.02 25.32 24.79 24.56 24.13 23.93 23.64 23.43 23.39 23.18 22.84 22.70 22.68 77 55 22.44 22.28 22.17 22.17 22.24 22.36 22.22 22.09 21.86 21.82 31.31 28.14 26.57 25.62 24.98 24.51 24.16 23.72 23.54 23.42 23.01 22.83 22.80 22.71 22.65 22.50 22.43 22.35 22.22 77 73 22.19 22.06 22.11 22.15 22.12 22.02 21.99 21.77 21.88
Diff.''
% 25.90 25.26 24.79 24.42 24.12 23.87 23.66 23.47 23.31 23.11 22.88 22.70 77,55 22.43 22.32 22.24 22.17 22.10 22.05 22.00 21.96 21.93 21.90 21.87 30.48 27.70 26.21 25.32 24.73 24.29 23.95 23.68 23.45 23.25 23.08 22.93 22.81 22.69 22.59 77 50 22.42 22.35 22.28 22.15 22.06 21.98 21.92 21.86 21.81 21.77 21.73 21.70 21.68
0.46 0.23 -0.01 0.57 0.04 0.26 -0.05 -0.16 0.36 0.32 -0.19 -0.01 0.58 0.56 0.51 0.18 0.03 0.31 0.86 1.59 1.18 0.75 -0.16 -0.25 2.66 1.56 1.37 1.18 1.02 0.90 0.84 0.19 0.41 0.71 -0.31 -0.46 -0.03 0.10 0.27 -0.02 0.04 0.03 -0.29 0.34 0.60 0.34 0.87 1.32 1.41 1.16 1.16 0.32 0.92
Volume 96, Number 6, November-December 1991
Journal of Research of the National Institute of Standards and Technology While we have observed that Cv*^^ values are a function of both T and p, C„ values are a function of T only. Hence, Ca data provide us with a valuable check of the accuracy of our measurements by direct comparison with published data. Figure 4 shows the behavior of C„ from near the N2 triple point to near the critical point temperature where it rises sharply. Also shown in Fig. 4 are results of Weber [2] and Giauque and Clayton [3], whose data have uncertainties of ±0.5% and ±1%, respectively. In order to intercompare the data sets, our data were fitted to the expression.
C=fl +fer+cr^+dr+er/V7^-rc
Table S. Coefficients of the function C,{T), Eq. {7)"* Value
Coefficient
0.469355x10' 0.211629x10° -0.490463x10-" 0.184354x10-' 0.129524x10' ' Units are J• mor' • K"' and K. *" Temperature range Is 64 to 118 K.
test of the internal consistency of the data derives from the relation
c,
Journal of Research of the National Institute of Standards and Technology [J. Res. Nat!. Inst. Stand. Technol. 96, 725 (1991)]
Molar Heat Capacity (Cv) for Saturated and Compressed Liquid and Vapor Nitrogen from 65 to 300 K at Pressures to 35 MPa
Volume 96 J. W. Magee National Institute of Standards and Technology, Boulder, CO 80303
Number 6
November-December 1991
Molar heat capacities at constant volume (C,) for nitrogen have been measured with an automated adiabatic calorimeter. The temperatures ranged from 65 to 300 K, while pressures were as high as 35 MPa. Calorimetric data were obtained for a total of 276 state conditions on 14 isochores. Extensive results which were obtained in the saturated liquid region (C^^^' and C„) demonstrate the internal consistency of
Glossary a,b,c,d,e
c.
a
C„
a
Vbamb
Vr, P P. AP T Tc TuT2
Ar
Q Go N P PP-
the Cv (fi,T) data and also show satisfactory agreement with published heat capacity data. The overall uncertainty of the Cy values ranges from 2% in the vapor to 0.5% in the liquid. Key words: calorimeter; heat capacity; high pressure; isochorlc; liquid; measurement; nitrogen; saturation; vapor. Accepted: August 30, 1991
ticular, the heat capacity at constant volume {Cv) is related to P(j^T) by:
Coefficients for Eq. (7) Molar heat capacity at constant volume Molar heat capacity in the ideal gas state Molar heat capacity of a two-phase sample Molar heat capacity of a saturated liquid sample Volume of the calorimeter containing sample Molar volume, dm' • mol"' Pressure, MPa Vapor pressure Pressure rise during a heating interval Temperature, K Critical-point temperature Temperature at start and end of heating Interval Temperature rise during a heating Interval Calorimetric heat energy input to bomb and sample Calorimetric heat energy input to empty bomb Moles of substance in the calorimeter Fluid density, mol • dm"' Saturated liquid density Chemical potential
Jo
(1)
where C? is the ideal gas heat capacity. Consequently, Cv measurements which cover a wide range of {P, p, T) states are beneficial to the development of an accurate equation of state for the substance. The amount of experimental data on the calorimetric properties of nitrogen is very limited. Measurements of Cv are mostly confined to atmospheric pressure. Only two published works concern Cv measurements at elevated pressure. First, Voronel et al. [1] obtained 69 experimental values of Cv at temperatures from 106 to 167 K at densities close to the critical density, with an emphasis on the temperature variation of Cv near the critical point (126.2 K). However, these authors give neither the pressures nor the densities at which the measurements were performed. Thus, comparisons with the Cv data of Voronel et al. are difficult at best. In the only other experimental study at elevated pressures, Weber [2] performed measurements at temperatures from 91 to 242 K using the same calorimeter as used in this work. The combined works of Voronel et al. and Weber
1. Introduction Accurate measurements of thermodynamic properties, including heat capacity, are needed to establish behavior of higher order temperature derivatives of an equation of state P(p, T). In par725
Volume 96, Number 6, November-December 1991
Journal of Research of the National Institute of Standards and Technology compare these measurements with published data and with predictions from published equations of state.
leave gaps in the Cv surface between the triple point (63.15 K) and 91 K, and for temperatures above 242 K. Published experimental results for the heat capacity of the saturated liquid (C„) are more available than those for Cv at elevated pressures. When combined, the data of Weber [2], Giauque and Clayton [3], and Wiebe and Brevoort [4] range from 65 to 125 K. However, none of these works spans the entire temperature domain for saturated liquid nitrogen. Thus, we cannot be certain how the various data will intercompare. In this work, the goals include extending the published data for Cv to temperatures as low as the triple point, and also to near ambient temperature. A second goal is to measure Ca over temperatures from the vicinity of the triple point to that of the critical point, and to
2.
Experimental
The apparatus in Fig. 1 has a long history dating to its original construction for liquid hydrogen calorimetry. Its mechanical details remain essentially unchanged since they were described by Goodwin [5]. Instrumentation, however, has been changed extensively. The older instruments were replaced with electronic versions, each equipped with an IEEE-488 standard interface for two-way communication with a microcomputer. The arrangement of the new instruments is shown in Fig. 2.
Access Tubes
Outer Vacuum Tube
Refrigerant Tubes
Inner Refrigerant Tanl
% J-mol-i-K-i -0.49 -0.24 -0.23 -0.10 0.01 0.16 0.32 0.67 1.06 1.27 1.43 1.54 -0.79 -0.29 -0.05 0.09 0.32 0.58 1.00 1.27 1.59 1.70 1.17 -0.60 -0.40 -0.13 -0.15 0.23 0.40 0.41 0.62 0.95 1.39 1.68 1.62 1.19 -0.76 -0.42 -0.15 -0.17 0.06 0.04 0.43 0.72 1.07 1.60
59.99 60.84 61.66 62.64 63.69 64.81 66.00 67.37 68.85 70.36 72.10 74.29 60.49 62.73 65.29 66.70 68.24 69.87 71.72 73.65 75.98 78.80 82.41 60.99 62.19 63.60 65.00 66.76 68.50 70.22 72.14 74.28 76.70 79.41 82.57 86.99 61.91 63.64 65.56 67.52 69.79 72.04 74.66 77.34 80.22 83.57
Volume 96, Number 6, November-December 1991
Journal of Research of the National Institute of Standards and Technology Table 4.
T K 66.1756 9.0867 71.9548 74.7849 77.5788 69.2774 72.6946 76.0585 72.6097 75.5013 78.3559 81.1743 83.9583 72.0307 74.9320 77.7934 80.6178 83.4075 77.0893 80.0185 82.9065 85.7558 88.5715 85.2388 88.2096 91.1399 94.0353 96.8947 99.7227 102.5197 92.3233 95.3475 98.3344 101.2850 104.2006 107.0820 109.9340 112.7578 105.7600 108.8264 111.8576 114.8599 117.8323 120.7784 123.6977 126.5950 129.4678 132.3201 135.1429 137.9433 112.3409 115.9124 119.4468 122.9472 126.4129 129.8462 133.2459 136.6150 119.3182 122.9365
Experimental single-phase heat capacities
P mol-dm"' 30.9599 30.8819 30.8328 30.8035 30.7869 30.8813 30.8246 30.7943 30.3311 30.2825 30.2515 30.2318 30.2188 30.3444 30.2907 30.2568 30.2352 30.2209 29.5526 29.5055 29.4743 29.4528 29.4368 28.1342 28.0972 28.0717 28.0522 28.0364 28.0232 28.0104 26.5920 26.5632 26.5439 26.5288 26.5166 26.5049 26.4947 26.4840 24.2453 24.2371 24.2317 24.2259 24.2205 24.2140 24.2071 24.1991 24.1907 24.1817 24.1724 24.1626 22.1595 22.1468 22.1408 22.1381 22.1302 22.1242 22.1177 22.1102 20.2246 20.2050
P MPa 8.5838 14.4587 20.2568 25.9553 31.5376 14.9188 21.7709 28.4964 11.8026 17.2998 22.6862 27.9586 33.1070 10.7150 16.2231 21.6323 26.9234 32.0913 8.6948 13.7919 18.7781 23.6465 28.3997 6.0948 10.4732 14.7565 18.9399 23.0260 27.0294 30.9381 3.1853 6.9012 10.5495 14.1182 17.6147 21.0309 24.3895 27.6783 4.8752 7.7000 10.4814 13.2159 15.9078 18.5546 21.1602 23.7239 26.2495 28.7374 31.1832 33.5919 3.1882 5.6836 8.1621 10.6204 13.0294 15.4143 17.7654 20.0821 3.7560 5.7012
N mol 2.2520 2.2477 2.2456 2.2449 2.2452 2.2478 2.2454 2.2449 2.2073 2.2051 2.2042 2.2042 2.2046 2.2080 2.2054 2.2044 2.2042 2.2045 2.1502 2.1481 2.1471 2.1468 2.1469 2.0469 2.0453 2.0446 2.0443 2.0442 2.0444 2.0446 1.9345 1.9334 1.9329 1.9327 1.9328 1.9329 1.9331 1.9333 1.7648 1.7650 1.7653 1.7657 1.7660 1.7663 1.7665 1.7667 1.7668 1.7669 1.7669 1.7670 1.6131 1.6128 1.6130 1.6135 1.6136 1.6138 1.6140 1.6141 1.4727 1.4717
rbomb
Ar
cm'
K
72.739 72.785 72.832 72.879 72.927 72.789 72.844 72.901 72.773 72.818 72.864 72.910 72.956 72.764 72.809 72.855 72.901 72.947 72.759 72.802 72.846 72.889 72.933 72.756 72.795 72.835 72.874 72.914 7X953 72.993 72.748 72.783 72.819 72.855 72.890 72.926 72.961 72.997 72.791 72.822 72.852 72.883 72.913 72.944 72.975 73.005 73.036 73.067 73.098 73.128 72.793 72.823 72.852 72.883 72.913 72.943 72.974 73.004 72.815 72.841
2.9305 2.8898 2.8506 2.8157 2.7814 3.4450 3.3915 3.3428 Z9139 2.8762 2.8386 2.8076 2.7718 2.9234 2.8824 2.8466 2.8122 2.7793 2.9544 2.9149 2.8759 2.8404 2.8069 2.9975 2.9579 2.9212 2.8869 2.8548 2.8259 2.7951 3.0508 3.0172 2.9797 2.9451 2.9134 2.8842 2.8541 2.8304 3.0766 3.0460 3.0164 2.9831 2.9560 2.9311 2.9064 2.8807 2.8633 2.8364 2.8135 2.7945 3.5832 3.5489 3.5135 3.4780 3.4438 3.4128 3.3829 3.3532 3.6281 3.6044
733
Q/^T JK-'
JK-i
107.357 108.710 110.186 111.573 112.954 108.863 110.553 112.208 107.734 109.104 110.564 111.831 113.210 107.377 108.874 110.217 111.579 112.913 106.205 107 J84 108.936 110.320 111.676 104.445 105.825 107.095 108.360 109.573 110.653 111.823 102.476 103.613 104.856 106.022 107.127 108.191 109.272 110.181 100.935 101.875 102.853 103.887 104.861 105.701 106.567 107.485 108.096 109.073 109.817 110.542 98.547 99.454 100.436 101.363 102.298 103.165 104.003 104.893 97.117 97.697
29.273 31.377 33.368 35.254 37.044 31.512 33.868 36.079 33.811 35.720 37.530 39.245 40.874 33.419 35.350 37.179 38.912 40.557 36.736 38.550 40.266 41.892 43.434 41.602 43.239 44.788 46.257 47.648 48.970 50.225 45.396 46.902 48.328 49.677 50.956 52.169 53.322 54.419 51.619 52.880 54.074 55.207 56.283 57.306 58.279 59.206 60.090 60.934 61.738 62.506 54.260 55.593 56.849 58.032 59.149 60.204 61.201 62.145 56.804 58.029
Co'
Adj."
Cv
t.y.calc
J-mol-'-K-■J 1.28 1.24 1.22 1.21 1.22 1.23 1.21 1.21 1.16 1.16 1.16 1.18 1.20 1.17 1.16 1.16 1.17 1.19 1.06 1.07 1.08 1.10 1.12 0.89 0.91 0.93 0.95 0.97 1.00 1.02 0.73 0.75 0.77 0.79 0.81 0.83 0.86 0.88 0.55 0.57 0.59 0.61 0.63 0.65 0.67 0.69 0.70 0.72 0.74 0.75 0.41 0.43 0.45 0.46 0.48 0.50 0.52 0.54 0.31 0.33
33.26 33.09 37 95 32.76 32.58 33.11 32.91 32.69 32.29 32.11 31.97 31.76 31.62 32.29 32.16 31.97 31.80 31.64 31.24 31.08 30.91 30.79 30.68 29.82 29.70 29.56 29.44 29.32 29.18 29.10 28.79 28.59 28.48 28.36 28.25 28.14 28.08 27.96 27.39 27.18 27.03 26.95 26.87 26.74 26.66 26.64 26.47 26.52 26.47 26.43 27.04 26.76 26.57 26.39 26.25 26.12 26.00 25.95 27.06 26.62
Diff.''
% 31.76 31.98 32.13 32.18 32.17 32.00 32.15 32.19 31.30 31.41 31.46 31.45 31.39 31.27 31.40 31.45 31.45 31.41 30.51 30.57 30.60 30.58 30.53 29.39 29.37 29.35 29.31 29.26 29.20 29.12 28.46 28.35 28.28 28.23 28.17 28.11 28.04 27.97 27.28 27.11 27.00 26.92 26.85 26.78 26.71 26.64 26.58 26.51 26.45 26.39 27.02 26.59 26.35 26.19 26.07 25.97 25.88 25.80 27.03 26.41
4.526 3.33 2.49 1.76 1.25 3.34 2.30 1.53 3.06 2.17 1.61 0.99 0.73 3.14 2.38 1.62 1.10 0.73 2.34 1.62 1.02 0.67 0.46 1.46 1.12 0.70 0.41 0.20 -0.07 -0.05 1.13 0.86 0.70 0.48 0.27 0.13 0.14 -0.04 0.40 0.26 0.11 0.12 0.08 -0.13 -0.18 -0.03 -0.43 0.04 0.09 0.17 0.07 0.64 0.85 0.76 0.71 0.57 0.46 0.58 0.08 0.80
Volume 96, Number 6, November-December 1991
Journal of Research of the National Institute of Standards and Technology Table 4.
T K 126.5253 130.0849 133.6139 137.1129 140.5803 147.4210 150.8021 127.3163 131.4649 135.5815 139.6662 126.4530 130.6765 134.9085 139.1213 143.3060 147.4574 130.2059 134.5362 138.8786 143.2083 147.5123 132.0747 136.5879 141.1204 145.6394 150.1322 132.5996 137.3223 142.0505 146.7525 151.4228 156.0526 160.6436 165.1919 169.6996 174.1710 178.6041 183.0001 187.3635 191.6890 195.9802 200.2466 204.4752 210.0585 218.3924 226.6318 234.7910 242.8663 250.8702 258.8035 266.6768 274.4971 282.2634 289.9925 297.6971 305.4009 130.8320 135.8440 140.8426
Experimental single-phase heat capacities—Continued
P raol-dra"* 20.1948 20.1876 20.1808 20.1750 20.1679 20.1529 20.1443 18.2448 18.2238 18.2155 18.2082 16.2966 16.0985 16.0823 16.0846 16.0869 16.0876 14.1938 14.2878 14.3485 14.3826 14.4028 11.7620 11.9194 11.9827 12.0146 12.0316 10.2076 10.1724 10.1587 10.1507 10.1446 10.1406 10.1369 10.1336 10.1302 10.1264 10.1225 10.1189 10.1153 10.1125 10.1105 10.1079 10.1060 10.1008 10.0959 10.0911 10.0834 10.0801 10.0748 10.0694 10.0636 10.0578 10.0524 10.0466 10.0405 10.0343 8.3415 8.2185 8.1615
P MPa 7.6456 9.5802 11.4985 13.4013 15.2807 18.9728 20.7859 5.2548 6.9785 8.7087 10.4320 3.8154 5.0768 6.4036 7.7470 9.0928 10.4346 4.4025 5.4914 6.6081 7.7332 8.8591 4.4567 5.3117 6.1771 7.0439 7.9074 4.3573 5.0568 5.7565 6.4513 7.1397 7.8212 8.4954 9.1617 9.8204 10.4716 11.1153 11.7521 12.3825 13.0069 13.6259 14.2391 14.8466 15.6420 16.8298 17.9990 19.1453 20.2847 21.4044 ?.7„5096 23.6003 24.6790 25.7471 26.8042 27.8527 28.8964 3.9188 4.4754 5.0222
N mol
Kbomb
Ar
cm»
K
e/AT J-K-i
J-K-'
1.4715 1.4715 1.4716 1.4717 1.4717 1.4717 1.4716 1.3291 1.3280 1.3279 1.3279 1.1869 1.1729 1.1721 1.1726 1.1732 1.1736 1.0340 1.0412 1.0459 1.0487 1.0505 0.8569 0.8686 0.8735 0.8760 0.8775 0.7437 0.7413 0.7405 0.7401 0.7399 0.7398 0.7397 0.7397 0.7396 0.7395 0.7395 0.7394 0.7393 0.7393 0.7394 0.7394 0.7395 0.7394 0.7394 0.7395 0.7393 0.7395 0.7395 0.7395 0.7395 0.7394 0.7394 0.7394 0.7394 0.7393 0.6076 0.5988 0.5948
72.867 72.893 72.920 72.947 72.974 73.028 73.055 72.848 72.874 72.901 72.928 72.834 72.856 72.879 72.902 7Z926 7Z951 72.849 7Z870 72.892 72.914 72.936 72.854 72.874 72.894 72.915 72.935 72.855 72.874 72.893 72.912 72.932 72.952 72.972 72.992 73.012 73.032 73.052 73.072 73.092 73.112 73.132 73.152 73.172 73.198 73.239 73.279 73.319 73.359 73.399 73.439 73.479 73.519 73.558 73.598 73.638 73.679 72.846 72.864 72.883
3.5761 3.5480 3.5169 3.4894 3.4628 3.4039 3.3782 4.1564 4.1314 4.1031 4.0666 4.2098 4.2449 4.2317 4.2110 4.1806 4.1517 4.3099 4.3446 4.3393 4.3162 4.2922 4.4820 4.5294 4.5279 4.5080 4.4773 4.7041 4.7362 4.7206 4.6912 4.6574 4.6183 4.5785 4.5417 4.5066 4.4733 4.4369 4.4042 4.3729 4.3382 4.3119 4.2886 4.2636 8.4399 8.3530 8.2747 8.1942 8.1251 8.0608 7.9993 7.9311 7.8800 7.8414 7.7978 7.7563 7.7187 5.0045 5.0201 4.9925
98.407 99.139 99.966 100.687 101.401 102.823 103.547 95.609 96.084 96.688 97.462 94.283 93.387 93.468 93.845 94.410 95.028 92.049 91.257 91.358 91.743 92.214 88.512 87.555 87.530 87.872 88.395 84.345 83.715 83.850 84.319 84.904 85.575 86.222 86.855 87.610 88.099 88.735 89.342 89.907 90.510 91.024 91.478 91.925 92.646 93.507 94.275 95.062 95.797 96.445 97.065 97.777 98.376 98.751 99.164 99.611 100.111 79.223 79.040 79.288
59.185 60.276 61.307 62.281 63.203 64.903 65.689 59.432 60.685 61.860 62.964 59.162 60.452 61.672 62.820 63.898 64.911 60.312 61.568 62.756 63.874 64.924 60.863 62.138 63.343 64.474 65.535 61.015 62.338 63.581 64.743 65.829 66.844 67.795 68.686 69.523 70.311 71.055 71.757 72.423 73.054 73.653 74.225 74.769 75.456 76.421 77.311 78.136 78.902 79.617 80.285 80.912 81.500 82.054 82.577 83.075 83.551 60.498 61.933 63.271
734
CB"
Adj."
Cv J-moI-'-K-
Ci.,ca]c
■'
0.35 0.36 0.38 0.39 0.41 0.44 0.45 0.25 0.27 0.28 0.30 0.17 0.19 0.20 0.22 0.23 0.24 0.15 0.16 0.17 0.18 0.19 0.12 0.13 0.14 0.15 0.15 0.11 0.11 0.12 0.12 0.13 0.13 0.14 0.14 0.15 0.15 0.16 0.16 0.17 0.17 0.18 0.18 0.19 0.20 0.20 0.21 0.22 0.23 0.24 0.25 0.26 0.27 0.27 0.28 0.29 0.30 0.09 0.09 0.10
26.30 26.05 25.89 25.70 25.55 25.33 25.28 26.97 26.39 25.95 25.69 29.41 27.89 26.93 26.25 25.78 25.43 30.54 28J6 27.18 26.40 25.79 32.14 29.13 27.56 26.57 25.90 31.27 28.73 27.26 26.33 25.66 25.19 24.77 24.42 24.30 23.89 23.75 23.61 23.48 23.43 23.31 23.15 23.01 23.06 22.90 22.72 22.66 22.60 22.51 22.46 22.60 22.63 22.40
V.75 22.16 22.15 30.73 28.48 26.84
Diff."
% 26.04 1.01 0.94 25.80 1.01 25.63 0.81 25.50 0.65 25.38 25.19 0.57 0.69 25.10 0.41 26.86 0.90 26.15 0.84 25.73 0.93 25.45 29.79 -1.26 0.21 27.83 0.96 26.67 0.99 25.99 0.92 25.55 0.74 25.24 30.34 0.67 1.33 27.98 26.72 1.70 1.59 25.98 1.14 25.49 31.55 1.86 28.63 1.75 27.08 1.74 1.49 26.17 25.58 1.24 31.44 -0.55 28.59 0.47 0.79 27.05 26.12 0.82 25.50 0.63 25.04 0.57 24.69 0.34 24.40 0.08 0.61 24.15 23.94 -0.21 23.76 -0.05 23.60 0.08 23.45 0.10 23.33 0.47 23.21 0.44 23.11 0.18 23.02 -0.02 22.91 0.65 0.58 22.77 0.29 22.65 22.55 0.47 0.60 22.47 0.53 22.40 22.33 0.56 1.40 22.28 22.24 1.74 0.91 22.20 0.39 22.16 0.12 22.13 22.11 0.21 31.55 -2.69 0.04 28.47 26.86 -0.08
Volume 96, Number 6, November-December 1991
Journal of Research of the National Institute of Standards and Technology Table 4.
T K 145.7985 150.7101 155.5657 160.3678 165.1232 169.8250 174.4834 179.1053 183.6860 190.3080 199.2457 208.0556 216.7534 225.3505 233.8541 242.2773 250.6135 258.8895 267.1020 275.2560 283.3544 291.4014 299.4287 307.4412 127.3144 132.7254 138.0861 143.3730 148.5902 153.7331 158.8084 163.8194 168.7682 173.6621 178.5030 183.2876 188.0301 192.7??2 197.3785 201.9963 206.5742 211.1170 215.6256 225.9475 234.7724 243.4888 252.1201 260.6670 269.1402 277.5386 285.8948 294.1859 302.4355
Experimental single-phase heat capacities—Continued
P mol-dm"^ 8.1292 8.1089 8.0962 8.0871 8.0808 8.0756 8.0714 8.0673 8.0631 8.0587 8.0544 8.0502 8.0455 8.0409 8.0362 8.0314 8.0268 8.0217 8.0167 8.0116 8.0065 8.0018 7.9968 7.9916 6.0901 6.1679 6.1711 6.1676 6.1628 6.1594 6.1569 6.1554 6.1542 6.1533 6.1525 6.1519 6.1506 6.1498 6.1487 6.1476 6.1467 6.1455 6.1443 6.1421 6.1397 6.1378 6.1352 6.1324 6.1297 6.1271 6.1237 6.1206 6.1171
P MPa 5.5589 6.0866 6.6057 7.1162 7.6198 8.1153 8.6044 9.0873 9.5638 10.2509 11.1748 12.0803 12.9687 13.8425 14.7024 15.5501 16.3857 17.2106 18.0258 18.8314 19.6284 20.4184 21.2024 21.9817 3.2938 3.7382 4.1600 4.5679 4.9645 5.3516 5.7305 6.1022 6.4671 6.8261 7.1796 7.5277 7.8706 8.2091 8.5435 8.8742 9.2013 9.5246 9.8447 10.5756 11.1968 11.8087 12.4110 13.0049 13.5919 14.1718 14.7451 15.3127 15.8745
N mol
V^^ cm^
0.5926 0.5913 0.5905 0.5900 0.5897 0.5895 0.5893 0.5892 0.5890 0.5889 0.5889 0.5889 0.5889 0.5888 0.5888 0.5888 0.5887 0.5886 0.5886 0.5885 0.5884 0.5884 0.5883 0.5882 0.4435 0.4493 0.4497 0.4495 0.4493 0.4492 0.4491 0.4491 0.4491 0.4492 0.4492 0.4493 0.4493 0.4494 0.4494 0.4494 0.4495 0.4495 0.4495 0.4496 0.4496 0.4497 0.4497 0.4498 0.4498 0.4498 0.4498 0.4498 0.4497
72.902 72.920 72.939 72.958 72.977 72.996 73.015 73.034 73.053 73.080 73.118 73.156 73.193 73.231 73.269 73.306 73.344 73.381 73.419 73.456 73.493 73.531 73.568 73.606 72.831 72.850 72.868 72.886 72.904 72.922 72.941 72.959 72.977 72.995 73.013 73.031 73.050 73.068 73.086 73.104 73.122 73.140 73.157 73.199 73.235 73.270 73.306 73.341 73.377 73.412 73.447 73.483 73.518
^T K 4.9437 4.8982 4.3486 4.7965 4.7509 4.7024 4.6666 4.6259 4.5857 9.0408 8.9245 8.8087 8.6985 8.6044 8.5230 8.4479 8.3741 8.3097 8.2442 8.1783 8.1280 8.0823 8.0399 7.9875 5.4232 5.3865 5.3243 5.2530 5.1815 5.1152 5.0505 4.9947 4.9387 4.8845 4.8418 4.7966 4.7514 4.7141 4.6762 4.6439 4.6119 4.5784 4.5517 8.9395 8.8400 8.7463 8.6624 8.5795 8.5140 8.4513 8.3925 8.3413 8.2861
"Derived from Eq. (3). Co=dQo/dT. *" Equation (6). ' Reference [8]. •*100(Cv-C,c.ic)/a.
735
G/A7-
Co* JK-'
Adj."
JK-' 79.989 80.696 81.440 82.299 82.975 83.729 84.377 85.022 85.724 86.587 87.626 88.670 89.692 90.566 91.372 92.085 92.764 93.448 94.122 94.784 95.267 95.733 96.127 96.620 73.354 73.729 74.524 75.465 76.438 77.392 78.312 79.120 79.975 80.791 81.426 82.111 82.818 83.461 84.077 84.619 85.171 85.692 86.159 87.304 88.190 88.958 89.740 90.456 91.088 91.647 92.204 92.662 93.249
64.513 65.668 66.740 67.739 68.673 69J46 70.365 71.136 71.864 72.855 74.093 75.214 76.237 77.177 78.044 78.848 79.595 80.292 80.944 81.556 82.129 82.670 83.183 83.674 59.431 61.052 62.544 63.915 65.178 66.343 67.421 68.422 69.354 70 773 71.038 71.802 72.522 73.200 73.843 74.453 75.032 75.583 76.109 77.239 78.134 78.959 79.725 80.437 81.100 81.720 82.303 82.851 83.370
0.10 0.11 0.11 0.11 0.12 0.12 0.13 0.13 0.14 0.14 0.15 0.16 0.16 0.17 0.18 0.19 0.19 0.20 0.21 0.22 0.22 0.23 0.24 0.24 0.08 0.08 0.08 0.08 0.09 0.09 0.10 0.10 0.10 0.11 0.11 0.11 0.12 0.12 0.12 0.13 0.13 0.13 0.14 0.14 0.15 0.16 0.16 0.17 0.18 0.18 0.19 0.19 0.20
c.
Cy^'
J-mol-'-K--1 26.02 25.32 24.79 24.56 24.13 23.93 23.64 23.43 23.39 23.18 22.84 22.70 22.68 77 55 22.44 22.28 22.17 22.17 22.24 22.36 22.22 22.09 21.86 21.82 31.31 28.14 26.57 25.62 24.98 24.51 24.16 23.72 23.54 23.42 23.01 22.83 22.80 22.71 22.65 22.50 22.43 22.35 22.22 77 73 22.19 22.06 22.11 22.15 22.12 22.02 21.99 21.77 21.88
Diff.''
% 25.90 25.26 24.79 24.42 24.12 23.87 23.66 23.47 23.31 23.11 22.88 22.70 77,55 22.43 22.32 22.24 22.17 22.10 22.05 22.00 21.96 21.93 21.90 21.87 30.48 27.70 26.21 25.32 24.73 24.29 23.95 23.68 23.45 23.25 23.08 22.93 22.81 22.69 22.59 77 50 22.42 22.35 22.28 22.15 22.06 21.98 21.92 21.86 21.81 21.77 21.73 21.70 21.68
0.46 0.23 -0.01 0.57 0.04 0.26 -0.05 -0.16 0.36 0.32 -0.19 -0.01 0.58 0.56 0.51 0.18 0.03 0.31 0.86 1.59 1.18 0.75 -0.16 -0.25 2.66 1.56 1.37 1.18 1.02 0.90 0.84 0.19 0.41 0.71 -0.31 -0.46 -0.03 0.10 0.27 -0.02 0.04 0.03 -0.29 0.34 0.60 0.34 0.87 1.32 1.41 1.16 1.16 0.32 0.92
Volume 96, Number 6, November-December 1991
Journal of Research of the National Institute of Standards and Technology While we have observed that Cv*^^ values are a function of both T and p, C„ values are a function of T only. Hence, Ca data provide us with a valuable check of the accuracy of our measurements by direct comparison with published data. Figure 4 shows the behavior of C„ from near the N2 triple point to near the critical point temperature where it rises sharply. Also shown in Fig. 4 are results of Weber [2] and Giauque and Clayton [3], whose data have uncertainties of ±0.5% and ±1%, respectively. In order to intercompare the data sets, our data were fitted to the expression.
C=fl +fer+cr^+dr+er/V7^-rc
Table S. Coefficients of the function C,{T), Eq. {7)"* Value
Coefficient
0.469355x10' 0.211629x10° -0.490463x10-" 0.184354x10-' 0.129524x10' ' Units are J• mor' • K"' and K. *" Temperature range Is 64 to 118 K.
test of the internal consistency of the data derives from the relation
c,
