Thermodynamic Properties of Propane WALTER V. STEARNSl AND EMMANUEL J. GEORGE Sun Oil Company, Marcus Hook, Penna.
HE use of propane as a refrigerant has increased substantially within the last few years, and thermodynamic data for this refrigerant have not been compiled for the whole region normally employed in refrigeration. While Dana et al. (2) published tables for the\saturated liquid and vapor, no satisfactory compilation has been made for the superheated vapor region. This paper represents a close correlation of the published experimental data of a number of authors on certain phases of the thermodynaniic properties of propane. While Sage, Schaafsma, and Lacey (IO) and Burgoyne (1) published thermodynamic charts, the data used in calculating these
charts did not show the agreement between the experimental data pointed out in this paper. By correlating the actual experimental data of the authors cited, we have been able to show close agreement between the results of these authors. This agreement may be best understood if the following processes are examined. If, for example, we take the saturated liquid a t -40" F., evaporate this liquid t o the saturated vapor, heat the resulting vapor a t constant pressure to 160" E', and compress it isothermally until the saturated vapor is reached, the actual heat content of the resulting vapor will then agree within about 0.2 €3. t. u. with the heat content of the vapor which would be obtained by heating the saturated liquid to 160" F. and then evaporating the liquid t o form a saturated vapor. Such agreement is possible
T
1
Present address, M. W.Kellogg Company 223 Broadway, New York,
N. Y.
Figure 1. Absolute Enthalpy Chart for Propane
602
May, 1943
INDUSTRIAL AND ENGINEERING CHEMISTRY
1 1 1 1
IIIIIIIII
1 1 1 1
1.1
I
S = B.T.U.
Figure 2.
I I I I I I I I I
1.3
1.4
I I I I I I I I I ,
I l l t l l l l L
1.5
OF.
Entropy-Temperature Chart for Propane
only if all these various thermodynamic factors are correct or if two or more of these factors will produce compensating errors over the complete range. The latter probability is somewhat remote, in view of the complexity of the functions involved. This paper presents the first correlation of the thermodjmamic properties of propane based on purely experimental data while these experimental data are not so complete as would be desired, the over-all picture is in close agreement. PROPERTIES INVESTIGATED
The vapor pressure values employed in these correlations are calculated from the formula: log P = A / T B log T C where A = -1018.502 B = -0.16646 C = +6.67979 P = absolute pressure, om. Hg T = absolute temperature, ' K.
+
I I I I I I I I I
1.2 PER L B . PER
603
+
These values agree well with those of Kemp and Egan (6) above -80" F., with the low-temperature values of Dana et al., and with the values of Deschner and Brown (3) to about +195' F. From +195" F. up to and including the critical point, the values of Deschner and Brown are utilized. For temperatures below -43.7' F. the spec& heats of the
liquid of Kemp and Egan (6) are employed. From -43.7' to $155" F., the values represent a smooth curve through the data of Dana et al. and of Sage and Lacey. The values of Sage and Lacey (9)are apparently a revision of the earlier data of Sage, Schaafsma, and Lacey (IO). Above +155' F. the values are drawn as a smooth curve roughly following the values of Sage, Schaafsma, and Lacey at the lower end and to the observed values of these authors a t the higher end corrected for their deviation from the apparent true critical temperature. The heats of fusion are taken from the observations of Kemp and Egan. The values for latent heat were taken from a smooth curve drawn through the experimental values of Kemp and Egan (6),Dana et d.@), and of Sage, Evans, and Lacey (8). The specific volume and density of the liquid are taken from a smooth curve through the values of Dana (2), Sage, Schaafsma, and Lacey (IO), and Deschner and Brown (3). The data for the compressed liquid are taken from Deschner and Brown. The specXc volumes of the saturated vapor show good agreement between the experimental values of Dana et al. and of Deschner and Brown. The tabulated calculated data of Dana are not in agreement and show increasing divergence with increasing temperature.
Vol. 35, No. 5
INDUSTRIAL AND ENGINEERING CHEMISTRY
604
Table I. Temperature t , ' F.
- 80 -78.75 - 78 - 76 -75.9 - 74 -73.2 - 72 -70.7 - 70
-68.4
- 68 -66.1 - 66 - 64
-63.9 62 -61.9
-
--58.1 60 58 -56.2
- 56 -54.4 - 54 -52.6 52 -51
-
- 50
-49.6 -48 -47.9 -46.5 -46 -44.9 -44 -43.71 - 42
Pressure. Lb./Sq. In. Absolute, Gage, P UP 5.65 18 in." 5.87
6.00 6.32 6.35 6.71 6.86 7.18 7.35
7.48 7.84 7.91 8.32 8.33 8.80 8.81 9.28 9.30 9.78 10.28 10.29 10.77 10.80 11.26 11.36 11.75 11.95 12.24 12.60 12.73 13.20 13.22 13.71 13.85 14.2 14.52 14.70 15.28
17 in. 16 in.
15 in. 14 in. 13 in. 12 in. 11 in.
Temperature Data for Saturated Propane Density Liquid Vapor (1/n), (l/V)? lb./gal. lb./ou. ft.
H e a t Content, B. T. U./Lb. Liquid h Vapor H
Latent Heat L, 8. T.U./LL.
Entropy
0.026: 0.0265 0.0266 0.0266 0.0266 0.0267 0.0267 0.0268 0.0268
16.2 15.6 15.3 14.6 14.6 13.8 13.5 13.0 12.7
5.052 5,043 5.041 5.030 5.030 5,020 5.019 5.009 5.002
0,062 0 064 0.065 0.068 0.068 0,072 0.074 0.076 0.079
162.6 163.2 163.6 164.6 164.6 165.6 166.0 166,6 167.2
354,O 354.4 354.6 355.2 355.2 355.8 356.0 356.4 366.5
191.4 191.2 191.0 190.6 190.6 190.2 190.0 189.8 189.5
B. T. U./Lb.jo 1. Liquid s Vapor S 0.8794 1.3832 0.8812 1.3826 0.8821 1.3822 0.8847 1.3812 0,8850 1.3811 0.8874 1.3801 0,8884 1.3797 0,8900 1.3791 0.8918 1,3785
0.0268 0.0268 0.0268 0.0268 0.0269 0.0269 0.0269 0.0270 0.0270
12.5 12.0 11.9 11.3 11.3 10.8 10.8 10.3 10.3
4,998 4,990 4.988 4.978 4.978 4.968 4.968 4.957 4.957
0,080 0.083 0.084 0,088 0,088 0.093 0.093 0.097 0.097
167.6 168.4 168.6 169.8 169,7 170.7 170.8 171.7 171.8
357.0 367.5 357.6 358.1 358.2 358.8 358.9 359.4 359.5
189 4 189.1 189.0 188.5 188.5 188.1 188.1 187.7 187.7
0.8927 0.8949 0.8954 0.8978 0.8980 0,9007 0.9008 0,9033 0,9034
1.3781 1,3775 1.3773 1,3766 1.3766 1.3756 1.3756 1.3748 1.3748
9.77 9.35 9.33 8.96 8.92 8.59 8.51 8.24 8.12 7.93
4.946 4.936 4,936 4.926 4.925 4.917 4.915 4,907 4,904 4.898
0.102 0.107 0.107 0.112 0.112 0.116 0.117 0.120 0.122 0.125
172.7 173.6 173.7 174.6 174.7 175.6 175.8 176.5 176.8 177.3
360.0 360.5 360.6 361.1 361.1 361.4 361.i 362.1 362.3 362.6
187.3 186.9 186.9 186.5 186.4 185.8 185.9 185 6 185.5 185.3
0.9060 0.9085 0.9086 0.9108 0,9111 0.9132 0.9137 0.9154 0.9162 0.9175
1.3740 1.3732 1,3732 1,3726 1,3725 1,3719 1.3717 1.3712 1.3710 1.3706
7.73 7.72 7.50 7.44 7.17 7.06 6.90 6.74 6.66 6.42
4,893 4.891 4.882 4.883 4,875 4.872 4.866 4.861 4.860 4.850
0.129 0.130 0.133 0.134 0.139 0.142 0.145 0.148 0.150 0.156
177.8 178.0 178.8 178.9 179.7 179.9 180.4 180.9 181.36 181.9
362.8 362.9 363.4 363.5 363.8 364.0 364.3 364.6 364.76 365.2
185.0 184.9 184.6 184.6 184.1 184.1 183.9 183.8 183,5 183 3
0.9188 0.9193 0.9213 0.9214 0,9232 0.9238 0.9252 0.9264 0.9266 0,9289
1.3702 1.3701 1.3696 1,3696 1.3691 1.3689 1 ,3686 1,3683 1.3682 1,3676
Volume, Cu. Ft./Lb. LiTuid-v Vapor V
10 in. 9 in. 8 in.
7 in. 6 in. 5 in.
4 in. 3 in. 2 in. 1 in. 0
- 40 - 38 -36 - 34
16.00 16.79 17.56 18.40 19.30
1.30 2.09 2.86 3.70 4.60
0,02763 0.02769 0.02775 0.02782 0.02788
6.16 5.92 5.66 5.44 5.22
4.839 4.828 4.818 4,807 4.797
0.162 0.169 0.177 0.184 0.192
183.0 184.0 185.1 186.2 187.3
366.7 366.3 366.9 367.5 368.0
182.7 182.3 181.8 181.3 180.7
0.9315 0,9340 0,9365 0.9391 0.9418
1.3670 1.3664 1.3668 1.3652 1.3646
- 30
20.18 21.05 22,Ol 22.98 23.98
5.48 6.35 7.31 8 28 9.28
0,02794 0.02800 0.02807 0.02813 0.02820
5.02 4.82 4.63 4.44 4.25
4,786 4.775 4.764 4.752 4.741
0,199 0.207 0.216 0.225 0.235
188.4 189.4 190.5 191.6 192.7
368.6 369.2 369.8 370.3 370.9
180.2 179,7 179.3 178.7 178.2
0.9441 0.9467 0,9492 0.9517 0,9543
1 3640 1.3634 1 ,3628 1,3622 1.3616
- 20 - 18 - 16 - 14
25.05 26.15 27.30 28.50 29.70
10.35 11.45 12.60 13.80 15.00
0.02826 0.02833 0.02839 0.02846 0.02852
4.06 3.90 3.76 3.61 3.47
4.730 4.719 4.708 4.697 4.686
0,246 0.256 0.266 0,277 0,288
193.8 194.9 196.0 197.1 198.2
371.5 372.A 372., 373.2 373.8
177.7 177.2 176.6 176.1 175.6
0.9568 0.9592 0.9617 0.9641 0.9666
1.3610 1.3604 1.3399 1.3593 1 3588
- 10
30.95 32.23 33.55 35.00 36.40
16.25 17.53 18.85 20.30 21.70
0.02859 0.02866 0.02873 0.02879 0.02886
3.33 3.20 3.08 2.98 2.86
4.675 4.664 4.652 4.641 4.629
0.300 0.313 0.325 0.336 0.350
199.4 200.5 201.6 202.7 203.8
374.4 375.0 375.5 376.: 376.t
175.0 174.5 173.9 173.4 172.8
0.9690 0.9714 0,9739 0.9763 0.9788
1.3582 1.3577 1,3671 1.3866 1.3660
8
37.81 39.30 40.85 42.50 44.13
23.11 24.60 26.15 27.80 29.43
0.02893 0.02900 0,02908 0,02915 0.02923
2.74 2.66 2.56 2.47 2.38
4.618 4.607 4,596 4.584 4.573
0.365 0.376 0.391 0.405 0.420
205.0 206.1 207.2 208.4 209.6
377.2 377.8 378.3 378.9 379.5
172.2 171.6 171.1 170.5 169.9
0.9812 0.9836 0.9860 0.9884 0,9908
1.3555 1.3560 1.3545 1.3541 1.3536
'I 0 12 14 16 18
45.85 47.55 49.35 51.20 53.10
31.15 32.85 34.65 36.50 38.40
0.02930 0.02938 0,02946 0.02994 0.02962
2.30 2.22 2.14 2.08 2.00
4.562 4.550 4.538 4.526 4,514
0.435 0.450 0.467 0.481 0,500
210.7 211.9 213.1 214.2 215.4
380.0 380.6 381.1 381.6 382.1
169.3 168.7 168.0 167.4 166.7
0.9932 0.9956 0.9979 1,0003 1,0026
1.3531 1.3527 1,3523 1.3518 1.3514
20 22 24 26 28
55.00 57.05 59.10 61.25 63.45
40.30 42.35 44.40 46.55 48.75
0.02970 0.02978 0,02986 0,02995 0.03003
1.93 1.86 1.79 1.73 1.67
4.502 4.590 4.477 4.465 4,452
0.518 0.538 0.559 0,578 0.598
216.6 217.7 218.8 220.0 221.2
382.6 383.1 383.6 384.1 384.6
166.0 165.4 164.8 164.2 163.5
1 ,0050 1,0073 1,0097 1,0120 1,0144
1.3510 1.3506 1,3502 1,3499 1.3495
30 .32 34 36 38
65.70 67.95 70.33 72.75 75.20
51.00 53.25 55.63 58.05 60.50
0.03011 0,03020 0.03029 0.03037 0.03046
1.60 1.54 1.48 1.43 1.39
4,440 4,427 4,414 4.401 4.388
0.625 0.649 0,676 0.699 0.719
222.3 223.4 224.5 225.6 226.8
385.1 385.6 386.1 386.6 387.1
162.8 162.2 161.5 160.8 160.2
1.0167 1.0190 1,0213 1.0237 1.0260
1.3491 1.3487 1.3484 1.3480 1.3477
7. 7 . . XO
80.40 83.05 85.83 88.65
63.10 65.70 68.35 71.13 73.95
0,03055 0.03064 0.03073 0.03083 0.03092
1.33 1.28 1.25 1.21 1.17
4.375 4.362 4.348 4.335 4.321
0.752 0.781 0.800 0.826 0.855
227.9 229.1 230.2 231.4 232.6
387.5 388.0 388.5 389.0 389.5
159.6 158.9 158.2 157.5 156.8
1,0283 1.0306 1,0329 1,0352 1.0375
1 3473 1.3470 1 3466 1,3463 1.3459
91.60 94.50 97.5 100.6 103.7
76.80 79.80 82.80 85.9 89.0
0.03101 0.03111 0.03121 0.03130 0.03140
1.14 1.10 1.07 1.04 1.01
4.308 4.294 4.281 4.267 4.254
0.877 0,909 0.935 0.962 0.990
233.8 234.9 236.1 237.3 238.5
389.9 390.4 390.8 391.3 391.7
156.1 155.4 154.7 154.0 163.3
1.0398 1.0421 1 ,0443 1.0466 1.0488
1.3456 1,3453 1.3460 1.3447 1.3444
- 32 - 28
-26 -24 - 22
- 12 - 8
- 6
- 4 - 2 - 0
+: 6
.40 42 44 46
48 50 52 54 56
58
Inches of mercury vacuum.
May, 1943
INDUSTRIAL AND ENGINEERING CHEMISTRY Table I.
Temperature Data for Saturated Propane (Concluded) Density
Pressure. Lb./Sq. In. Temperature t , F.
Absolute.
Gage, gP
605
Volume, Cu. Ft./Lb. Vapor Liquid D
Heat Content, B. T. U./Lb.
2 s :
239.6 240.8 242.0 243.2 244.4
Vapor H 392.2 392.7 393.1 393.5 394.0
B. T. U./?tb. 152.6 151.8 151.1 150.3 149.5
1.171 1.202 1.235 1.269 1.305
245.7 246.9 248.1 249.4 250.2
394.4 394.8 395.2 395.6 396.0
4.103 4.088 4.074 4.059 4.045
1.342 1.379 1.420 1.462 1,508
251.9 253.1 254.4 255.6 256.9
0.643 0.626 0.609 0.592 0.575
4.030 4.015 4.001 3.986 3.972
1.555 1.597 1.642 1.689 1.739
0.03390 0.03402 0.03415 0.03427 0.03439
0.558 0.544 0.530 0.516 0.502
3,957 3.941 3.925 3.910 3.894
200.1 205.7 211.3 216.9 222.6
0.03452 0.03468 0.03484 0.03500 0.03516
0.487 0.475 0.463 0.451 0.439
243.4 249.7 255.7 261.7 267.9
228.7 235.0 241.0 247.0 253.2
0.03532 0.03548 0.03564 0.03580 0.03596
130 132 134 136 138
274.5 281.1 287.9 294.7 301.4
259.8 266.4 273.2 280.0 286.7
140 142 144 146 148
308.4 315.5 322.8 330.2 337.6
150 152 154 156 158
Liquid h
V
60 62 64 66 68
P 106.9 110.2 113.6 117.1 120.6
92.2a 95.5 98.9 102.4 105.9
0.03150 0.03162 0.03174 0.03185 0.03197
0.984 0.958 0.932 0.906 0.880
4.240 4.226 4.213 4.199 4.186
1.018 1.044 1.073 1,104 1.136
70 '72 74 76 78
124.3 127.9 131.7 135.6 139.6
109.6 113.2 117.0 120.9 124.9
0.03209 0,03221 0,03233 0.03245 0.03257
0.854 0.832 0.810 0.788 0,766
4.172 4.158 4,144 4.131 4.117
80 82 84 86 88
143.6 147.7 151.8 156.2 160.6
128.9 133.0 137.1 141.5 145.9
0,03269 0,03281 0.03293 0.03305 0.03317
0.745 0.725 0.704 0.684 0 663
90 92 94 96 98
165.0 169.6 174.2 178.9 183.7
150.3 154.9 159.5 164.2 169.0
0.03329 0,03341 0.03353 0,03366 0.03378
100 102 104 106 108
188.7 193.8 198.9 204.1 209.3
174.0 179.1 184.2 189.4 194.6
110 112 114 116 118
214.8 220.4 226.0 231.6 237.3
120 122 124 126 128
Entro y
B. T. U./L%.)* F. Liquid
8
Vspor
S
1.0511 1.0534 1.0556 1.0579 1 * 0601
1.3441 1.3438 1.3435 1.3433 1,3430
148.7 147.8 147.0 146.2 145.4
1.0624 1.0647 1.0669 1.0692 1.0714
1.3427 1,3424 1.3421 1,3419 1.3416
396.4 396.8 397.2 397.6 398.0
144.5 143.7 142.8 141.9 141.0
1.0737 1 .0760 1.0782 1 ,0805 1.0827
1.3413 1.3410 1.3408 1.3405 1.3403
258.2 259.5 260.8 262.1 263.3
398.3 398,7 399.1 399.5 399.9
140.1 139.2 138.3 137.4 136.5
1 .OS50 1.0873 1,0895 1.0918 1.0940
1.3400 1.3398 1.3395 1.3393 1.3390
1.792 1.838 1,887 1,938 1.992
264.6 265.9 267.2 268.5 269.8
400.2 400.5 400.9 401.2 401.6
135.6 134.6 133.7 132.7 131.8
1.0963 1.0986 1.1010 1.1033 1.1057
1.3388 1.3386 1.3384 1.3382 1.3380
3.878 3.862 3.846 3.830 3.814
2.053 2.105 2.160 2.217 2.278
271.1 272.5 273.9 275.2 276.6
401.9 402.3 402.7 403.0 403.4
130.8 129.8 128.8 127.8 126.8
1,1080 1.1103 1.1126 1,1149 1.1172
1.3378 1.3376 1.3374 1.3372 1.3370
0.426 0.415 0.404 0.393 0.382
3.798 3.780 3.763 3.745 3.728
2.347 2.410 2.475 2.544 2.618
278.0 279.4 280.9 282.3 283.8
403.8 404.1 404.5 404.8 405.2
125.8 124.7 123.6 122.5 121.4
1.1195 1.1218 1.1241 1.1264 1.1287
1.3368 1.3366 1.3363 1.3361 1.3358
0.03612 0.03630 0.03648 0.03666 0.03684
0,370 0.360 0.350 0.340 0.330
3.710 3.692 3.674 3.657 3.639
2,703 2.778 2.857 2.941 3,030
285.2 286.7 288.2 289.7 291.2
405.4 405.7 406.1 406.4 406.7
120.2 119.0 117.9 116.7 115.5
1.1310 1,1334 1.1358 1.1382 1.1406
1.3356 1.3353 1.3350 1.3348 1.3345
293.7 300.8 308.1 315.5 322.9
0.03702 0.03725 0.03748 0.03771 0.03794
0.320 0.312 0.303 0.295 0.286
3.621 3.600 3.578 3.557 3.535
3.125 3.205 3.300 3,390 3.496
292.7 294.2 295.7 297.2 298.6
407.0 407.3 407.6 407.8 408.0
114.3 113.1 111.9 110.6 109.4
1.1430 1,1454 1.1479 1.1503 1.1528
1.3347 1.3339 1.3336 1.3332 1.3329
345.4 352.9 360.8 368.6 376.6
330.7 338.2 346.1 353.9 361.9
0.03817 0.03846 0.03875 0.03904 0.03933
0.278 0.270 0.263 0.255 0.248
3.514 3.487 3.460 3.434 3.407
3,597 3.704 3.802 3.922 4,032
300.2 301.8 303.4 305.1 306.8
408.2 408.4 408.6 408.7 408.8
108.0 106.6 105.2 103.6 102.0
1.1552 1.1578 1.1603 1.1629 1.1654
1.3326 1.3321 1.3317 1.3312 1.3308
160 162 164 166 168
385.0 392.9 401.0 409.3 417.8
370.3 378.2 386.3 394.6 403.1
0.03962 0.03996 0.04030 0.04064 0.04098
0.240 0.234 0.227 0.221 0.214
3.380 3.351 3.322 3.292 3.263
4.167 4.273 4.405 4.525 4.673
308.4 310.2 312.0 313.9 315.7
408.8 408.8 408.9 408.9 408.8
100.4 98.6 96.9 95.0 93.1
1.1680 1.1707 1.1734 1.1762 1.1789
1.3303 1 .3297 1.3291 1.3284 1.3278
170 172 174 176 178
426.0 436.4 445.9 455.2 464.1
411.3 421.7 431.2 440.5 449.4
0.04132 0.04179 0,04226 0.04273 0.04320
0.208 0.202 0.197 0.191 0.186
3.234 3.201 3.168 3.136 3.103
4.808 4,950 5.076 5.236 5.376
317.5 319.5 321.5 323.5 325.5
408.6 408.6 408.6 408.4 408.2
91.1 89.1 87.1 84.9 82.7
1.1816 1.1847 1,1878 1.1908 1.1939
1.3272 1.3262 1.3252 1.3243 1.3233
180 182 184 186 188 190 200
473.2 483.0 492.9 503.1 512.8 523.4 575.0
458.5 468.3 478.2 488.4 498.1 508.7 560.3
0.04367 0.04436 0.04505 0.04574 0.04643 0.04712 0.0521
0.180 0.174 0.168 0.161 0.165 0.149 0.113
3.07 3.03 2.99 2.95 2.91 2.87 2.59
5.556 5.747 5.952 6.211 6.452 6.711 8.850
327.5 329.8 332.2 334.5 336.9 339.2 353.5
407.6 407.4 407.1 406.6 405.9 404.6 398.3
80.1 77.6 74.9 72.1 69.0 65.7 44.8
1.1970 1.2004 1 .2038 1.2072 1.2106 1.2140 1.2360
1.3223 1.3210 1.3196 1.3183 1.3169 1.3156 1.3040
0
I
Inches of mercury vacuum.
Specific volumes of superheated vapor were calculated from compressibility factors as based on Deschner and Brown. These values were plotted add extrapolated on a largescale chart. A few of them deviate from the smooth curve by amounts which indicate a strong possibility that the tabulated values were either misread from the original chart or that a typographical error had been made. These values were smoothed as indicated; in addition, the deviation of the saturated specific volumes from those calculated from the simple gas law were plotted as unique or limiting values for the compressibility factors a t any given temperature. The compressibility factors were then
interpolated and extrapolated for the vapor to cover the whole range above -70" F. Except in the case of the saturated liquid, the data substantially below 86" F. may be considered purely imaginative, without experimental basis. Actually, the curves drawn are merely similar to those in the known experimental regions, and the accuracy of these values must be judged in the light of their agreement or disagreement with other experimental data. From the compressibility factors as plotted above, the corresponding isobars were plotted and their slopes accurately evaluated; the corresponding values for (dZ/dT) were plotted against pressure.
606
INDUSTRIAL AND ENGINEERING CHEMISTRY
From the smoothed values t h e isothermal change of enthalpy with pressure was calculated a t constant temperature by the well-known formula:
Temp.
Satd. 70 60 - 60 -40 30 20 10
12.72 12.78 13.11 13.46 13.79 14.13 14.47 14.81
356.5 357.0 360.3 363.5 366.8 370.1 373.4 376.8
1.3785 1.3791 1.3869 1,3946 1.4023 1.4100 1.4177 1.4253
The values of the function -H at constant tempera-
0 10 20 30 40 50 60 70 80 90 100
15.14 15.48 15.82 16.16 16.50 16.83 17.17 17.51 17.85 18.19 18.52
380.2 383.8 387.4 391.1 394.8 398.6 402.4 406.3 410.2 414.3 418.4
1.4329 1.4405 1.4481 1.4557 1.4633 1.4709 1,4785 1.4861 1.4937 1.5013 1.5088
Table 11. F.
-
--
Properties" of Superheated Propane Vapor P = 10 In. H g , t = - 6 O O F . P = 5 In.
P = 15 In. H g , t = -70.6'F. H S
v
Vol. 35, No. 5
H
S
.... ....
360.0
...
1.3740
10.042 10.30 10.55 10.81 11.06
36312 366.5 369.8 373.1 376.6
1.3816 1.3893 1.3970 1.4045 1.4121
11.321 11.57 11.83 12.08 12,34 12.59 12.85 13.10 13.36 13.61 13.87
380.0 383.6 387.2 390.9 394.6 398.4 402.2 406.1 410.0 414.1 418.2
1.4197 1,4273 1.4349 1.4425 1.4501 1.4577 1.4652 1 ,4727 1,4802 1.4877 1.4952
V 9.80
....
....
V 7.90
Hg, t
=
H
-51OF. 5
362.75
...
1.3718
7.978 8.182 8.387 8.591 8.796
362:s 366.2 369.6 373.0 376.4
1.3720 1.3796 1.3872 1.3948 1.4024
9.000 9.204 9.409 9.613 9.818 10.02 10.23 10.43 10.64 10.84 11.050
379.9 383.4 387.0 390.7 394.4 398.2 402.0 406.0 410.0 414.0 418.1
1.4100 1.4176 1.4252 1.4328 1.4404 1,4480 1.4556 1.4630 1.4706 1.4780 1.4854
....
. . I .
.... ....
t u r e are obtained by graphical integration of the values for the change in 110 18.86 422.5 1.6162 14.12 422.3 11.25 1.5026 422.1 1.4928 enthalpy with pressure a t 120 1.5235 19.20 426.6 1.5101 14.38 426.4 426.2 1.6002 11.45 130 19,54 1.5308 430.8 1.5174 430.6 14.63 430,6 11.66 1.5075 constant temperature when 1.5380 140 19.88 435.2 1.5245 435.9 14.89 435,O 1.5148 11.86 150 20.21 1.5452 15.14 439.4 439.6 1.5317 439.3 1.5221 12.07 plotted against absolute 1.5524 160 20.55 444.1 1,5389 16.40 443.9 12.27 443.8 1.5293 pressure. 170 20.89 448.6 1.5596 1,5461 448.4 1.5365 15.65 448.4 12.47 21.23 1.5668 180 453.1 15.91 1.5533 452.9 1,5437 452.9 12.68 The agreement between 1.5740 190 21.57 457.9 1,5605 457.7 16.16 457.6 1.5509 12.88 200 21.90 462.5 1.5812 13.09 16.42 1,5677 462.4 1.5581 462.4 our values for 190" F. and t h o s e of D e s c h n e r a n d P = 14.696 Lb. Aba., t = Brown for 194' F. is strik-43.708' F. P = 20 Lb. Abs., t = -30.30° F. ing. The disagreement be6.66 364.6 1.3681 Satd. 5.050 368.4 1.3640 6.775 365.8 1.3710 40 .... .... tween our 160" values and 6.949 369.3 1.3788 -30 5.060 3&:6 1.3642 7.123 372.8 1.3866 20 1.3719 5.186 372.2 those of Deschner and 7.297 376.3 1.3943 - 100 7.471 1.3796 5.313 375.8 Brown at 158" F. is sub379.8 1.4020 1,3873 5.439 739.3 stantial; but since errors 10 7.644 383.3 1.4096 7.007 383.2 1.4056 5,567 1,3949 382.9 7.816 386.8 1.4772 386.6 20 7.166 386.8 1.4132 5.695 1.4025 occur in their tabulated 390.6 1.4248 390.2 30 7.988 7.324 390.4 1.4208 5.823 1.4101 figures for this range, the 394.3 1.4324 393.9 40 8.160 7.482 394.2 1.4284 5.951 1,4177 8.332 398.1 1.4399 397.7 50 7.640 398.0 1,4359 6.079 1.4252 results of the correlation 8.503 1.4434 401.9 1,4474 401.6 7.798 401.8 6.207 1.4327 60 405.8 405.5 8.674 1.4549 7.955 405.8 1.4508 6.334 1.4402 70 weigh strongly in favor of 409.4 8.844 409.8 1.4623 1,4582 1.4477 80 8.112 409.8 6.461 413.5 9.016 413.9 1.4698 our 160"figures. 8.269 413.8 1.4656 6.588 1.4551 90 417.6 9.187 418.0 1.4772 8.426 417.9 1.4730 6.716 1.4625 100 In the field of specific 9.358 422.1 1.4845 8.583 6.843 421.7 1.4698 110 421.9 1,4804 heat of propane vapor, the 9.528 426.2 1.4918 8.740 426.1 1.4878 6.969 425.9 1.4771 120 values in the literature have 130 9.699 430.4 1.4991 8.897 430.4 1.4962 7.095 430.2 1.4844 9.869 434.6 1.4917 434.8 1.5064 1.5026 7.221 140 9.054 434.8 no satisfactory agreement. 10.040 439.2 1.5137 9.211 439.2 1.6099 7.347 439.0 1.4990 150 9.368 443.7 1.5172 7.473 443.6 1,5063 10.21 443.7 1.5210 160 The values of Edmister 170 10.38 448.3 1.5283 9.525 448.2 1.5245 7.599 448.0 1.5136 (6) are based on a correla10.51 452.9 1.5256 7.725 452.6 1.5209 9.682 462.8 1.5317 180 10.72 457.5 1.5428 9.839 467.4 1.5389 7.851 457.3 1.5282 190 tion and have no inde7.977 461.9 1.5355 200 10.84 462.4 1.5500 9.996 462.2 1.5460 pendent value unless confirmed by experimental P = 2 4 L b , A b s . , t = -21.97'F. P = 3 0 L b . A b s . , t = -11.52'F. P = 4 0 L b . A b ~ . , t - +2.90°F. data. This is particularly 4.25 370.9 1.3615 3.30 374.00 1.3588 2.61 378.2 1.3648 Satd. 4.279 371.7 1.3632 .... .... ... .... --20 true in the case of propane, 4.390 375.3 1.3712 3.47 3?4:6 1.3597 .... ... .... 10 4.499 378.9 1.3790 3.559 378.3 1.3678 .... ... .... 0 which deviates substantially 2.684 380.9 1,3603 382.0 1.3754 in most correlations. 4.608 382.5 1.3806 3.647 10 3.735 385.7 1.3830 2.753 384.7 1.3684 386.2 1.3942 4.716 20 The values of Kistia1.3905 2.821 388.5 1.3761 3.823 389.4 4.824 389.9 1.4018 30 2.889 392.2 1.3838 4.932 393.6 1.4094 3.911 393.1 1.3980 40 kowsky and Rice (7) for 3.999 396.9 1.4055 2.957 396.1 1.3914 397.4 1,4170 5.040 50 3.025 400.8 1,4130 400.0 1.3990 propane have no confirma4.087 5.147 401.3 1.4245 60 3.092 404.0 1.4065 404.7 1.4205 5.254 405.2 1.4320 4.174 70 tion from other sources. 408.0 1,4140 1.4280 3.159 5.361 409.2 1.4394 4.261 408.7 80 1.4354 3.224 412.1 1.4215 1.4468 4.347 412.8 5.467 413.3 90 Their experimental values 1.4290 3.289 416.2 1.4542 4.432 417.0 1.4428 5.573 417.4 100 for other gases obtained 3.354 420.4 1.4365 421.2 1.4502 1.4616 4.517 110 421.5 5.679 with the same equipment 1.4576 3.419 424.6 1.4440 4.602 425.4 1.4690 0.780 425.6 120 429.6 1.4650 3.484 429.0 1.4514 5.891 429.8 1.4764 4.687 130 have had substantial con434.0 1.4724 3.549 433.4 1.4588 1.4837 4.772 5.997 434.3 140 firmation, however, and this 4.857 438.4 1.4898 3.614 437.9 1.4662 438.8 1,4910 6.103 150 443.0 1 4872 3.679 442.5 1.4736 1.4983 4.942 6.209 443.3 160 correlation also checks their 1.5056 5.027 447.6 1.4946 3.744 447.1 1,4810 6.315 447.9 170 452.2 1.5020 3.809 451.8 1.4884 1.5128 5.112 6.420 452.5 180 data. When used as a basis 456.9 1.5094 3.874 456.5 1.4957 5.197 457.1 1.5200 6.525 190 461.8 1.5168 3.939 461.3 1.6030 for calculation of the ab1.5272 5.282 6.630 462.0 200 solute enthalpy values, their values give extremely good agreement with heat content data for the saturated On this basis we have assumed that the data of Kistialiquid over the whole range of experimental work. kowsky and Rice (7) are correct. As a matter of fact, no The values of Dobratz ( 4 ) are based on assumptions conother values will produce a satisfactory correlation, and the cerning certain potential barriers producing hindered rotation correlation indicates that they are probably accurate to about of the methyl groups in this compound; he gives different one in the third decimal place. data for different assumed values of this potential barrier. .
I
.
.
I N D U S T R I A L A N D E N G I N E E R I N G CHEMISTRY
May, 1943 ~~~
T
F.
Table 11. Properties* of Superheated Propane Vapor (Concluded) P~ = 50 P = 60 Lb. Abs., t = 24.80' F. P = 80 Lb. Abs., t ~ Lb. . Abs., t = 14.7' F. V H S V H s V H
~
= 41.69'
Satd. 20 30 40 50 60 70 80 90 100
2.115 2.159 2.217 2.275 2.331 2.386 2.441 2.495 2.549 2.602
381.2 383.5 387.4 391.3 395.2 399.1 403.1 407.1 411.2 415.4
1.3521 1.3562 1.3647 1.3726 1.3804 1.3881 1.3957 1.4033 1.4109 1.4185
1.76
383.8
1.3501
1.32
387.8
1.814 1.863 1.911 1.959 2.006 2.053 2,099 2.145
38611 390.1 394.1 398.2 402.2 406.3 410.5 414.8
1:3547 1.3630 1.3710 1.3789 1.3808 1.3948 1.4025 1.4102
....
S 1 3470
.... ....
1.36 1.424 1.462 1.500 1.537 1.573
39i:e 396.1 400.3 404.6 408.9 413.2
1.3540 1.3624 1.3707 1.3785 1.3863 1.3940
110 120 130 140 150 160 170 180 190 200
2.656 2.709 2.762 2.815 2.868 2.921 2.975 3.027 3.079 3.131
419.6 423.9 428.3 432.8 437.3 441.9 446.6 451.3 456.1 460.9
1.4261 1.4337 1.4412 1,4487 1.4562 1.4637 1.4711 1.4785 1.4859 1.4933
2.190 2.235 2.280 2.325 2.370 2.415 2.460 2.505 2,549 2.593
419.0 423.4 427.8 432.2 436.8 441.4 446.1 450.8 455.6 460.5
1,4179 1.4254 1.4330 1.4404 1.4479 1.4554 1.4629 1.4703 1,4777 1.4851
1.609 1.644 1.679 1.714 1.749 1.784 1.818 1.852 1.886 1.920
417.6 421.8 426.3 430.9 435.6 440.3 445.0 449.8 454.7 459.7
1.4017 1.4094 1.4171 1.4248 1.4325 1.4402 1.4478 1.4554 1.4629 1.4704
0
P
= 100 Lb. Abs., t = 55.62'
....
F. P = 130 Lb. Abs., t = 73.20' F.
Satd. 60 70 80 90 100
1.06 1.094 1.131 1.164 1.196 1.227
391.2 393.5 398.3 402.6 406.9 411.4
1.3448 1.3488 1.3573 1.3656 1.3736 1.3816
110 120 130 140 150 160 170 180 190 200
1.258 1,289 1.318 1.347 1,375 1.400 1.432 1.460 1.488 1.516
415.7 420.3 424.9 429.6 434.4 439.1 444.0 448.8 453.8 458.8
1.3893 1.3962 1,4050 1.4130 1.4209 1.4286 1.4362 1.4440 1.4518 1.4598
0.8165
P
= 160 Lb. Abs.,
t
87.71' F. 1.3404
I
1.3424
0.8456 0.8762 0.9045
398:s 403.6 408.3
1.3486 1.3571 1.3659
0.6695 0.6969
399:2 404.7
1.3423 1.3521
0.9315 0.9588 0.9815 1.006 1.029 1.052 1.076 1.098 1.120 1.143
412.9 417.8 420.7 425.7 430.7 435.7 440.7 445.3 450.9 456.1
1,3740 1.3822 1.3903 1.3987 1,4059 1.4160 1,4230 1.4310 1.4389 1.4468
0.7222 0.7464 0,7691 0.7908 0.8118 0.8319 0,8520 0.8712 0.8903 0.9093
409.6 414.6 419.7 424.8 429.9 434.9 440.0 445.1 450.9 456.1
1.3610 1.3698 1.3784 1.3867 1.3949 1.4031 1.4113 1.4195 1.4276 1.4357
.... ....
0.6685
.... .... ....
...
.... ....
395.0
... ...
397.9
.... .... ....
....
... .
I
F
.
....
....
607 the values on the saturated vapor curve within 0.2 B. t. u. in most cases. Over the range from -40' to +200° F., independent of the interpolations and extrapolations on the compressibility chart, the values of Kistiakowsky and Rice are in good agreement, since - A H a t -40" F. is relatively small. However, the values obtained from the compressibility chart correlate well with the other data. Specific heats of the vapor a t constant pressure for 0 pound absolute were taken from Kistiakowsky and Rice; and for the higher pressures, they were read from the heat content chart.
ENTROPY - TEMPERATURE.
Figure 2 gives a second correlation of data. The reference value for the entropy of the liquid a t its boiling point was taken from the experimental values of P 220 Lb. Abs., t = 111.85'' F. P = 250 Lb. Ab%, t 122.12O F. P = 190 Lb. Kemp and Egan. T h e 0.4738 402.5 1.3375 0.4130 404.2 1.3355 0.5540 Satd. .... .... .... ... ... 0.5774 110 saturated liquid and satu0.4911 407:7 1.3460 .... 120 0.5995 413.7 1.3558 0.4283 0.5121 130 rated vapor curves were 0.6208 0.5314 0.4473 419.2 1.3650 0.6415 140 then calculated in the con0.5498 0.4649 424.5 1.3739 0.6607 150 0.4816 429.7 1.3827 0.5673 0.6792 160 ventional manner. The 0.5846 0.4972 435.3 1.3913 0.6971 170 0.5121 440.6 1.3999 0.7144 0.5998 180 lines of constant quality, 0.6149 0.5266 445.9 1.4080 0.7311 190 expressed as per cent vapor, 0.6302 0.5408 451.2 1.4161 200 ' 0.7472 were calculated directly I., t = 137.55' F. from these values. The 1.6 1.3345 * Pressurea below atmospheria are expressed in inches of HK 1.7 1.3372 lines of constant pressure in the superheat region were calculated from our values for the specific heat of the vapor a t constant pressure. The lines of constant volume were calculated from the compressibility CORRELATION O F RESULTS chart and plotted against the temperature coordinate and the ABSOLUTE ENTHALPY. Figure 1 gives the first correlation pressure parameters. The enthalpy parameters were read from of data. The reference value for the heat content of the the heat content chart and plotted in the same manner, saturated liquid a t atmospheric pressure was obtained by All data are reported on the B. t. us-" F.-pound system, graphical integration of the specific heat values of Kemp except as noted. The actual molecular weights employed by and Egan between absolute zero and the boiling point at each author were used in calculating data from the molal atmospheric pressure. Therefore, these data give the basis, and in each case the author's value for the absolute enthalpy of propane above the solid a t absolute zero and &re temperature was used in calculating the Fahrenheit temperabased on the assumption that the entropy a t this point is zero. ture. The data of Deschncr and Brown were corrected for From this reference value for the liquid and from the ethane content. of their sample. H signifies the absolute specific heats, specific volumes, and latent heats previously enthalpy referred t o the solid a t absolute zero. S refers to discussed, the saturated liquid and saturated vapor curve was absolute entropy on the same basis, V is in cubic feet per calculated. From a reference point at -40' F. on the satupound units, and J is taken as 0.18511. rated vapor line, H o was calculated at -40' F. and infinite LITERATURE CITED dilution from our - A H data. From this point the absolute (1) Burgoyne, Proc. Roy. Soc. (London), A176, 280-94 (1940). values were calculated for the heat content a t infinite dilution (2) Dana, Jenkins, Burdick, and Timm, Refrig.Eng., 12,387 (1926). a t various temperatures between -70" and +200° F. from (3) Deschner and Brown, IND.ENQ.CHEM.,32,837 (1940). the data of Kistiakowsky and Rice as extrapolated. From (4) Dobratz, Ibid., 33, 758 (1941). these reference values and the -AH data previously cal(6) Edmister, Ibid., 30, 354 (1938). (6) Kemp and Egan, J. Am. Chem. SOC.,60, 1521 (1938). culated, the absolute heat contents a t various temperatures (7) Kistiakowsky and Rice, J . Chem. Phys., 8,616 (1940). and pressures were obtained. Then the extension of the (8) Sage, Evans, and Laoey, IND.ENGI. CHEM.,31, 763 (1939). lines showing the change in enthalpy with pressure a t constant (9) Sage and Lacey, Ibid., 27, 1487 (1935). temperature, as expressed in absolute values, agrees with (10) Sage, Schaafsma, and Lacey, Ibid., 26, 1218 (1934).
-
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