Thermodynamic Data for Carbon Dioxide at High Pressure and Temperature P. E. LILEY' Imperial College of Science and Technology, London, S.W.7, England D u r i n g a research program undertaken to investigate the thermodynamic properties of certain mixtures containing carbon dioxide as one component, it was discovered that very few data for pure carbo3 dioxide were available at temperatures above 150" C. Table I lists recent work on the thermodynamic properties of this vapor. At the period of compilation of these data, the only information available for temperatures above 1 5 0 ° C . was that provided by Sweigert, Weber, and Allen (44) [which had been questioned b y Granet and Kass (S)], the oriqinal NBS-NACA C, 25-15@ 1948 Michels, A,, de Groot, S. R. (22) H,S,Cp, etc. 25-150" 1948 Michels, A., de Groot, S. R. (23) H,S,PV,etc. 25-150' 1949 Gratch, S. ( 8) c' ,etc. 100(misc.) 5000"R. 1949 Oishi, J. (33) [V,T 0,100 1950 Gratch, S. ( 7 ) c' 100(misc.)5000"R. (17) h ? S J -80( 10)150 1950 Huggill, J. A. W., others 1950 MacCormack, K . E., Schneider, W. G. (74) P,V,T O( 50)200(100)600 1950 MacCormack, K. E., Schneider, W. G. (75) H,S,Cp,etc. O( 50)200(100)600 (27) CL 20-40 1950 Michels, A,, Stryland, J. C. (28) Vapor pressure -56 to 3 1950 Michels, A., others (37) H,S,C ,etc. 60(10)800(50)2700" K. 1950 N.B.S.-N.A.C.A. Tables 1951 Kendall, B. J., Sage, B. H. (72) P , V , j 40-460" F. (47) c,. Critical temp. 1951 Schneider, W. G., Chynometh, A. (6) C 100-1500°F. 1952 Granet, I., Kass, P. -30,0,50,90 1952 Masi, J. F., Petkof, B. (78) 35-350 1952 Schrock, V. E. (42) 31.02-31,lO 1952 Wentorf, R. H., Jr. (45) dV,T 1953 Price, D. (36) H,S,PV,Cp,etc. 0-1000 1953 Woolley, H. W. (46) c/c, 23.8 O( 10)1000" K. 1954 Kennedy, G. C. (73) LV,T ( 7 7 ) C , review 250-1500" K. 1954 Masi, J. F. 1954 Price, D. (37) If,S,PV,C,,etc. 100(50)500(100)1000 1954 Woolley, H. W. (47) H A C 50(10)1000(50)1500( 100)5000"K. 1955 N.B.S. (30) H,S,?,etc. 50(10)1OOO(50)1500 (100)5000' K. 1955 Pfefferle, W. C . , others (34) P,V,+ 30 (35) P,V,H,S 100(50)500(1OO)lOOO 1955 Price, D. 1956 Baker, H. W. (7) H -140 1956 Din, F., ed. ( 4) H,S, V,etc.-80(10)150,etc. 1956 Wentorf, R. H., Jr. (45) P,V,T 31.02-31.10 1957 Cook, D. ( 2) P,V,T -60 to 30 1957 This work . . . H, V 150(10)650 "Tabulated principally at 25" C. intervals. ,
+
-
T(aV!aT)pldP
Pressure Range, Atm. 16-250 7 0 -3000 Misc. 18-3117 36.32-98.45 0-600 amagats 1(25)100(50)200..2500 0-10000 p.s.i.a. 1000
... 1-200 0-10000 p.s.i.a. 0.15-3000 p.s.i.a. 0-3000 0-2000 1-600 1-2000 0
0.57 to 1.23 0
1-3000 0-50 0(10)50 and 1 140 to 425 amagats 5-37 0
200-100000 p.s.i.a.
... 0-2000 p.s.i.a. 0.5, 1,1.5 1-67 72.723-72.974 0-40 amagats ( < 100) 0-22.22 25-1400 bars 1 50-1400 bars 0
0-100 3.684-53.633 50-1400 bars -1400 p.s.i.a. 0.5-3000 72.723-72.974 0.5-2.5 1-200
JOURNAL OF CHEMICAL AND ENGINEERING DATA
reduces to H(P,T)
=
H(O,7)
+
+ (C - TdC/dT)P2/2 + ( D - T d D / d T ) P 3 / 3 + ... ( 2 )
( B - TdB/dT)P
so that, from a knowledge of the zero pressure function H(O,T), the virial coefficients and their temperature derivatives, the enthalpy at any pressure, P,and temperature, 7,can readily be computed. T h e actual form used for the computation of the enthalpy data was H(P,T)
H(0,T) + ( B
=
-
TdB/dT)P -
c
(3)
i.e., it has been assumed that all virial coefficients higher than the second are negligible. This assumption was postulated by Schneider (74)from experimental work and has also been shown to be valid by analysis of a few compressibility measurements made by the author in a similar pressure and temperature range. I n Equation 3, c is a correction factor inserted so that the zero of enthalpy occurs at 0" C. and 1 a t m .
6'
{ V - T ( a V / a T ) p ) d Pat 7
c =
=
To
=
273.16" K.
According to MacCormack and Schneider ( 1 5 ) ,c = -12.53 cal. per mole. T h e zero pressure data of Gratch (8) as tabulated by Woolley (37) have been interpolated to give values of H ( 4 T ) for every 10" from 150" to 6 5 0 ° C . Values of the function B - T d B / d T were then determined for temperatures of 150", 200", 300", 400", 500", and 6 0 0 ° C . by fitting the data of MacCormack and Schneider ( 1 5 ) to Equation 3. Values of B - T d B j d 7 f o r all other temperatures were found by interpolation of these values. T h e enthalpy function H(P, T ) was then calculated for all pressures and temperatures by applying Equation 3. These values are reproduced in Table 11. T h e data of Table I1 are compared with other work in Table 111. Despite the numerous tabulations of thermodynamic functions listed in Table I, only MacCormack and Schneider listed zero pressure values in 1952, apart from the source values (37). T h e comparison in Table 111 for zero pressure shows that good agreement in the data is obtained. T h e agreement of the data for higher pressures is fairly satisfactory except possibly for the highest pressures a t 150" C. T h e divergence in values here can be taken as indicative of the uncertainty existing in the virial coefficients and shows that high
Table II. Enthalpy of Carbon Dioxide (Units: Calories per mole. Enthalpy zero, 0' C., 1 atm.) Prcssurr .Aimorphrrrq
T, 'C
0
150 160 170 180 190
14150 15159 1617.6 1720 1 18234
200 210 220 230 240 250 260 270 280 290
2
3
4
5
IO
15
20
25
30
35
40
45
50
60
'0
80
14101 15113 1613.2 17159 18194
14052 1506.6 16088 1711 7 18154
14003 1502.0 16043 1707 5 18114
1395.4 14973 15999 1703 3 18073
13905 1492.7 15955 1699 1 18033
13659 14694 1573.3 1678.0 17832
13414 14461 15512 1656 9 17631
13168 14429 15290 16358 I7431
12923 13996 15069 1614.8 17230
126-8 13'63 14847 15937 17029
1243 2 1353 I 14626 I5726 1682.8
12187 1329.8 1440.4 1551 5 16627
11942 13065 14142 1.5305 1642.6
11696 12833 1396 I I5094 16225
1120 1237 1352 1467 1582
1071 1190 1307 1425 1542
1022 1144 1263 1383 1502
973 1097 1219 1341 1462
924 1051 1175 1299 1422
875 802 679 556 433 1004 934 818 702 585 1064 1004 953 842 731 1256 1193 1088 982 877 1381 1321 1221 1120 1020
19274 20322 21377 22439 23509
19236 2028 5 2134 2 22406 23477
19198 20249 21307 22373 2344 5
19159 2021 2 2127 2 22339 2341 4
19121 20176 21237 22306 2338 2
19083 20139 21203 2227 3 23350
18891 I995 7 21029 22107 23192
18699 197'4 2085 5 2194 1 23034
1850' 19592 2068 1 21'-6 2287 5
18316 19409 20507 2161 0 2271 7
18124
I922 6 2033 3 21444 22559
1'932 19044 20158 21278 22401
1774.1 18861 19984 2111.2 2224.2
17549 18679 19810 2094.6 22084
17357 18496 19636 20'8.1 21926
1697 1813 1929 2045 2161
1659 1777 1894 2012 2129
1621 1740 1859 1979 2098
1582 1704 1824 1945 2066
3544 1667 17'x) 1912 2034
1506 1630 1755 1879 2003
1448 1576 1703 1829 1955
1352 1484 1616 1746 1876
2458 5 2566.8 2675.7 2785.3 2895.5
2455.5 2563.9 2672 9 2782 6 28930
2452 4 2561 0 2670 1 2779 9 28904
2449.4 2558.0 2667.3 2777 3 28878
2446 4 2555 1 2664 6 2774.6 2885 3
2443 3 2552.2 2661.8 2771.9 2882 7
2428 2 2537.7 2647.8 2785.6 28699
2413.0 2523.2 2633.9 2745.2' 2857 1
2397.9 2508.6 2620.0 2731 8 2844 3
2382 8 2494 1 2606.1 2718 4 2831 5
2367.6 24796 2592 I 2705 7 2818 7
2352.5 24650 2578.2 2691 7 2805 9
2337 3 24505 2564 3 26783 2?93.1
2332.2 24360 2550 4 2665.0 27803
2307 0 2421.4 2536 4 2561 6 2767.5
2277 2392 2509 2625 2742
2246 2363 2481 2598 2716
2216 2334 2453 2571 2691
2186 2305 2425 2545 2665
2156 2276 2397 2538 2639
2125 2247 2369 2491 2614
2080 2203 2328 2451 2575
M04 1928 1853 2131 2258 2384 2511
2058 2188 2317 2446
1985 2119 2251 2383
300 3006 5 30040 3001 5 2999 I 2996.6 2994.1 2981.8 2969.5 29572 2944.9 2932.5
1
90
100
110
I25
150
1'5
200
1256 1391 1529 1663 1797
1161 1302 1442 1581 1718
310 320 330 340
3117.9 3230.0 3342.7 34558
31155 3227 7 3340 5 3453'
3113.1 3225 5 3338 3 3451 6
31108 3223 2 3336 1 34494
31084 32209 3333 9 3447 3
31060 3218 6 3331.7 3445 2
3094.0 3207 1 3320 7 34347
30821 31957 33097 3424 1
30702 3184 2 3298 8 3413 6
30582 31727 3287.8 3403 1
30463 3161 3 3276.8 3392 5
2920.2 3034 3 31498 3265.8 3382.0
2907 9 3022.4 31384 32548 3371 4
2895 6 30104 3126.9 32438 3360.9
2883 3 2998 5 31154 3232.8 33503
2859 2975 3093 3211 3329
2834 2951 3070 3189 3308
2809 2927 3047 3167 32S7
2785 2903 3024 3145 3266
2760 2879 3001 3123 3245
2736 2855 2978 3101 3224
2698 2819 2144 3068 3192
2637 2760 2886 3013 3139
2575 2700 2829 2958 3387
2514 2640 2772 2903 3034
350 360 370 380 390
3569 6 3683.6 37985 39141 4030 7
3567 6 3681 7 37966 3912.3 4029 0
3565.5 3679.7 3794.8 3910.5 4027.3
3563 5 3617 8 3792.9 3908.9 4025 6
3561 5 36759 3791 1 3906.9 4023.9
3559.5 36739 37892 3905 1 4022.2
3549.4 36642 37799 38962 4013 6
3539 3 3654 5 37706 38872 4005 0
3529 2 36448 3761 3 3878.3 3996 5
3519 1 3635.1 37520 38694 3987 9
3509 0 36254 37427 3860.4 3979 3
3498.9 36158 3733 4 38515 3970.8
3488.8 3606 1 3724.1 38426 39622
3478 7 35964 3714 8 38336 39536
3468 6 35867 3705 5 3824.7 39450
3448 3567 368' 3807 3928
3428 3548 3668 3789 3911
3408 3529 3650 3771 3894
3388 3509 3631 3753 3876
3368 3490 3612 3735 3859
3347 3471 3594 3717 3842
3317 3441 3565 3691 3816
3267 3393 3519 3646 3774
3216 3344 3473 3601 3731
3166 3296 3426 3557 3688
400 410 420 430 440
4147.4 4264.3 4381.8 4499 9 46194
41457 4262.7 4380.3 4498 5 4618.0
41441 4261.1 4378.8 4497.0 4616.6
4142.5 42595 437.3 4495.6 4615.2
4140.8 4258.0 4375.8 4494 2 4613.8
41392 42564 4374 3 4492.7 4612.5
4131.0 4248 5 4366 8 4485.5 46056
41228 4240.6 4359 3 4478 3 4598.7
4114.5 42328 4351.7 4471.1 4591.7
41063 4224.9 4344 2 4463.9 4584.8
4098.1 4217.0 4336 7 4456 7 45779
4089.9 42091 43292 4449.5 4571.0
4081.7 4201 3 4321 7 4442 3 4564 1
4073.5 41934 43142 4435 1 4557 2
40653 4185.5 4306.7 4427.9 45503
4049 4170 4292 4414 4537
4032 4154 42F 4399 4523
4016 4138 4262 4385 4509
4000 4122 4247 4370 4495
3983 4107 4232 4356 4481
3967 4091 4217 4341 4467
3942 4066 4194 4320 4447
3901 4027 4157 4284 4412
3860 3988 4119 4248 4378
3819 3949 4082 4212 4343
450 460 470 480 490
4737.9 4856.9 4976.5 5096 7 5211.9
4736.6 4855.7 4975.3 5095 5 52108
4735.2 48544 4O74.I 5094 3 5209.7
47339 4853.1 4972.9 5093 2 5208 6
4732.6 4851.9 4971.7 5092.0 5207.5
4731.3 4850.6 4970.5 5090.9 5206 4
47247 4844.3 4964.4 5085.1 5200.8
47180 4837.9 4958 3 5079.3 5195 3
4711 4 4831.6 4952.3 5073 5 5189.7
47048 4825 3 4946 2 5067 7 5184.2
4698.2 48189 4940 2 5061 9 5178 6
4691 6 48126 4934.1 50561 5173.1
4685.0 4806.3 4928.0 50503 5167.5
4678.4 4799.9 4922 0 50445 51620
4671.8 41936 4915 9 5038.7 5156.5
4658 4781 4904 5027 5145
4645 4768 4892 5015 5134
4632 4756 4880 5004 5123
4619 4743 4867 4992 5112
4606 4730 4855 4981 5101
4592 4718 4843 4969 5090
4513 4699 4825 4952 5073
4540 4667 4795 4923 5046
4507 4635 4764 4894 5018
4473 4604 4734 4965 4990
500 510 520 530 540
5338.6 5459.9 5582.6 5705.5 5828.1
5337.5 5458.9 5581.7 5704.5 5827 3
5336.4 5457.9 5580.7 5703.6 5826.4
5335.4 5456 9 5579.7 5702.7 5825.5
5334.3 5455.9 5578.7 5701 8 5824.6
5333.2 5454.8 5577.8 5700.9 5823.8
5327 9 5449 8 5572 9 5696.3 58194
5322.6 5444 7 5568 1 5691 7 58150
5317.3 5430.7 5563.3 5687.1 58106
5312.0 5434 6 5558.4 5682.5 5806.2
5307.0 5429.5 5553.6 5677 9 5801.8
5301.4 5424.5 5548.7 56733 5797.5
5296.1 54194 5543.9 5668.7 5793.1
5290.8 5414.3 5539.0 5664.1 5788.7
5285.5 5409.3 55342 5659.5 5784.3
5275 5399 5525 5650 5776
5264 5389 5515 5641 5767
5254 5379 5505 5632 5758
5243 5369 5495 5623 5749
5232 5359 5486 5613 5740
5222 5348 5476 5604 5733
5206 5338 5462 5590 5719
5179 5308 5438 5567 5698
5153 5283 5414 5545 5676
5126 5258 5389 5522 5654
550 560 570 580 590
5951.4 6075.1 619') 1 6323 6 6448.4
5950.6 6074.3 6198.4 6322.9 64477
5949.8 6073.5 6197.6 6322.1 64470
5948.9 60727 61969 6321.4 6446.3
5948.1 6071.9 6196.1 6320.7 6445 7
5947 3 6071 1 6195.4 6320.0 6445.0
5943.1 60672 6191.6 6316.5 6441.7
5938 9 60632 6187 9 6312 9 6438.3
5934.7 6059.2 6184 1 6309.4 64350
5930.6 60553 6180.4 6505.8 6431.6
5926 4 6051 3 6176.6 6302 3 6428 3
5922.2 60473 6172.9 62987 6424 9
5918.1 60434 6169.1 6295.2 6421.6
5913.9 60394 6165.4 6291.6 6418 2
5909.7 6035 5 6161.6 6288.1 6414 9
5901 6028 6154 6281 6408
5893 6020 6147 6274 6401
5885 6012 6139 6267 6395
5876 6004 6132 6260 6388
5868 5996 6124 6253 6381
5860 5988 6117 6245 6375
5847 5976 6105 6235 6365
5826 5956 6087 6217 6348
5805 5936 6068 6199 6331
5785 5917 6049 6182 6314
600 610 620 630 640 650
6573.5 6699.1 6824.9 6951.1 7077.8 72045
6572.9 6698 5 6824.3 6950.6 7077.4 7204 1
6572.2 6697.9 6823.8 6950 1 7076.9 7203.6
6571.6 6697.3 6823.2 6949.6 7076.4 '203.2
6571.0 6696.7 6822.6 6949.0 70759 72028
6570.3 6696.1 6822 1 6948.5 7075.4 7202.3
6567.2 6693.1 6819.3 6945.9 7073.0 7200.1
6564.0 6690.2 6816 6 6943.4 7070.6 7197 9
6560.9 6687.2 6813.8 6940.8 7068.2 71956
6557 7 6684 3 6811 0 6938.2 7065.8 71934
6554 5 6681.3 6808.3 6935.6 70634 7191.2
6551.4 6678.3 6805 5 6933 1 7061 0 7188 9
6548.2 6675.4 68027 69305 7058.6 7186.7
6545 1 66724 6800.0 6927.9 1056 2 71845
6541.9 6669.5 6797.2 69254 7053 8 7182.3
6536 6664 6792 6920 7049 7178
6529 6658 6786 6915 7044 7173
6523 6652 6781 6910 7039 7169
6517 6646 6775 6905 7035 7164
6510 6640 6770 6900 7030 7160
6504 6634 6764 6894 7025 7156
6495 6625 6756 6887 7018 7149
6479 6610 6742 6874 7006 7138
6463 6595 6728 6861 6994 7127
6447 6581 6714 6848 6982 7115
VOL. 4, No. 3, JULY 1959
239
precision is necessary if accurate virial derivatives are to be obtained. The estimated uncertainty of these values is given in Table IV; with the exception mentioned above, all the published values fall inside the limits assigned in Table IV.
VOLUMETRIC BEHAVIOR Values are given, in Table V, of the first and second virial coefficients for the temperature range 150" to 650' C., so that
Table 111. Comparison of Enthalpy Dataa for Carbon Dioxide Pressure, Atm. Temp., "C. 150
200
0
1414.99 1415.05
1927.42 1927.48
1 1410.1 1410.1 1414.9 1409.8 1397.6 1923.6 1923.6 1928.5
10 1365.9 1366.0 1384.1 1369.9 1889.1
50 1169.6 1169.7 1209.8 1162.9 1735.7 1735.8
100 924 930 897 892.6 1544
1893.7 1517.5 2455.5 2156 2428.2 2461.5 2433.8 21 16.8 3006.46 3004.0 2891.8 300 2883.3 2760 2880.8 3006.59 3004.1 301 1.9 2988.1 2729.7 350 3567.6 3549.4 3368 2478.0 3558.0 3343.1 4147.38 4145.7 400 4131.0 4065.3 3983 4147.22 4145.6 4065.7 4156.7 4141.0 3959.7 450 4736.6 4724.7 4606 4749.0 4735.4 4783.4 500 5338.55 5337.5 5327.9 5385.5 5232 5339.1 5 5338.1 5286.0 521 1.4 5352.5 5341.1 550 5950.6 5943.1 5868 5967.8 5958.5 5846.7 6573.50 6572.9 6567.2 6541.9 6510 600 6573.73 6573.1 6542.3 6591.7 6584.1 6487.5 650 7204.1 7200.1 7160 7224.7 7134.8 7218.3 At 150"C., and 150 atm., H = 679 (This) and 683 ( 7 7 ) . At 150°C and 200 atm., H = 433 (This), 459 ( I I ) , and 374 (23). OEnthalpy unit, cal./mole. Enthalpy zero, 0"C. 1 atm. One amagat unit of energy = R T , / A , = 539.02 cal./mole. R = 1.98718 cal./mole "K. To = 273.16" K. A, = volume per mole of CO,/volume per mole perfect gas. 250
Table IV. Estimated Uncertainties in Values of Table I1 for the Enthalpy of Carbon Dioxide Vaporo (Cal./Mole)
Temp., "C. Pressure Atm. 1 10 50 100 150 200
150 200 250 300 400 500 600 0.15 0.15 0.15 0.18 0.20 0.25 0.30 2.6 2.1 1.8 1.4 1.0 0.8 0.6 13 10 7.7 6.5 4.1 2.7 1.8 25 20 15 13 8 6 3.5 38 30 23 12 19.5 9 5.3 51 40 30 26 16 11 7
"These uncertainties are those introduced in interpolation of original NBS zero pressure data (31) and in estimation of coefficients B-TdB/dT at various temperatures from a plot of values deduced from Equation 3. Zero pressure data have been revised (47) since this material was completed, and uncertainties do not include differences between two sets of zero-pressure tabulations (37,47).
volumetric data can readily be obtained by applying the virial equation PV
=
A
+ BP
(4 )
These values were obtained by interpolation of those quoted by MacCormack and Schneider (74) for six temperatures from 150" to 650" C. A few compressibility measurements made by the author in this temperature range gave virial values in excellent agreement with those quoted in Table V. Since completion of this work, a discussion of such data has appeared (30) which will enable the agreement between the values of MacCormack and Schneider (74) and other data to be assessed. The fuller
Table V. Virial Coefficients of Carbon Dioxide Interpolated from the Work of MacCormack and Schneider (15). A 7" P V ( P = 50)" - 103 T.,OC. 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 320 330 340 350 360 370 380 390
McC&S This 1.560050 1.560050 . . . 1.596917 . . . 1.633784 , , . 1,670560 , , , 1,707517 1.744383 1.744380 . . . 1.781250 . . . 1,818120 . . . 1.854980 . . . 1.891850 . . . 1.928720 . . . 1.965580 . . . 2.002450 . . . 2.039320 . . . 2.076183 2.113050 2.113050 . . . 2.149920 , . , 2.186783 , , . 2.223650 , , , 2.260520 . . . 2.297380 . . . 2.335250 , , . 2.371117 , , , 2.407983 . . . 2.444850
McC&S This McC&S 1.44640 1.446400 2.273 . . . 1.491267 . . . . . . 1.535784 . . . , , . 1.582050 ... , , . 1,624017 ... 1.66785 1.667880 1.531 . . . 1.710000 . . . . . . 1,752070 . . . , . . 1.793580 . . . . . . 1.835500 . .. . . . 1.877070 . . . . . . 1.918430 .., . . . 1.959750 . . . . . . 2.007270 ... . . . 2.041583 . . . 2.08257 2.082400 0.610 . . . 2.122870 . . . , . . 2.163333 ... . . . 2.203650 ... , , . 2.243720 ... . . . 2.283180 . . . . . . 2.322400 ... , , . 2.360417 ... , , . 2.400533 . , . . . . 2.439500 ...
. 400 410 420 430 440 450 460 470 480 490 500 510 520 530 540 550 560 570 580 590 600 610 620 630 640 650
2.481717 2.481720 2.47818 2.478220 . . . 2.518584 . . . 2.517134 . . . 2.555450 . . . 2.555900 . . . 2.592320 . . . 2.594620 . . . 2.629184 . . . 2.633284 . . . 2.666050 . . . 2.673900 . , . 2.702910 . . . 2.710410 . , . 2.739784 . . . 2.748934 . . . * 2.776650 . . . 2.787300 . . . 2.815317 . . . 2.825717 2.850384 2.850383 2.86400 2.864033 . , . 2.887250 . . . 2.902350 . . . 2.924120 . . . 2.904620 . . . 2.960383 . . . 2.978383 . . . 2.997850 . . . 3.017350 . . . 3.034717 . . . 3.055467 . . . 3.071583 . . , 3.036983 . . . 3.108449 . . . 3.131849 . . . 3.145317 . . . 3.170017 . . . 3.182183 . . . 3.208133 3.219050 3.219050 3.2465 3.246250 . . . 3.255917 . . . 3.284367 . . . 3.292784 . . , 3.322434 . . . 3.329650 . . . 3.360550 . . . 3.366517 . . . 3.398567 . . . 3.403384 . . . 3.436634
' A T , BT, PVare in amagat units. Ao
'Normal volume
=
=
This 2.273 2.113 1.951 1.772 1.670 1.530 1.425 1.321 1.228 1.127 1.033 0.943 0.854 0.781 0.692 0.613 0,541 0.469 0.400 0.336 0.284 0.237 0.194 0.149 0.107
1 0 ~ ~ ~ 0
-0.071
. . . . . . . . .
.. .. .. .. .. .. .. .. ..
0.272
... ... ... . . . . . .
... . . .
... t
.
.
0.544 .
.
t
. . .
...
-0.070 -0.029 -0.009 0.046 0.082 0.117 0.150 0.183 0.213 0.244 0.273 0.302 0.330 0.362 0.391 0.415 0.442 0.468 0.494 0.519 0.544 0.569 0.593 0.618 0.641 0.665
1.00705.
22258.2 cc./mole.
~
240
JOURNAL OF CHEMICAL AND ENGINEERING DATA
discussion of the NBS tabulation by Masi (30) has not yet appeared.
OTHER WORK Since the above computations were completed, extensive tables of thermodynamic properties (4, 30, 35-37) have appeared. Some (4,30)are revisions of tables (77,37) incorporated in the comparisons above, while the data of Price (35-37) are based upon volumetric determinations of Kennedy (73). Values given by Kennedy d o not appear to be sufficiently accurate for comparison of virial coefficients with those of Table V. T h e newer tabulation (30) contains zero pressure values for carbon dioxide (47) which differ from the original data (31). The second portion of Table 111 compares the d a t a of Table I 1 and (30).Except at the higher pressures and at 150” C . agreement to 1yoexists.
ACKNOWLEDGMENT T h e author is indebted to the Admiralty, London, England, for permission to publish this material and for providing the support under which the major portion of this work was performed. H e also thanks D. M . Newitt, Department of Chemical Engineering, Imperial College, London, England, for supervision of this work.
LITERATURE CITED Baker, H. W.,“Technology of Heat,” p. 57, Longmans Green, London, 1956. Cook, D., Can. 3. Chem. 35,268 (1957). Deming, W. E., Deming, L. S., Phys. Reu. 56, 108 (1939). Din, F., ed., “Thermodynamic Functions of Gases,’’ val. 11, Butterworths, London, 1956. Ellenwood, F. O., Kulik, N., Gay, N. R., Cornell Univ. Eng. Expt. Sta., Bull. 30 (1942). Granet, I., Kass, P., Pelrol. Refiner 31, 137 (1952). Gratch, S., Office of Technical Services, Rept. PB124957 (1950). Gratch, S., Trans. Am. Soc. Mech. Engrs. 71, 897 (1949). Gratch, S., Univ. of Pennsylvania Research Lab. Preprint, 1947; Trans. Am. Soc. Mech. Engrs. 70, 631 (1948). de Groot, S. R., Michels, A., Physica 14, 218 (1948). Huggill, J. A. W., Newitt, D. M., Pai, M . U., Mech. Eng. Research Lab., Gt. Brit. Dept. Sci. Ind. Research, Rept. 8 (1950). Kendall, B. J., Sage, B. H., Pelroleum14, 184 (1951). Kennedy, G. C., Am. J . Scz. 252,225 (1954). MacCormack, K. E., Schneider, W. G., J . Chem. Phys. 18, 1269 (1950).
(15) (16) (17) (18)
Ibid., p. 1273. Maron, S. H . , Turnbull, D.,J. Am. Chem.SOC. 64,2195 (1942). Masi, J . F., Trans. Am. Sw.Mech. Engrs. 76, 1067 (1954). Masi, J. F., Petkof, B., Natl. Bur. Standards. Rept. 1185, (1951); 7. Research .Vat/. Bur. Standards48, 179 (1952). (1 9) ‘Meyers, C. H., Ibzd., 29, 157 (1 942). (20) Michels, A., Bijl, A., Michels, C. Roc. Roy. SOL.(London) A160, 376 (1937). (21) Michels, A., Blaisse, B., Michels, C., Ibid., A160, 358 (1937). (22) Michels, A., de Groot, S. R., Appl. Sic. Research Al, 94 (1948) (revision of 21). (23) Ibzd., p. 103. (24) Michels, A., Michels, C., R o c . Roy. SOC.(London) A153, 201 (1935). (25) Ibid., A160,348 (1937). (26) Michels, A., Michels, C., Wouters, H., Ibzd., A153, 214 (1935). (27) Michels, A,, Stryland,J. C., Physicn16, 813 (1950). (28) Michels, A., Wassenaar, T., Zweitering, T., Smits, P., Ibid., 16, 501 (1950). (29) Michels-Veraan, C. M., thesis, Amsterdam, 1937. (30) Natl. Bur. Standards, Circ. 564, Chap. 4 (1955). (31) Natl. Bur. Standards-Natl. Advisory Cornrn. for Aeronaut., “Tables of Thermal Properties of Gases,’’ Table 13.10, 1950. (32) Natl. Defense Research Comm., Summary Technical Rept., Division 1 1 1946. (33) Oishi.-J., .%z. Papers Insf. Phys. C‘hem. Research ( T o k y o ) , A3, 22 (1 940). (34) PfeKerle, W. C., Goff, J. A. Miller, J. G., 3. Chem. Phys. 23, 509 (1955). (35) Price, D., Ind. Eng. Chem. 47, 1649 (1955). (36) Price, D., Naval Ordnance Lab. NAVord Rept. 2876 (1933). (37) Ibzd., 3846 (1954). (38) Quinn, E. L., Jones, C. L., “Carbon Dioxide,” Reinhold, New York, 1936. (39) Reamer, H. H., Olds, R. H., Sage, B. H., Lacey, W. N.,Ind. Eng. Chem. 36,88 (1944). (40) Roebuck, J . R., Murrell, T. A,, Miller, E. E., 3. Am. Chem. Soc. 64,400 (1942). (41) Schneider, W. G., Chynometh, A., 3. Chem. Phys. 19, 1607 (1951). (42) Schrock, V. E., Natl. Advisory Comm. Aeronaut., Tech. Note 2838 (1952). (43) Smallwood, J . C., Ind. Eng. Chem 34,863 (1942). (44) Sweigert, R. L., Weber, P., Allen, R. L., Ibzd., 38, 185 (1946): (45) Wentorf, R. H., Jr., Univ. Wis. Naval Research Lab., Rept. CM 724 (1952); 3. Chem. Phys. 24,607 (1956). (46) Woolley, H. W., Can. 3. Phys. 31,604 (1953). (47) Woolley, H. W., .7. Research “Vat/. Bur. Shndards 52, 289 (1954). RECEIVED for review May 5, 1958. Accepted November 10, 1958.
Measurement of the Thermal Properties of Carbonaceous Materials J. D. BATCHELOR, P. M. YAVORSKY and EVERETT GORIN
Reasearch and Development Division, Consolidation Coal Co., Library, Pa.
M a n y processes for the treatment of coal involve thermal conversion. I n process devebpment, thermal data on the materials are desirable. This work was designed to supply such thermal d a t a for carbonaceous materials. Heat capacity measurements were made o n a bituminous coal from the Pittsburgh Seam and its low-temperature char. Thermal conductivity was measured o n a coal-char-pitch briquet. Finally, a n estimate was m a d e of the heat transfer film coefficient from a fluidized heating medium to a spherical briquet. This latter work was carried out so that the thermal parameters could be applied to the calculation of heating rates for carbonaceous briquets, a n application which is described in a n article in the July issue of I / E C o n heat transfer in the carbonization of briquets ( 7 7 ) . VOL. 4, No. 3, JULY 1959
The companion article on ”Heat Transfer and Thermal Stresses in Carbonization of Briquets” appears in the July issue of Industrial and Engineering Chemistry, Vol. 5 1, page 833.
LITERATURE SURVEY T h e heat capacity data for coal and coke were reviewed by Clendenin and others ( 3 ) .A correlationequation for the specific heat capacity of moisture-free coal is presented, based on data for 23 American bituminous coals. T h e equation expresses heat capacity as a h e a r function of temperature and volatile matte] content, but is not expected to hold into the temperature range in which coal becomes plastic. I n fact, the very limited d a t a included in the correlation for temperatures above 100”C . make its use above about 150”C. a n unjustifiable extrapolation. T h e heat capacity of a material undergoing thermal decomposition such as bituminous coal in the plastic range loses
24 1
