Thermal Properties of Hydrocarbons under Pressure. I1 JAMES D. LINDSAY‘ AND GEORGE GRANGER BROWN University of Michigan, Ann Arbor, Mich.
I
N THIS paper the effect of pressure on the
in which the constants have the following values,
isothermal change in enthalpy (H or “heat content”) for n-pentane vapor is calculated, using the equation of state suggested by Young, and is found to agree with the experimental data previously reported (5). The effect of pressure on the enthalpy of benzene vapor has been experimentally determined and used in the construction of an enthalpy-pressure-temperature chart. The values for benzene are found to be similar to those for pentane when compared on the basis of the isothermal decrease in enthalpy in B. t. u. per R. per pound mole at the same reduced temperature and over the same increment in reduced pressure.
Constant R e A
Metric Units 863.56 7.473 5,420,800.0 3.135 6.695
k
0
Engineering Units 0.1486 0.1197 26.895 0.0502 0.0000275
was differentiated analytically for the value of (SV/ST)p which value was substituted in the following thermodynamic relationship, (2)
Calculated Enthalpy of Pent-ane Vapor
which may be demonstrated :
+-VdP + PdV PdV + VdP
In view of the importance and the recent experimental determinations (3, 6, 8) of the enthalpy of hydrocarbon vapors, the following computation based upon rigorous thermodynamic equations and the equation of state for n-pentane developed by Young ( I O ) was made for comparative purposes. The equation of state, -
dH = dU d U = TdS d H = TdS ( g ) T
dF
= =
($)T
VdP
+
6T6P 6p (x) - (&S) =
T
6P6T
- SdT
~
The values for (6H/ST)p were calculated for three temperatures, 284”,500°, and 536’ F. with pressures up to 1000 p o u n d s p e r s q u a r e inch. These curves were then integrated graphically, giving H as a function of P a t constant temperature to which must be added the value for H a t the initial or atmospheric pressure as a constant, of integration. Similar d e t e r m i n a t i o n s were made by an e n t i r e l y graphical method based on the isotherms determined by Young ( I O ) by transforming the thermodynamic equation into the form
FIGURE 1. ORIGIXALDATAON ISOENTHALPIC EXPANSION OF BENZENE Each pair of symbols, along the same isoenthalpic line, represent the initial and final pressures. and temperatures observed. For example, A at 665 pounds per square Inch and 741O F.Indicates this as the inltial pressure and temperature. The final ,state 16 also shown by h 40 be 30 pounds per square inch and 698O F. Along the same ieoenthrtlpio line, 0 indlcates another experlment in whtch 357 pounds per aquare inch and 721° F are the initial conditions and 67 pounds per square inch and 703’ F. the final.
817
and obtaining the values for (6V/6 In T ) , s u b t r a c t i n g them from V , and integrating the result as before. A comparison of the results obtained by the two different methods is given in Table I, with values read from the curves of Pattee and B r o m 1 Preaent address, T e n n e s s e e Valley Authority, I” 0.Boa 147% Wilson Dam, Ala.
INDUSTRIAL AKD ENGIXEERING CHEMISTRY
818
w
TEMPERATURE AT ATMOSPHERIC PRESSURE IN F'
COEFFICIENT OF Beszasxs FIGURE 2. JOI.JLE-THOMSON
(5) based on direct cleteriniiialioiis of the Joule-Thomson coefficient of pentane. The agreement between the exper.imental and computd results is good.
Enthalpy o f Benzene Vapor The apparatus and general procedure for determining the Joule-Thomson coefficient were similar t o those already described (6). A radiant heater using radiation from electric resistance wires was substituted for the low-voltage resistance heater. The pump valve box was machined from a single steel bar and equipped with spool-shaped valves Fith leather seats. The pistons were packed with Johns Manville No. 323 with satisfactory results. The experimental results on hen-, zene of c. P. grade are given in Table 11. When plotted as lines of constant enthalpy on a pressuretemperature diagram (Figure l), the data of Table I1 give straight lines within the experimental limits. Therefore the slopes of these lines, as computed in Table 11,enable the data
HEATOF BESZENEAT FIGURE 3. SPECIFIC ATMOSPHERIC PRESSURE
0 Devjardin (1) A 'Cliedrnanu ( 9 ) + Thiboui ( 7 ) 0 Leduc ( 4 ) X RegnairlL ( 6 )
to be extrapolated to atmospheric pressure as indicated in the last column, The slopes are not identical for all ternperaturebut, when plotted on semi-log paper (Figure 2), were found to vary in the manner indicated by the follon-ing eqitatiori
I
where t
=
temp. at atm,
~ F ~ B B U FP ~ ,
T a s e ~I. RELATIVE E N T ~ L PQF Y %-PENTANE VAPOR (111B. t. u. per pound, referred t o latrnospherio pressure at the indicated ternperature) ~ b s Pres. -284' E'.----r 392' E'.-r---464° P.-500' F-. lure, Lb./Ss. Bnalyti.411alytiIn. eel Graphicel Exptl. Graphical Exptl. &aphid Bxptl. ea1 Graphical Espti. 0 0 0 0 0 0 0 0 14 7 0 - 3 - 2.8 -3 - 2 . 8 - 03 - 2.6 2 - 3 - 2 - 3 8 50 5 . 7 7 . 6 8 6 5 . 5 - 5,0 5 5.0 -5 - 7 7 100 200 -17 8 -18.4 -19 -12.4 -13 -11.4 -11 -10.1 -11.0 -11 .... .. -32.4 -34 -24.6 -25 -21,6 -22.0 -23 400 , . . , .. .,.. -41,7 -41 -35.2 -35.8 -38 600 .... ... -66.6 -66' -51.7 -51,6 -52 800 .... .. -61.4 -67.8 -65G 1000 6 E:Itrspolated. I
j
.
.
.
O
*
.
.
1 o
-----_
536' F, hnalytical Graphical 0 0 -2.2 - 2 4.6 -. 8
--20.0 9.4 -32.0 -45.0 -56.3
-11 -20.7 -31.8 --45,4
--.BY
Exr,ti 0 2 ._5
--
-EX
-28
...sw
-.a6 .." 87 1
JULY, 1935
INDUSTRIAL AND ENGINEERING CHEMISTRY
819
TABLE11. RESULTS ON BENZENE bbs. Pressure, Lb./Sq. I n . High Low
Run
Temperature,
F. High Low
A T , tbbp/' O
F. Sq. In.
aT AP
t F. a t 15 Lb. Prf>ssure
Run
Abs. Pressure, Lb./Sq. In. High Low
t
Temperature, ' F. High Low
4P
Q T Lb.) F.'Sq. I n .
O F .
a t 15
%
Lb. PresAP sure
10
99 100 59 59
0.152 0.150 0.170 0.170
443 442 441 442
41 42 43 44
352 162 162 162
21 19 18 18
459 490 476 465
404 467 452 441
55 23 24 24
331 143 144 144
0.166 403 0.161 466 0.166 452 0.166 441
30 32 33 93
312 320 311 305
0.096 544 540 0.100 0.106 533 0.305 348
45 46 47 48
162 162 175 175
18 18 18 18
465 465 420 419
441 441 392 391
24 24 28 28
144 144 157 157
0.166 0.166 0.178 0.178
441 441 391 390
703 678 682 596
18 21 22 61
290 287 282 675
0.062 700 0.073 674 0.078 678 594 0.080
49 50 51 52
175 177 179 179
18 18 18 18
418 417 417 417
390 388 387 387
28 29 30 30
157 159 161 161
0.178 0.182 0.186 0.186
389 387 386 386
428 604 609 688
192 533 552 645
236 71 57 43
282 647 551 542
0.084 0.110 0,103 0.079
031 550 644
I88
53 54 55 56
180 182 182 183
18 18 18 18
417 418 421 422
387 388 391 393
30 30 30 29
162 164 164 165
0.185 0.167 0.167 0.168
386 387 390 392
29 29 44 44
657 683 642 635
613 642
44
542 557
660
528
92 107
808
910
0.081 0.014 0.114 0.118
612 641 547 524
57 58 59 60
182 677 677 672
18 31 31 31
421 692 723 733
391 645 677 689
30 47 46 44
164 646 646 641
0.167 390 0.074 644 0.071 676 0.069 688
962 976 983 989
52 412 417 424
622 609 609 609
513 520 518 518
109 89 91 91
910 564 566 565
0.120 0.158 0.161 0.161
509 457 453 452
61 62 63 64
669 667 665 662
30 30 30 31
739 741 741 746
695 697 698 703
44 44 43 43
639 637 635 631
0.069 0.069 0.068 0.068
694 696 697 702
25 26 27 28
996 1010 1007 994
427 517 511 317
609 614 616 605
519 537 538 488
90 77 78 117
569 493 496 677
0.158 0.156 0.157 0.173
454 459 460 437
65
68
657 655 653 653
30 30 30 30
722 724 711 705
677 680 665 658
45 44 46 47
627 625 623 623
0.072 0.071 0.074 0.076
676 679 664 657
29 30 31 32
999 1008 1017 1017
317 312 312 312
602 606 609 611
487 487 495 497
116 119 114 114
672 686 705 705
0.171 0.173 0.162 0.162
434 434 444 446
69 70 71 72
654 655 655 655
30 30 221 221
705 709 709 709
659 662 676 676
46 47 33 33
224 625 434 434
0.074 0.075 0.076 0.076
658 661 660 660
33 34 35 36
1014 1012 1015 992
309 112 112 107
612 607 605 606
501 464 459 466
111 143 146 140
705 900 903 885
0.158 0.159 0.162 0.158
454 449 443 452
73 74 75 76
656 656 676 676
222 221 368 368
707 707 707 705
674 673 682 681
33 34 25 24
434 435 308 308
0.081
37 38 39 40
353 354 354 353
21 21 21 21
455 459 459 459
398 403 404 404
57 56 55 55
332 333 333 332
0.172 0.168 0.165 0.166
397 402 403 403
77 78 79
723 721 722
494 493 494
705 706 707
687 687 689
18 19 18
229 228 228
0.079 649 0.083 647 0.079 651
22 21 62 62
459 458 459 460
444 443 449 450
15
2 3 4
121 121 121 121
5 6 7 8
364 372 363 382
52 52 52 77
578 576 570 460
548 544 537 367
9 10 11 12
357 353 346 712
67 64 37
721 699 704 657
13 14 15 16
302 682 583 571
20 35 32 29
17 18 19 20
571 586 852 962
21 22 23 24
1
66
15 10
41
66 67
Cp =
C p = 0.000374t sp. heat, B. t. u./lb.
t = temp.,
+ 0.251
658 657 653 0.078 653
corresponding critical temperature or pressure) combined with the molecular quantity, have been found satisfactory. I n Table I11 the calculated data for pentane, the experimental data for pentane (6) and for benzene have been compared on this basis, using 847" R. (387' F. 460') and 485 pounds per square inch absolute as the critical temperature and pressure for pentane, and 1011O R. and 702 pounds as the critical temperature and pressure for benzene. The computed values of Table I were plotted to obtain values for the reduced pressures and temperatures as used in Table 111, and the experimental values were read from the
The available specific heat data on benzene vapor a t atmospheric pressure are in good agreement as indicated in Figure 3 and may be represented by the equation: nhere
0.076 0.078
+
(5)
' F.
The increase in enthalpy (AH) 011 heating benzene from liquid a t 32' F. to vapor a t 176', under one atmosphere of pressure, is 232 B. t. u. per pound ( 2 ) . Combining this value with the sDecific heat data for the benzene vapor gives the following equation as the enthalpy of superheated benzene vapor referred to liquid benzene a t 32 ' F., TABLE111. COMPARISON OF EFFECT OF PRESSURE AT CONSTANT TEMPERATORE ON ENTHALPY OF PENTANE AND BENZENE VAPOR,ON BASISOF REDUCED (0.0003741 0.251)dt = 232 TEMPERATURES AND REDUCED PRESSURES L 6
+
+
(In B. t. u. per pound mole per
Rankine: values are for decrease in enthalpy per Rankine per pound mole, - A H / T ) Reduced Temperature Reduced Temperature Reduced Temperature
which, when integrated, gives -
H
=
+
0.000187t2 0.251t $. 182
(6)
By use of Equations 4 and 6, lines of constant enthalpy may be drawn on a pressure-temperature diagram as sho6.n in Figure 4.
Comparison o f Effect of Pressure on Enthalpy of Benzene and Pentane Vapor As a basis for comparison of the properties of different hydrocarbons, the reduced temperatures and pressures (found by dividing the absolute temperature or pressure by the
Reduced Pressure
0.03 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8
0.9 1.0 1.2 1.3 1.4 1.6 a
= 0.9
= 1.1
= 1.0
-Pentane-Calcd. Exptl. Benzene
--Pentane-Pentane--Calcd. Exptl. Benzene Calcd. Exptl.
0
0
0.28 0.7 1.2 1.75 2.3
0 0 28
0.71 1.22 I .78 2.36
0
0.25 0.7 1.25 1.77 2.33
0.22 0.45 0.72 1.1 1.45 1.73 2.22
0
0.24 0.49 0.76 1.12 1.49 1.8 2.3 2.6 3.1 3.6
0
0.22 0.45 0.72 1.1
1.45
.... .... 1.7 .... .... .... 2.2 .... .... .,.. .... 2.55 .... .... .... .... 3.1 .... .... .... .... 3.7 .... .... .... .... .... .... . . . . . . . . . . . . . . . . . . . . 6.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ....
Extrapolated.
0
0.2 0.43 0 57 0.83 1.07 1.3 1.5 1.73 2.05 2 28 3.0
Benzene
0
0
0.8
0.8
0.22 0.4 0.55 1.05 1.3 1.55 1.77 2.1 2.32 2.95
0.2 0.36 0.52 1.02 1.27 1.52 1.76 2.1 2.35 3.0
. . . . . . . . . . . .
3.8 4.43
3.85 4.5
3.ga
....
INDUSTRIAL AND ENGINEERING CHEMISTRY
820
enthalpy-pressure-temperature charts for pentane (5) and benzene as in Figure 4. The values given in Table I11 represent the decrease in enthalpy per pound mole per " Rankine (' F. 460), or - AH, T referred to the enthalpy of the same vapor a t the same temperature under a pressure of one atmosphere.
+
Literature Cited (1) Desjardin, Ann. phus., 11, 253 (1919). (2) Frock, Ginnings, and Rolton, Bur. Standaids J. Reseaich, 6, 893 (1931).
VOL. 27, NO. 7 ,
(3) Gary, W. W., Rubin, L.C., and Ward, J, T., INU.E m . C a m . , 25, 178 (1933). (4) Leduc, Compt. rend., 152, 1762 (1911). (5) Pattee, E. C., and Brown, Q. O . , IND. ENG.CHEX., 26, 511 (1934). (6) Regnault, Inst. de France Mem. d e E'Acod.,26, 1 (1862). ( 7 ) Thibout, Ann. Phgsrk, 35, 349 (1911). (8) Weir, H. ha., and Eaton, G . L.,XND. EN^. Cmm., 24, 211 (1932)" (9) Viedmann, Ann. Phystk u. Chem., 2, 195 (1877). (10) Young, SidneypPhil. Mag., 67,353 (8899) RECEIVED December 17, 1934
rsion Factors HOW-IRD S. NUTTING, Dow- Chemical, Company, Rlidland, Mich.
HE reduction of the volume of a gas saturated with water vapor to standard conditions (dry, 0" C., 760 mm. pressure) is a simple process in itself, but in routine vork it often becomes a tedious and time-consuming operation. The various tables (1) and charts ( 2 ) of conversion factors available in the literature offer considerable assistance, but they all have the disadvantage of requiring either supplementary calculations or inconvenient mechanical manipulations. It is possible to arrange conversion factors, which automatically correct for the partial pressure of the water vapor in the forin of a chart in such a manner that the factor corresponding to the observed temperature and pressure may be determined simply and directly. The conversion factors for such a chart are calculated by means of the well-known equation : Factor
P
= -
-p 760
273.3 _ 273.1 t
X ~
+
_
where P
p
= =
total pressure partial pressure of vvater vapor at, t o
The chart is constructed by plotting two or more factors for each temperature on Cartesian coordinates against their respective total pressures, and drawing the straight-line isotherms as illustrated in the accompanying figure. Thus, in order to reduce t o standard condit'ions the volume of a gas collected over n-atcr-for example, at' 25" C,and 780 mm. pressure----it is necessary only to multiply the observed volume by 0.911, the factor found at, the intersection of the 25" isotherm and 780 mm. ordinate. A typical table of conversion factors is given for the convenience o€ those x h o may wish to construct charts of their own. This method of representing gas conversion facOors can be used with any other units of temperature and pressure. It is also applicable to t'hose cases in n-hich the gas is in contact with other retaining liquids, such as saturated salt solutions but', in so doing, care must be taken to use t'he proper pnrtialpressure data in calculating the conversion fact'ors. COSVERSIOX FACTORS FOR GASESIS Cos~.ic,rWITH WATER T ~ , ~ ----.---At ~ , , OC.
Following Preasure, i n Mrn.:---.----.-700 750 SO0 900
0.6405 0.6347 0.6289 0.6230
0.7502 0.8998 0.7635 0.8921 0 , 7 5 6 7 0,8845 0.7499 0.8768
0.9647 0.9566 0,9485 0,9403
10295 1.0210 1,0123 1.0040
1000 1.1592 1.2883 1.1497 1.2785 1.1402 1.2681 1.1307 1.2576
14 16 15 20
12
0.6170 0.6108 0.6045 0.5981 0.5915
0,7430 0.7860 0.7288 0.7216 0.7141
0,8690 0.8611 0.8531 0.8449 0,8367
0,9320 0,9237 0.9153 0.9067 0.8982
0.9951 0,9863 0.9774 0.9684 0.9893
1.1211 1.1116 1 1017 1.0919 1.0819
1.2472 1.2372 1.2260 1.2153 1.2043
22 24 26 28 30
0.5847 0.5777 0,5704 0.5629 0.5550
0.7065 0.8282 0.6986 0.8196 0.6906 0.8107 0.6822 0.8016 0.6738 0,7922
0.8891 0.8801
0,9500 0.9405 0.9308 0.9209 0.9107
1.0718 1.0615 1.0510 1,0403 1.0293
1.1936 1.1824 1.1711 1.1596 1.1478
32 34 36 38 40
0.5469 0.5394 0.5295 0.5201 0.5104
0.8647 0.7824 0.8413 0.9002 0.6554 0.7724 0.8309 0.8894 0.6457 0.7620 0.8201 0.8782 0.6359 0.7511 0.8089 0.8667 0.625- 0,7399 0.7973 0.8547
1.0180 1.0064 0.9946 0.9828 0.9694
1.1358 1.1234 1.1107 1,0977 1.0842
42 44 46 48 50
0,5012 0.4893 0.4778 0.4659 0.4532
0,6141 0.6026 0,5905 0,5778 0,5644
0.7862 0.8422 0.9562 0.7726 0.8292 0.9425 0,7594 0,8157 0.9283 0,7456 0,8016 0 , 9 1 3 5 0.7312 0.7868 0.8981
1.0703 1.0558 1.0409
4 6 5
10
500
600
0.7292 0.7159 0,7031 0.6887 Q.6756
0.8708 0.8612
0.8515
1,0254
1.0093
Literature Cited 740
780
820
P R E S S U R E IN MM. CHART FOR D E T E H h I l Y I S G COhVEASIOX
FACTOE
(1) Lange's Handbook of Chemistry, p. 1244 (1934) ; l'an Nostrand'a Chemical Annual, 7th ed., p. 152 (1934). (2) Patton, T. C., Chem. & M e t . Eng., 41, 488 (1934); Tropsch, H., and Mattox, JY~J., 1x11. ENG.CHEM.,,4nal. Ed., 6, 409 (1934). Rmcm96m r'iouember 30, 1934.
